Question 1

Fill in the blank to make the trinomial a perfect square trinomial. $4 x ^ { 2 } -  \underline { (  \quad  ) } + 9$

Accepted Answer

A)  $4 x^{2}-\underline{(26 x)}+9$ 
B)  $4 x ^ { 2 } -\underline{(6 x)}+ 9$ 
C)  $4 x ^ { 2 } - \underline{(24 x)} + 9$ 
D)  $4 x ^ { 2 } - \underline{(12 x)} + 9$ 
A)  $4 x^{2}-\underline{(26 x)}+9$ 
B)  $4 x ^ { 2 } -\underline{(6 x)}+ 9$ 
C)  $4 x ^ { 2 } - \underline{(24 x)} + 9$ 
D)  $4 x ^ { 2 } - \underline{(12 x)} + 9$ D

Question 2

Factor the sum or difference of cubes. $$27 u ^ { 3 } + 64$$

Accepted Answer

A)  $( 3 u + 4 ) ^ { 2 } ( 3 u - 4 )$ 
B)  $( 3 u + 4 ) \left( 9 u ^ { 2 } - 24 u + 16 \right)$ 
C)  $( 3 u - 4 ) \left( 9 u ^ { 2 } + 12 u + 16 \right)$ 
D)  $( 3 u + 4 ) \left( 9 u ^ { 2 } - 12 u + 16 \right)$ 
A)  $( 3 u + 4 ) ^ { 2 } ( 3 u - 4 )$ 
B)  $( 3 u + 4 ) \left( 9 u ^ { 2 } - 24 u + 16 \right)$ 
C)  $( 3 u - 4 ) \left( 9 u ^ { 2 } + 12 u + 16 \right)$ 
D)  $( 3 u + 4 ) \left( 9 u ^ { 2 } - 12 u + 16 \right)$ D

Question 3

The function defined by $P ( t ) = 0.0523 t ^ { 2 } - 0.8384 t + 8.817$ approximates the public debt of the United States in trillions of dollars for the years 1997 to 2004. In the function, t = 7 corresponds to The year 1997, t = 8 corresponds to 1998, etc. Evaluate P(11) to the nearest tenth of a trillion dollars And interpret the result in the context of this problem.

Accepted Answer

A)  P(11) = 5.9; the public debt in 2001 was $5.9 trillion dollars. 
B)  P(11) = 5.3; the public debt in 2001 was $5.3 trillion dollars. 
C)  P(11) = 62.9; the public debt in 2001 was $62.9 trillion dollars. 
D)  P(11) = 24.4; the public debt in 2001 was $24.4 trillion dollars. 
A)  P(11) = 5.9; the public debt in 2001 was $5.9 trillion dollars. 
B)  P(11) = 5.3; the public debt in 2001 was $5.3 trillion dollars. 
C)  P(11) = 62.9; the public debt in 2001 was $62.9 trillion dollars. 
D)  P(11) = 24.4; the public debt in 2001 was $24.4 trillion dollars. A

Question 4

Fill in the blank to make the trinomial a perfect square trinomial. $64 s ^ { 4 } + \underline { ( \quad   ) }+ 81$

Accepted Answer

A)  $64 s ^ { 4 } + \underline { \left( 72 s ^ { 2 } \right) } + 81$ 
B)  $64 s ^ { 4 } + \underline { \left( 144 s ^ { 2 } \right) } + 81$ 
C)  $64 s ^ { 4 } + ( \underline { 144 s } ) + 81$ 
D)  $64 s ^ { 4 } +  { \left( 36 s ^ { 2 } \right) } + 81$ 
A)  $64 s ^ { 4 } + \underline { \left( 72 s ^ { 2 } \right) } + 81$ 
B)  $64 s ^ { 4 } + \underline { \left( 144 s ^ { 2 } \right) } + 81$ 
C)  $64 s ^ { 4 } + ( \underline { 144 s } ) + 81$ 
D)  $64 s ^ { 4 } +  { \left( 36 s ^ { 2 } \right) } + 81$

Question 5

Divide the polynomials by using long division. $$\left( 2 r ^ { 5 } - 6 r ^ { 4 } - 7 r ^ { 3 } - 21 r ^ { 2 } + 2 r + 3 \right) \div \left( 2 r ^ { 2 } - 8 r - 3 \right)$$

Accepted Answer

A)  $r ^ { 3 } + 2 r - \frac { 1 } { 2 r ^ { 2 } - 8 r - 3 }$ 
B)  $r ^ { 3 } + r ^ { 2 } + 2 r - 1$ 
C)  $r ^ { 3 } + r ^ { 2 } + 2 r - \frac { 1 } { 2 r ^ { 2 } - 8 r - 3 }$ 
D)  $r ^ { 3 } + 2 r - 1$ 
A)  $r ^ { 3 } + 2 r - \frac { 1 } { 2 r ^ { 2 } - 8 r - 3 }$ 
B)  $r ^ { 3 } + r ^ { 2 } + 2 r - 1$ 
C)  $r ^ { 3 } + r ^ { 2 } + 2 r - \frac { 1 } { 2 r ^ { 2 } - 8 r - 3 }$ 
D)  $r ^ { 3 } + 2 r - 1$

Question 6

Find the x- and y-intercepts for the function defined by y = f (x). $$f ( x ) = x ^ { 2 } + 4 x + 4$$

Accepted Answer

A)  $x$-intercept: $( - 2,0 ) ; y$-intercept: $( 0,4 )$ 
B)  $x$-intercept: $( 2,0 ) ; y$-intercept: $( 0,4 )$ 
C)  $x$-intercept: $( 2,0 ) ; y$-intercept: $( 0,0 )$ 
D)  $x$-intercepts: $( - 2,0 ) , ( 2,0 ) ; y$-intercept: $( 0,4 )$ 
A)  $x$-intercept: $( - 2,0 ) ; y$-intercept: $( 0,4 )$ 
B)  $x$-intercept: $( 2,0 ) ; y$-intercept: $( 0,4 )$ 
C)  $x$-intercept: $( 2,0 ) ; y$-intercept: $( 0,0 )$ 
D)  $x$-intercepts: $( - 2,0 ) , ( 2,0 ) ; y$-intercept: $( 0,4 )$

Question 7

Multiply the polynomials by using the distributive property. $$( - 2 r - 3 s + 6 t ) ( - 5 r - 2 s + 7 t )$$

Accepted Answer

A)  $10 r ^ { 2 } + 19 r s - 44 r t - 33 s t + 42 t ^ { 2 }$ 
B)  $10 r ^ { 2 } - 5 s + 42 t ^ { 2 }$ 
C)  $10 r ^ { 2 } + 19 r s - 44 r t + 6 s ^ { 2 } - 33 s t + 42 t ^ { 2 }$ 
D)  $- 7 r ^ { 2 } + 19 r s - 44 r t - 5 s ^ { 2 } - 33 s t + 13 t ^ { 2 }$ 
A)  $10 r ^ { 2 } + 19 r s - 44 r t - 33 s t + 42 t ^ { 2 }$ 
B)  $10 r ^ { 2 } - 5 s + 42 t ^ { 2 }$ 
C)  $10 r ^ { 2 } + 19 r s - 44 r t + 6 s ^ { 2 } - 33 s t + 42 t ^ { 2 }$ 
D)  $- 7 r ^ { 2 } + 19 r s - 44 r t - 5 s ^ { 2 } - 33 s t + 13 t ^ { 2 }$

Question 8

Factor completely using the difference of squares along with factoring by grouping. $16 p ^ { 3 } - 48 p ^ { 2 } - 25 p + 75$

Accepted Answer

A)  $( p - 3 ) \left( 16 p ^ { 2 } - 25 \right)$ 
B)  $( p - 3 ) ( 4 p - 5 ) ^ { 2 }$ 
C)  $( p - 3 ) ( 4 p + 5 ) ( 4 p - 5 )$ 
D)  Prime 
A)  $( p - 3 ) \left( 16 p ^ { 2 } - 25 \right)$ 
B)  $( p - 3 ) ( 4 p - 5 ) ^ { 2 }$ 
C)  $( p - 3 ) ( 4 p + 5 ) ( 4 p - 5 )$ 
D)  Prime

Question 9

Multiply the polynomials by using the distributive property. $$\left( x ^ { 2 } + 6 \right) ( - 7 x - 7 )$$

Accepted Answer

A)  $- 7 x ^ { 3 } - 49 x - 42$ 
B)  $- 7 x ^ { 3 } - 1$ 
C)  $- 7 x ^ { 3 } - 7 x ^ { 2 } - 42 x - 1$ 
D)  $- 7 x ^ { 3 } - 7 x ^ { 2 } - 42 x - 42$ 
A)  $- 7 x ^ { 3 } - 49 x - 42$ 
B)  $- 7 x ^ { 3 } - 1$ 
C)  $- 7 x ^ { 3 } - 7 x ^ { 2 } - 42 x - 1$ 
D)  $- 7 x ^ { 3 } - 7 x ^ { 2 } - 42 x - 42$

Question 10

Factor the polynomial by grouping (if possible). $3 v ^ { 2 } w - 21 v w - 3 v ^ { 2 } + 21 v$

Accepted Answer

A)  $\left( 3 v ^ { 2 } - 21 w \right) ( w - 1 )$ 
B)  $3 v w ( v - 7 ) - 3 v ( v - 7 )$ 
C)  $3 v ( v - 7 ) ( w - 1 )$ 
D)  Cannot be factored 
A)  $\left( 3 v ^ { 2 } - 21 w \right) ( w - 1 )$ 
B)  $3 v w ( v - 7 ) - 3 v ( v - 7 )$ 
C)  $3 v ( v - 7 ) ( w - 1 )$ 
D)  Cannot be factored

Question 11

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $$g ( x ) = 2 ( x + 2 )$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Multiply the polynomials by using the distributive property. $3 s ^ { 2 } t ^ { 2 } \left( s ^ { 2 } t ^ { 4 } + 6 s t ^ { 2 } + 4 s ^ { 2 } \right)$

Accepted Answer

A)  $3 s ^ { 4 } t ^ { 6 } + 6 s t ^ { 2 } + 4 s ^ { 2 }$ 
B)  $3 s ^ { 4 } t ^ { 6 } + 18 s ^ { 3 } t ^ { 4 } + 12 s ^ { 4 }$ 
C)  $3 s ^ { 4 } t ^ { 6 } + 18 s ^ { 3 } t ^ { 4 } + 12 s ^ { 4 } t ^ { 2 }$ 
D)  $3 s ^ { 4 } t ^ { 6 } + 6 s ^ { 3 } t ^ { 4 } + 4 s ^ { 2 }$ 
A)  $3 s ^ { 4 } t ^ { 6 } + 6 s t ^ { 2 } + 4 s ^ { 2 }$ 
B)  $3 s ^ { 4 } t ^ { 6 } + 18 s ^ { 3 } t ^ { 4 } + 12 s ^ { 4 }$ 
C)  $3 s ^ { 4 } t ^ { 6 } + 18 s ^ { 3 } t ^ { 4 } + 12 s ^ { 4 } t ^ { 2 }$ 
D)  $3 s ^ { 4 } t ^ { 6 } + 6 s ^ { 3 } t ^ { 4 } + 4 s ^ { 2 }$

Question 13

Consider the function below. (a) Find the values of $x$ for which $f ( x ) = 0$.
(b) Find $f ( 0 )$.
$$f ( x ) = x ^ { 2 } - 15 x + 56$$

Accepted Answer

A)  a. $- 7 , - 8$
b. $f ( 0 ) = 56$ 
B)  a. 7,8
b. $f ( 0 ) = 56$ 
C)  a. $- 7 , - 8$
b. $f ( 0 ) = 0$ 
D)  a. 7,8
b. $f ( 0 ) = 0$ 
A)  a. $- 7 , - 8$
b. $f ( 0 ) = 56$ 
B)  a. 7,8
b. $f ( 0 ) = 56$ 
C)  a. $- 7 , - 8$
b. $f ( 0 ) = 0$ 
D)  a. 7,8
b. $f ( 0 ) = 0$

Question 14

Simplify the expression. Write your answer with positive exponents only. $\frac { 18 ^ { 12 } } { 18 ^ { 5 } }$

Accepted Answer

A)  $18 ^ { 17 }$ 
B)  $18 ^ { 12 } - 18 ^ { 5 }$ 
C)  $18 ^ { 7 }$ 
D)  $18 ^ { 12 / 5 }$ 
A)  $18 ^ { 17 }$ 
B)  $18 ^ { 12 } - 18 ^ { 5 }$ 
C)  $18 ^ { 7 }$ 
D)  $18 ^ { 12 / 5 }$

Question 15

Factor completely. $4 n ^ { 8 } - 100$

Accepted Answer

A)  $4 \left( n ^ { 8 } - 25 \right)$ 
B)  $4 \left( n ^ { 4 } - 5 \right) \left( n ^ { 4 } + 5 \right)$ 
C)  $4 \left( n ^ { 2 } - 5 \right) ^ { 2 } \left( n ^ { 2 } + 5 \right) ^ { 2 }$ 
D)  $4 \left( n ^ { 2 } - 5 \right) \left( n ^ { 2 } + 5 \right) \left( n ^ { 4 } - 25 \right)$ 
A)  $4 \left( n ^ { 8 } - 25 \right)$ 
B)  $4 \left( n ^ { 4 } - 5 \right) \left( n ^ { 4 } + 5 \right)$ 
C)  $4 \left( n ^ { 2 } - 5 \right) ^ { 2 } \left( n ^ { 2 } + 5 \right) ^ { 2 }$ 
D)  $4 \left( n ^ { 2 } - 5 \right) \left( n ^ { 2 } + 5 \right) \left( n ^ { 4 } - 25 \right)$

Question 16

Solve the equation. $$t ( 12 t - 23 ) = 9$$

Accepted Answer

A)  $t = 0 ; t = \frac { 23 } { 12 }$ 
B)  $t = - \frac { 9 } { 4 } ; t = \frac { 1 } { 3 }$ 
C)  $t = \frac { 9 } { 4 } ; t = - \frac { 1 } { 3 }$ 
D)  $t = \frac { 9 } { 4 } ; t = \frac { 1 } { 3 }$ 
A)  $t = 0 ; t = \frac { 23 } { 12 }$ 
B)  $t = - \frac { 9 } { 4 } ; t = \frac { 1 } { 3 }$ 
C)  $t = \frac { 9 } { 4 } ; t = - \frac { 1 } { 3 }$ 
D)  $t = \frac { 9 } { 4 } ; t = \frac { 1 } { 3 }$

Question 17

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $2 w ^ { 2 } - 2 w - 6$

Accepted Answer

A)  $2 ( w + 3 ) ( w - 1 )$ 
B)  $2 ( w - 3 ) ( w + 1 )$ 
C)  $2 ( w + 3 ) ( w + 1 )$ 
D)  $2 \left( w ^ { 2 } - 1 w - 3 \right)$; Not a perfect square trinomial 
A)  $2 ( w + 3 ) ( w - 1 )$ 
B)  $2 ( w - 3 ) ( w + 1 )$ 
C)  $2 ( w + 3 ) ( w + 1 )$ 
D)  $2 \left( w ^ { 2 } - 1 w - 3 \right)$; Not a perfect square trinomial

Question 18

Multiply the polynomials by using the distributive property. $$( m + 9 n ) \left( m ^ { 2 } + 8 m n - 2 n ^ { 2 } \right)$$

Accepted Answer

A)  $m ^ { 3 } + 87 m ^ { 2 } n ^ { 2 } - 18 n ^ { 3 }$ 
B)  $m ^ { 3 } + 17 m ^ { 2 } n + 70 m n ^ { 2 } - 18 n ^ { 3 }$ 
C)  $m ^ { 3 } + 9 m n + 70 m n ^ { 2 } - 18 n ^ { 3 }$ 
D)  $m ^ { 3 } + 9 n + 8 m n - 18 n ^ { 3 }$ 
A)  $m ^ { 3 } + 87 m ^ { 2 } n ^ { 2 } - 18 n ^ { 3 }$ 
B)  $m ^ { 3 } + 17 m ^ { 2 } n + 70 m n ^ { 2 } - 18 n ^ { 3 }$ 
C)  $m ^ { 3 } + 9 m n + 70 m n ^ { 2 } - 18 n ^ { 3 }$ 
D)  $m ^ { 3 } + 9 n + 8 m n - 18 n ^ { 3 }$

Question 19

Divide the polynomials. $$\left( - 10 n ^ { 2 } + 4 n ^ { 4 } - 10 n ^ { 5 } \right) \div ( 2 n )$$

Accepted Answer

A)  $- 5 n ^ { 3 } + 2 n ^ { 5 } - 5 n ^ { 6 }$ 
B)  $- 5 + 2 n ^ { 3 } - 5 n ^ { 4 }$ 
C)  $- 5 n ^ { 2 } + 2 n ^ { 4 } - 5 n ^ { 5 }$ 
D)  $- 5 n + 2 n ^ { 3 } - 5 n ^ { 4 }$ 
A)  $- 5 n ^ { 3 } + 2 n ^ { 5 } - 5 n ^ { 6 }$ 
B)  $- 5 + 2 n ^ { 3 } - 5 n ^ { 4 }$ 
C)  $- 5 n ^ { 2 } + 2 n ^ { 4 } - 5 n ^ { 5 }$ 
D)  $- 5 n + 2 n ^ { 3 } - 5 n ^ { 4 }$

Question 20

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $4 n ^ { 2 } - 12 n + 32$

Accepted Answer

A)  $4 ( n - 8 ) ( n + 1 )$ 
B)  $4 ( n - 8 ) ( n - 1 )$ 
C)  $4 ( n + 8 ) ( n + 1 )$ 
D)  $4 \left( n ^ { 2 } - 3 n + 8 \right)$; Not a perfect square trinomial 
A)  $4 ( n - 8 ) ( n + 1 )$ 
B)  $4 ( n - 8 ) ( n - 1 )$ 
C)  $4 ( n + 8 ) ( n + 1 )$ 
D)  $4 \left( n ^ { 2 } - 3 n + 8 \right)$; Not a perfect square trinomial

Fill in the blank to make the trinomial a perfect square trinomial. $4 x ^ { 2 } - \underline { ( \quad ) } + 9$

Factor the sum or difference of cubes. $27 u ^ { 3 } + 64$

Fill in the blank to make the trinomial a perfect square trinomial. $64 s ^ { 4 } + \underline { ( \quad ) }+ 81$

Divide the polynomials by using long division. $\left( 2 r ^ { 5 } - 6 r ^ { 4 } - 7 r ^ { 3 } - 21 r ^ { 2 } + 2 r + 3 \right) \div \left( 2 r ^ { 2 } - 8 r - 3 \right)$

Find the x- and y-intercepts for the function defined by y = f (x). $f ( x ) = x ^ { 2 } + 4 x + 4$

Multiply the polynomials by using the distributive property. $( - 2 r - 3 s + 6 t ) ( - 5 r - 2 s + 7 t )$

Factor completely using the difference of squares along with factoring by grouping. $16 p ^ { 3 } - 48 p ^ { 2 } - 25 p + 75$

Multiply the polynomials by using the distributive property. $\left( x ^ { 2 } + 6 \right) ( - 7 x - 7 )$

Factor the polynomial by grouping (if possible). $3 v ^ { 2 } w - 21 v w - 3 v ^ { 2 } + 21 v$

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $g ( x ) = 2 ( x + 2 )$

Multiply the polynomials by using the distributive property. $3 s ^ { 2 } t ^ { 2 } \left( s ^ { 2 } t ^ { 4 } + 6 s t ^ { 2 } + 4 s ^ { 2 } \right)$

Consider the function below. (a) Find the values of $x$ for which $f ( x ) = 0$ . (b) Find $f ( 0 )$ . $f ( x ) = x ^ { 2 } - 15 x + 56$

Simplify the expression. Write your answer with positive exponents only. $\frac { 18 ^ { 12 } } { 18 ^ { 5 } }$

Factor completely. $4 n ^ { 8 } - 100$

Solve the equation. $t ( 12 t - 23 ) = 9$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $2 w ^ { 2 } - 2 w - 6$

Multiply the polynomials by using the distributive property. $( m + 9 n ) \left( m ^ { 2 } + 8 m n - 2 n ^ { 2 } \right)$

Divide the polynomials. $\left( - 10 n ^ { 2 } + 4 n ^ { 4 } - 10 n ^ { 5 } \right) \div ( 2 n )$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $4 n ^ { 2 } - 12 n + 32$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

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Exam 4: Polynomials

Fill in the blank to make the trinomial a perfect square trinomial. 4x2−()‾+94 x ^ { 2 } - \underline { ( \quad ) } + 94x2−()​+9

Factor the sum or difference of cubes. 27u3+6427 u ^ { 3 } + 6427u3+64

Fill in the blank to make the trinomial a perfect square trinomial. 64s4+()‾+8164 s ^ { 4 } + \underline { ( \quad ) }+ 8164s4+()​+81

Divide the polynomials by using long division. (2r5−6r4−7r3−21r2+2r+3)÷(2r2−8r−3)\left( 2 r ^ { 5 } - 6 r ^ { 4 } - 7 r ^ { 3 } - 21 r ^ { 2 } + 2 r + 3 \right) \div \left( 2 r ^ { 2 } - 8 r - 3 \right)(2r5−6r4−7r3−21r2+2r+3)÷(2r2−8r−3)

Find the x- and y-intercepts for the function defined by y = f (x). f(x)=x2+4x+4f ( x ) = x ^ { 2 } + 4 x + 4f(x)=x2+4x+4

Multiply the polynomials by using the distributive property. (−2r−3s+6t)(−5r−2s+7t)( - 2 r - 3 s + 6 t ) ( - 5 r - 2 s + 7 t )(−2r−3s+6t)(−5r−2s+7t)

Factor completely using the difference of squares along with factoring by grouping. 16p3−48p2−25p+7516 p ^ { 3 } - 48 p ^ { 2 } - 25 p + 7516p3−48p2−25p+75

Multiply the polynomials by using the distributive property. (x2+6)(−7x−7)\left( x ^ { 2 } + 6 \right) ( - 7 x - 7 )(x2+6)(−7x−7)

Factor the polynomial by grouping (if possible). 3v2w−21vw−3v2+21v3 v ^ { 2 } w - 21 v w - 3 v ^ { 2 } + 21 v3v2w−21vw−3v2+21v

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. g(x)=2(x+2)g ( x ) = 2 ( x + 2 )g(x)=2(x+2)

Multiply the polynomials by using the distributive property. 3s2t2(s2t4+6st2+4s2)3 s ^ { 2 } t ^ { 2 } \left( s ^ { 2 } t ^ { 4 } + 6 s t ^ { 2 } + 4 s ^ { 2 } \right)3s2t2(s2t4+6st2+4s2)

Consider the function below. (a) Find the values of xxx for which f(x)=0f ( x ) = 0f(x)=0 . (b) Find f(0)f ( 0 )f(0) . f(x)=x2−15x+56f ( x ) = x ^ { 2 } - 15 x + 56f(x)=x2−15x+56

Simplify the expression. Write your answer with positive exponents only. 1812185\frac { 18 ^ { 12 } } { 18 ^ { 5 } }1851812​

Factor completely. 4n8−1004 n ^ { 8 } - 1004n8−100

Solve the equation. t(12t−23)=9t ( 12 t - 23 ) = 9t(12t−23)=9

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. 2w2−2w−62 w ^ { 2 } - 2 w - 62w2−2w−6

Multiply the polynomials by using the distributive property. (m+9n)(m2+8mn−2n2)( m + 9 n ) \left( m ^ { 2 } + 8 m n - 2 n ^ { 2 } \right)(m+9n)(m2+8mn−2n2)

Divide the polynomials. (−10n2+4n4−10n5)÷(2n)\left( - 10 n ^ { 2 } + 4 n ^ { 4 } - 10 n ^ { 5 } \right) \div ( 2 n )(−10n2+4n4−10n5)÷(2n)

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. 4n2−12n+324 n ^ { 2 } - 12 n + 324n2−12n+32

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Fill in the blank to make the trinomial a perfect square trinomial. $4 x ^ { 2 } - \underline { ( \quad ) } + 9$

Factor the sum or difference of cubes. $27 u ^ { 3 } + 64$

Fill in the blank to make the trinomial a perfect square trinomial. $64 s ^ { 4 } + \underline { ( \quad ) }+ 81$

Divide the polynomials by using long division. $\left( 2 r ^ { 5 } - 6 r ^ { 4 } - 7 r ^ { 3 } - 21 r ^ { 2 } + 2 r + 3 \right) \div \left( 2 r ^ { 2 } - 8 r - 3 \right)$

Find the x- and y-intercepts for the function defined by y = f (x). $f ( x ) = x ^ { 2 } + 4 x + 4$

Multiply the polynomials by using the distributive property. $( - 2 r - 3 s + 6 t ) ( - 5 r - 2 s + 7 t )$

Factor completely using the difference of squares along with factoring by grouping. $16 p ^ { 3 } - 48 p ^ { 2 } - 25 p + 75$

Multiply the polynomials by using the distributive property. $\left( x ^ { 2 } + 6 \right) ( - 7 x - 7 )$

Factor the polynomial by grouping (if possible). $3 v ^ { 2 } w - 21 v w - 3 v ^ { 2 } + 21 v$

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $g ( x ) = 2 ( x + 2 )$

Multiply the polynomials by using the distributive property. $3 s ^ { 2 } t ^ { 2 } \left( s ^ { 2 } t ^ { 4 } + 6 s t ^ { 2 } + 4 s ^ { 2 } \right)$

Consider the function below. (a) Find the values of $x$ for which $f ( x ) = 0$ . (b) Find $f ( 0 )$ . $f ( x ) = x ^ { 2 } - 15 x + 56$

Simplify the expression. Write your answer with positive exponents only. $\frac { 18 ^ { 12 } } { 18 ^ { 5 } }$

Factor completely. $4 n ^ { 8 } - 100$

Solve the equation. $t ( 12 t - 23 ) = 9$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $2 w ^ { 2 } - 2 w - 6$

Multiply the polynomials by using the distributive property. $( m + 9 n ) \left( m ^ { 2 } + 8 m n - 2 n ^ { 2 } \right)$

Divide the polynomials. $\left( - 10 n ^ { 2 } + 4 n ^ { 4 } - 10 n ^ { 5 } \right) \div ( 2 n )$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $4 n ^ { 2 } - 12 n + 32$