Question 1

Add $\left( 3 s ^ { 2 } + 7 s + 2 \right)$ to $\left( 5 s ^ { 2 } + 9 s - 1 \right)$

Accepted Answer

A)  $8 s ^ { 4 } + 16 s + 1$ 
B)  $8 s ^ { 2 } + 16 s + 1$ 
C)  $8 s ^ { 2 } + 16 s + 3$ 
D)  $- 2 s ^ { 2 } - 2 s + 1$ 
A)  $8 s ^ { 4 } + 16 s + 1$ 
B)  $8 s ^ { 2 } + 16 s + 1$ 
C)  $8 s ^ { 2 } + 16 s + 3$ 
D)  $- 2 s ^ { 2 } - 2 s + 1$

Question 2

Translate from English form to algebraic form. The square of the product of 12 and z

Accepted Answer

A)  $\left( \frac { 12 } { z } \right) ^ { 2 }$ 
B)  $( 12 z ) ^ { 2 }$ 
C)  $( 12 + z ) ^ { 2 }$ 
D)  $12 ^ { 2 } + z ^ { 2 }$ 
A)  $\left( \frac { 12 } { z } \right) ^ { 2 }$ 
B)  $( 12 z ) ^ { 2 }$ 
C)  $( 12 + z ) ^ { 2 }$ 
D)  $12 ^ { 2 } + z ^ { 2 }$

Question 3

Fill in the blank to make the trinomial a perfect square trinomial. $64 y ^ { 2 } + \underline{( \quad ) }+ 9$

Accepted Answer

A)  $64 y ^ { 2 } + \underline{(12 y)} + 9$ 
B)  $64 y ^ { 2 } + \underline{(48y)}+ 9$ 
C)  $64 y ^ { 2 } + ( 24 y ) + 9$ 
D)  $64 y ^ { 2 } + \underline{(24 y)} + 9$ 
A)  $64 y ^ { 2 } + \underline{(12 y)} + 9$ 
B)  $64 y ^ { 2 } + \underline{(48y)}+ 9$ 
C)  $64 y ^ { 2 } + ( 24 y ) + 9$ 
D)  $64 y ^ { 2 } + \underline{(24 y)} + 9$

Question 4

Write an expression for the area and simplify your answer.  
[The figure is not necessarily drawn to scale]

Accepted Answer

A)  $40 x ^ { 2 } - 41 x + 21$ 
B)  $40 x ^ { 2 } + 21$ 
C)  $40 x ^ { 2 } - 71 x + 21$ 
D)  $40 x ^ { 2 } + 71 x + 21$ 
A)  $40 x ^ { 2 } - 41 x + 21$ 
B)  $40 x ^ { 2 } + 21$ 
C)  $40 x ^ { 2 } - 71 x + 21$ 
D)  $40 x ^ { 2 } + 71 x + 21$

Question 5

Subtract $\left( 9 m ^ { 3 } + 2 m + 4 \right)$ from $\left( - 6 m ^ { 3 } - 9 m - 9 \right)$.

Accepted Answer

A)  $- 15 m ^ { 3 } - 7 m - 5$ 
B)  $- 15 m ^ { 3 } - 11 m - 13$ 
C)  $- 6 m ^ { 3 } - 9 m ^ { 2 } - 11 m - 13$ 
D)  $15 m ^ { 3 } + 11 m + 13$ 
A)  $- 15 m ^ { 3 } - 7 m - 5$ 
B)  $- 15 m ^ { 3 } - 11 m - 13$ 
C)  $- 6 m ^ { 3 } - 9 m ^ { 2 } - 11 m - 13$ 
D)  $15 m ^ { 3 } + 11 m + 13$

Question 6

Simplify the expression. Write your answer with positive exponents only. $$\left( - 2 a ^ { 3 } b ^ { 6 } c ^ { 6 } \right) ^ { 3 }$$

Accepted Answer

The answer of Simplify the expression. Write your answer with...

Question 7

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $$f ( x ) = ( x - 1 ) ( x - 3 )$$

Accepted Answer

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

Question 8

Multiply. $$( 2 p - 4 q ) ^ { 3 }$$

Accepted Answer

A)  $8 p ^ { 3 } - 16 p q - 64 q ^ { 3 }$ 
B)  $8 p ^ { 3 } - 64 q ^ { 3 }$ 
C)  $8 p ^ { 3 } - 48 p ^ { 2 } q + 96 p q ^ { 2 } - 64 q ^ { 3 }$ 
D)  $8 p ^ { 3 } - 32 p ^ { 2 } q + 64 p q ^ { 2 } - 64 q ^ { 3 }$ 
A)  $8 p ^ { 3 } - 16 p q - 64 q ^ { 3 }$ 
B)  $8 p ^ { 3 } - 64 q ^ { 3 }$ 
C)  $8 p ^ { 3 } - 48 p ^ { 2 } q + 96 p q ^ { 2 } - 64 q ^ { 3 }$ 
D)  $8 p ^ { 3 } - 32 p ^ { 2 } q + 64 p q ^ { 2 } - 64 q ^ { 3 }$

Question 9

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $32 r ^ { 2 } - 16 r s + 2 s ^ { 2 }$

Accepted Answer

A)  $2 ( 4 r - s ) ( 4 r + s )$ 
B)  $2 ( 4 r - s ) ^ { 2 }$ 
C)  $32 r ^ { 2 } - 16 r s + 2 s ^ { 2 }$; Not a perfect square trinomial 
D)  $2 \left( 16 r ^ { 2 } - 8 r s + s ^ { 2 } \right)$; Not a perfect square trinomial 
A)  $2 ( 4 r - s ) ( 4 r + s )$ 
B)  $2 ( 4 r - s ) ^ { 2 }$ 
C)  $32 r ^ { 2 } - 16 r s + 2 s ^ { 2 }$; Not a perfect square trinomial 
D)  $2 \left( 16 r ^ { 2 } - 8 r s + s ^ { 2 } \right)$; Not a perfect square trinomial

Question 10

Fill in the blank to make the trinomial a perfect square trinomial. $81 t ^ { 2 } + \underline { ( \quad    ) } + 16$

Accepted Answer

A)  $81 t ^ { 2 } + \underline { ( 18 t ) } + 16$ 
B)  $81 t ^ { 2 } +\underline { ( 72 t ) }+ 16$ 
C)  $81 t ^ { 2 } +\underline { (  36 t )} + 16$ 
D)  $81 t ^ { 2 } + ( 36 ) + 16$ 
A)  $81 t ^ { 2 } + \underline { ( 18 t ) } + 16$ 
B)  $81 t ^ { 2 } +\underline { ( 72 t ) }+ 16$ 
C)  $81 t ^ { 2 } +\underline { (  36 t )} + 16$ 
D)  $81 t ^ { 2 } + ( 36 ) + 16$

Question 11

Factor the polynomial by grouping (if possible). $$2 x y - 9 c x - 18 c y + 81 c ^ { 2 }$$

Accepted Answer

A)  $c ( 2 y - 9 \mathrm { c } ) ( x - 9 )$ 
B)  $x ( 2 y - 9 c ) - 9 \left( 2 c y - 9 c ^ { 2 } \right)$ 
C)  $( 2 y - 9 c ) ( x - 9 c )$ 
D)  Cannot be factored 
A)  $c ( 2 y - 9 \mathrm { c } ) ( x - 9 )$ 
B)  $x ( 2 y - 9 c ) - 9 \left( 2 c y - 9 c ^ { 2 } \right)$ 
C)  $( 2 y - 9 c ) ( x - 9 c )$ 
D)  Cannot be factored

Question 12

Solve the equation. $$y ^ { 2 } + 8 y - 11 = ( y + 2 ) ( y - 3 )$$

Accepted Answer

A)  $y = \frac { 5 } { 9 }$ 
B)  $y = 2 ; y = - 3$; 
C)  $y = \frac { 5 } { 9 } ; y = - \frac { 5 } { 9 }$ 
D)  $y = - 2 ; y = 3$; 
A)  $y = \frac { 5 } { 9 }$ 
B)  $y = 2 ; y = - 3$; 
C)  $y = \frac { 5 } { 9 } ; y = - \frac { 5 } { 9 }$ 
D)  $y = - 2 ; y = 3$;

Question 13

Factor out the GCF. $7 q ( 6 q + 5 ) + 9 ( 6 q + 5 )$

Accepted Answer

A)  $( 7 q + 5 ) ( 6 q + 9 )$ 
B)  $( 7 q - 9 ) ( 6 q + 5 )$ 
C)  $6 q + 5$ 
D)  $( 7 q + 9 ) ( 6 q + 5 )$ 
A)  $( 7 q + 5 ) ( 6 q + 9 )$ 
B)  $( 7 q - 9 ) ( 6 q + 5 )$ 
C)  $6 q + 5$ 
D)  $( 7 q + 9 ) ( 6 q + 5 )$

Question 14

Multiply the polynomials. $$\left( - 3 t ^ { 2 } u ^ { 3 } \right) \left( 5 t ^ { 7 } u ^ { 8 } \right)$$

Accepted Answer

A)  $- 15 t ^ { 14 } u ^ { 24 }$ 
B)  $- 15 t ^ { - 5 } u ^ { - 5 }$ 
C)  $- 15 t ^ { 9 } u ^ { 11 }$ 
D)  $2 t ^ { 9 } u ^ { 11 }$ 
A)  $- 15 t ^ { 14 } u ^ { 24 }$ 
B)  $- 15 t ^ { - 5 } u ^ { - 5 }$ 
C)  $- 15 t ^ { 9 } u ^ { 11 }$ 
D)  $2 t ^ { 9 } u ^ { 11 }$

Question 15

A rectangular swimming pool has a concrete walk around it of width x. The pool has a length l = 36 feet and a width w = 25 feet (see figure). Find an expression representing the combined area A of the pool And the walk. Simplify the result.

Accepted Answer

A)  $A = x ^ { 2 } + 1800 x + 900$ 
B)  $A = 900 + x ^ { 2 }$ 
C)  $A = 4 x ^ { 2 } + 122 x + 900$ 
D)  $A = x ^ { 2 } + 900$ 
A)  $A = x ^ { 2 } + 1800 x + 900$ 
B)  $A = 900 + x ^ { 2 }$ 
C)  $A = 4 x ^ { 2 } + 122 x + 900$ 
D)  $A = x ^ { 2 } + 900$

Add $\left( 3 s ^ { 2 } + 7 s + 2 \right)$ to $\left( 5 s ^ { 2 } + 9 s - 1 \right)$

Translate from English form to algebraic form. The square of the product of 12 and z

Fill in the blank to make the trinomial a perfect square trinomial. $64 y ^ { 2 } + \underline{( \quad ) }+ 9$

Write an expression for the area and simplify your answer. [The figure is not necessarily drawn to scale]

Subtract $\left( 9 m ^ { 3 } + 2 m + 4 \right)$ from $\left( - 6 m ^ { 3 } - 9 m - 9 \right)$ .

Simplify the expression. Write your answer with positive exponents only. $\left( - 2 a ^ { 3 } b ^ { 6 } c ^ { 6 } \right) ^ { 3 }$

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $f ( x ) = ( x - 1 ) ( x - 3 )$

Multiply. $( 2 p - 4 q ) ^ { 3 }$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $32 r ^ { 2 } - 16 r s + 2 s ^ { 2 }$

Fill in the blank to make the trinomial a perfect square trinomial. $81 t ^ { 2 } + \underline { ( \quad ) } + 16$

Factor the polynomial by grouping (if possible). $2 x y - 9 c x - 18 c y + 81 c ^ { 2 }$

Solve the equation. $y ^ { 2 } + 8 y - 11 = ( y + 2 ) ( y - 3 )$

Factor out the GCF. $7 q ( 6 q + 5 ) + 9 ( 6 q + 5 )$

Multiply the polynomials. $\left( - 3 t ^ { 2 } u ^ { 3 } \right) \left( 5 t ^ { 7 } u ^ { 8 } \right)$

A rectangular swimming pool has a concrete walk around it of width x. The pool has a length l = 36 feet and a width w = 25 feet (see figure). Find an expression representing the combined area A of the pool And the walk. Simplify the result.

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

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Exam 4: Polynomials

Add (3s2+7s+2)\left( 3 s ^ { 2 } + 7 s + 2 \right)(3s2+7s+2) to (5s2+9s−1)\left( 5 s ^ { 2 } + 9 s - 1 \right)(5s2+9s−1)

Translate from English form to algebraic form. The square of the product of 12 and z

Fill in the blank to make the trinomial a perfect square trinomial. 64y2+()‾+964 y ^ { 2 } + \underline{( \quad ) }+ 964y2+()​+9

Write an expression for the area and simplify your answer. [The figure is not necessarily drawn to scale]

Subtract (9m3+2m+4)\left( 9 m ^ { 3 } + 2 m + 4 \right)(9m3+2m+4) from (−6m3−9m−9)\left( - 6 m ^ { 3 } - 9 m - 9 \right)(−6m3−9m−9) .

Simplify the expression. Write your answer with positive exponents only. (−2a3b6c6)3\left( - 2 a ^ { 3 } b ^ { 6 } c ^ { 6 } \right) ^ { 3 }(−2a3b6c6)3

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. f(x)=(x−1)(x−3)f ( x ) = ( x - 1 ) ( x - 3 )f(x)=(x−1)(x−3)

Multiply. (2p−4q)3( 2 p - 4 q ) ^ { 3 }(2p−4q)3

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. 32r2−16rs+2s232 r ^ { 2 } - 16 r s + 2 s ^ { 2 }32r2−16rs+2s2

Fill in the blank to make the trinomial a perfect square trinomial. 81t2+()‾+1681 t ^ { 2 } + \underline { ( \quad ) } + 1681t2+()​+16

Factor the polynomial by grouping (if possible). 2xy−9cx−18cy+81c22 x y - 9 c x - 18 c y + 81 c ^ { 2 }2xy−9cx−18cy+81c2

Solve the equation. y2+8y−11=(y+2)(y−3)y ^ { 2 } + 8 y - 11 = ( y + 2 ) ( y - 3 )y2+8y−11=(y+2)(y−3)

Factor out the GCF. 7q(6q+5)+9(6q+5)7 q ( 6 q + 5 ) + 9 ( 6 q + 5 )7q(6q+5)+9(6q+5)

Multiply the polynomials. (−3t2u3)(5t7u8)\left( - 3 t ^ { 2 } u ^ { 3 } \right) \left( 5 t ^ { 7 } u ^ { 8 } \right)(−3t2u3)(5t7u8)

A rectangular swimming pool has a concrete walk around it of width x. The pool has a length l = 36 feet and a width w = 25 feet (see figure). Find an expression representing the combined area A of the pool And the walk. Simplify the result.

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

Add $\left( 3 s ^ { 2 } + 7 s + 2 \right)$ to $\left( 5 s ^ { 2 } + 9 s - 1 \right)$

Fill in the blank to make the trinomial a perfect square trinomial. $64 y ^ { 2 } + \underline{( \quad ) }+ 9$

Subtract $\left( 9 m ^ { 3 } + 2 m + 4 \right)$ from $\left( - 6 m ^ { 3 } - 9 m - 9 \right)$ .

Simplify the expression. Write your answer with positive exponents only. $\left( - 2 a ^ { 3 } b ^ { 6 } c ^ { 6 } \right) ^ { 3 }$

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $f ( x ) = ( x - 1 ) ( x - 3 )$

Multiply. $( 2 p - 4 q ) ^ { 3 }$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $32 r ^ { 2 } - 16 r s + 2 s ^ { 2 }$

Fill in the blank to make the trinomial a perfect square trinomial. $81 t ^ { 2 } + \underline { ( \quad ) } + 16$

Factor the polynomial by grouping (if possible). $2 x y - 9 c x - 18 c y + 81 c ^ { 2 }$

Solve the equation. $y ^ { 2 } + 8 y - 11 = ( y + 2 ) ( y - 3 )$

Factor out the GCF. $7 q ( 6 q + 5 ) + 9 ( 6 q + 5 )$

Multiply the polynomials. $\left( - 3 t ^ { 2 } u ^ { 3 } \right) \left( 5 t ^ { 7 } u ^ { 8 } \right)$