Question 1

Factor completely. If the polynomial cannot be factored, write "prime."
-$4 x^{2}-5 x+9$

Accepted Answer

A)  $(4 x-1)(x-9)$ 
B)  prime 
C)  $(2 x-9)(2 x-1)$ 
D)  $(4 x-9)(x-1)$ 
A)  $(4 x-1)(x-9)$ 
B)  prime 
C)  $(2 x-9)(2 x-1)$ 
D)  $(4 x-9)(x-1)$

Question 2

For the given functions $f(x)$ and $g(x)$, perform the indicated operation.
-$f(x)=\left(2 x^{6}-15 x^{3}-14\right), g(x)=\left(4 x^{6}-18 x^{3}+4\right)$ Find $f(x)-g(x)$.

Accepted Answer

A)  $-17 \mathrm{x}^{9}$ 
B)  $-2 x^{6}-11 x^{3}-10$ 
C)  $-2 x^{6}+3 x^{3}-10$ 
D)  $-2 x^{6}+3 x^{3}-18$ 
A)  $-17 \mathrm{x}^{9}$ 
B)  $-2 x^{6}-11 x^{3}-10$ 
C)  $-2 x^{6}+3 x^{3}-10$ 
D)  $-2 x^{6}+3 x^{3}-18$

Question 3

Find a quadratic equation with integer coefficients that has the given solution set.
-$\{6,10\}$

Accepted Answer

A)  $x^{2}-10 x+6=0$ 
B)  $x^{2}+16 x+60=0$ 
C)  $x^{2}+16 x-60=0$ 
D)  $x^{2}-16 x+60=0$ 
A)  $x^{2}-10 x+6=0$ 
B)  $x^{2}+16 x+60=0$ 
C)  $x^{2}+16 x-60=0$ 
D)  $x^{2}-16 x+60=0$

Question 4

Determine which factoring technique is appropriate for the given polynomial.
-$8 \mathrm{x}^{3}-125$

Accepted Answer

A)  difference of squares 
B)  sum of squares 
C)  difference of cubes 
D)  factoring by grouping 
A)  difference of squares 
B)  sum of squares 
C)  difference of cubes 
D)  factoring by grouping

Question 5

Factor completely. If the polynomial cannot be factored, write "prime."
-$3 x^{3}+15 x^{2}-18 x$

Accepted Answer

A)  $x(x+6)(3 x-3)$ 
B)  $3 x(x+6)(x-1)$ 
C)  $3\left(x^{2}+6 x\right)(x-1)$ 
D)  $x(3 x+18)(x-1)$ 
A)  $x(x+6)(3 x-3)$ 
B)  $3 x(x+6)(x-1)$ 
C)  $3\left(x^{2}+6 x\right)(x-1)$ 
D)  $x(3 x+18)(x-1)$

Question 6

Factor completely. If the polynomial cannot be factored, write "prime."
-$216-343 t^{3}$

Accepted Answer

A)  $(6+7 t)\left(36-42 t+49 t^{2}\right)$ 
B)  $(216-7 t)\left(1+42 t+49 t^{2}\right)$ 
C)  $(6-7 t)\left(36+42 t+49 t^{2}\right)$ 
D)  $(6-7 t)\left(36+49 t^{2}\right)$ 
A)  $(6+7 t)\left(36-42 t+49 t^{2}\right)$ 
B)  $(216-7 t)\left(1+42 t+49 t^{2}\right)$ 
C)  $(6-7 t)\left(36+42 t+49 t^{2}\right)$ 
D)  $(6-7 t)\left(36+49 t^{2}\right)$

Question 7

Factor completely. If the polynomial cannot be factored, write "prime."
-$2 x^{2}+2 x y+y^{2}$

Accepted Answer

A)  $2(x+y)^{2}$ 
B)  $(2 x+y)(x+y)$ 
C)  $(2 x+y)(x-y)$ 
D)  Prime 
A)  $2(x+y)^{2}$ 
B)  $(2 x+y)(x+y)$ 
C)  $(2 x+y)(x-y)$ 
D)  Prime

Question 8

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\frac{z^{-7}}{z^{-3}}$

Accepted Answer

A)  $z^{4}$ 
B)  $z^{10}$ 
C)  $\frac{1}{z^{-4}}$ 
D)  $\frac{1}{z^{4}}$ 
A)  $z^{4}$ 
B)  $z^{10}$ 
C)  $\frac{1}{z^{-4}}$ 
D)  $\frac{1}{z^{4}}$

Question 9

Evaluate the given function
-$f(x)=x^{7}, f\left(b^{3}\right)$

Accepted Answer

A)  $b^{10}$ 
B)  21 
C)  $x^{7} b^{3}$ 
D)  $b^{21}$ 
A)  $b^{10}$ 
B)  21 
C)  $x^{7} b^{3}$ 
D)  $b^{21}$

Question 10

Find a quadratic equation with integer coefficients that has the given solution set.
-$\{-7,-10\}$

Accepted Answer

A)  $x^{2}-17 x+70=0$ 
B)  $x^{2}+17 x+70=0$ 
C)  $x^{2}+3 x+70=0$ 
D)  $x^{2}-3 x-70=0$ 
A)  $x^{2}-17 x+70=0$ 
B)  $x^{2}+17 x+70=0$ 
C)  $x^{2}+3 x+70=0$ 
D)  $x^{2}-3 x-70=0$

Question 11

$\left(x^{3}-4 x^{2}+23 x\right)-\left(6 x^{2}-6 x+10\right)$

Accepted Answer

A)  $x^{3}+10 x^{2}-17 x-10$ 
B)  $x^{3}-10 x^{2}+17 x-10$ 
C)  $x^{3}-10 x^{2}+17 x+10$ 
D)  $x^{3}-10 x^{2}+29 x-10$ 
A)  $x^{3}+10 x^{2}-17 x-10$ 
B)  $x^{3}-10 x^{2}+17 x-10$ 
C)  $x^{3}-10 x^{2}+17 x+10$ 
D)  $x^{3}-10 x^{2}+29 x-10$

Question 12

For the given functions $f(x)$ and $g(x)$, perform the indicated operation.
-$f(x)=4 x^{3}-6 x^{2}+3 x-10, g(x)=x^{3}+12 x^{2}-5$
Find $f(x)-g(x)$.

Accepted Answer

A)  $5 x^{3}-6 x^{2}+3 x-5$ 
B)  $3 x^{3}+18 x^{2}+3 x+5$ 
C)  $3 x^{3}-18 x^{2}-3 x+5$ 
D)  $3 x^{3}-18 x^{2}+3 x-5$ 
A)  $5 x^{3}-6 x^{2}+3 x-5$ 
B)  $3 x^{3}+18 x^{2}+3 x+5$ 
C)  $3 x^{3}-18 x^{2}-3 x+5$ 
D)  $3 x^{3}-18 x^{2}+3 x-5$

Question 13

$(x-4)(-4 x+6)$

Accepted Answer

A)  $-4 x^{2}-24 x+22$ 
B)  $-4 x^{2}+22 x+22$ 
C)  $-4 x^{2}+20 x-24$ 
D)  $-4 x^{2}+22 x-24$ 
A)  $-4 x^{2}-24 x+22$ 
B)  $-4 x^{2}+22 x+22$ 
C)  $-4 x^{2}+20 x-24$ 
D)  $-4 x^{2}+22 x-24$

Question 14

Evaluate the polynomial
-$b^{2}$ - 4ac for $a=4, b=-6$ and $c=3$

Accepted Answer

A)  -8 
B)  -12 
C)  -22 
D)  -18 
A)  -8 
B)  -12 
C)  -22 
D)  -18

Question 15

Perform the indicated calculation. Express your answer using scientific notation.
-$\left(9.3 \times 10^{-4}\right) \div\left(3.1 \times 10^{7}\right)$

Accepted Answer

A)  $6 \times 10^{-11}$ 
B)  $3.0 \times 10^{3}$ 
C)  $3.0 \times 10^{-11}$ 
D)  $6 \times 10^{3}$ 
A)  $6 \times 10^{-11}$ 
B)  $3.0 \times 10^{3}$ 
C)  $3.0 \times 10^{-11}$ 
D)  $6 \times 10^{3}$

Question 16

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\frac{x^{-3}}{x^{-8}}$

Accepted Answer

A)  $\frac{1}{x^{5}}$ 
B)  $x^{5}$ 
C)  $\frac{1}{x^{11}}$ 
D)  $x^{11}$ 
A)  $\frac{1}{x^{5}}$ 
B)  $x^{5}$ 
C)  $\frac{1}{x^{11}}$ 
D)  $x^{11}$

Question 17

Convert the given number to scientific notation
-0.000426

Accepted Answer

A)  $4.26 \times 10^{4}$ 
B)  $4.26 \times 10^{-5}$ 
C)  $4.26 \times 10^{-3}$ 
D)  $4.26 \times 10^{-4}$ 
A)  $4.26 \times 10^{4}$ 
B)  $4.26 \times 10^{-5}$ 
C)  $4.26 \times 10^{-3}$ 
D)  $4.26 \times 10^{-4}$

Question 18

Factor the GCF out of the given expression.
-$4 w x-4 w y-10 w z$

Accepted Answer

A)  $2 w(2 x-4 w y-10 w z)$ 
B)  $4 \mathrm{w}(\mathrm{x}-4 \mathrm{y}-10 \mathrm{z})$ 
C)  $2(2 w x-2 w y-5 w z)$ 
D)  $2 \mathrm{w}(2 \mathrm{x}-2 \mathrm{y}-5 \mathrm{z})$ 
A)  $2 w(2 x-4 w y-10 w z)$ 
B)  $4 \mathrm{w}(\mathrm{x}-4 \mathrm{y}-10 \mathrm{z})$ 
C)  $2(2 w x-2 w y-5 w z)$ 
D)  $2 \mathrm{w}(2 \mathrm{x}-2 \mathrm{y}-5 \mathrm{z})$

Question 19

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\left(x^{-2} y^{6}\right)^{-2}$

Accepted Answer

A)  $\frac{y^{4}}{x^{-4}}$ 
B)  $\frac{1}{x^{4} y^{12}}$ 
C)  $\frac{x^{-4}}{y^{4}}$ 
D)  $\frac{x^{4}}{y^{12}}$ 
A)  $\frac{y^{4}}{x^{-4}}$ 
B)  $\frac{1}{x^{4} y^{12}}$ 
C)  $\frac{x^{-4}}{y^{4}}$ 
D)  $\frac{x^{4}}{y^{12}}$

Question 20

$\mathrm{x}^{2}+14 \mathrm{x}+49=0$

Accepted Answer

A)  $\{7,7\}$ 
B)  $\{7\}$ 
C)  $\{7\}$. 
D)  $\{0,7\}$ 
A)  $\{7,7\}$ 
B)  $\{7\}$ 
C)  $\{7\}$. 
D)  $\{0,7\}$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{2}-5 x+9$

For the given functions $f(x)$ and $g(x)$ , perform the indicated operation. - $f(x)=\left(2 x^{6}-15 x^{3}-14\right), g(x)=\left(4 x^{6}-18 x^{3}+4\right)$ Find $f(x)-g(x)$ .

Find a quadratic equation with integer coefficients that has the given solution set. - $\{6,10\}$

Determine which factoring technique is appropriate for the given polynomial. - $8 \mathrm{x}^{3}-125$

Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{3}+15 x^{2}-18 x$

Factor completely. If the polynomial cannot be factored, write "prime." - $216-343 t^{3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $2 x^{2}+2 x y+y^{2}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac{z^{-7}}{z^{-3}}$

Evaluate the given function - $f(x)=x^{7}, f\left(b^{3}\right)$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{-7,-10\}$

$\left(x^{3}-4 x^{2}+23 x\right)-\left(6 x^{2}-6 x+10\right)$

For the given functions $f(x)$ and $g(x)$ , perform the indicated operation. - $f(x)=4 x^{3}-6 x^{2}+3 x-10, g(x)=x^{3}+12 x^{2}-5$ Find $f(x)-g(x)$ .

$(x-4)(-4 x+6)$

Evaluate the polynomial - $b^{2}$ - 4ac for $a=4, b=-6$ and $c=3$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(9.3 \times 10^{-4}\right) \div\left(3.1 \times 10^{7}\right)$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac{x^{-3}}{x^{-8}}$

Convert the given number to scientific notation -0.000426

Factor the GCF out of the given expression. - $4 w x-4 w y-10 w z$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(x^{-2} y^{6}\right)^{-2}$

$\mathrm{x}^{2}+14 \mathrm{x}+49=0$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents, Polynomials, and Factoring Polynomials

Factor completely. If the polynomial cannot be factored, write "prime." - 4x2−5x+94 x^{2}-5 x+94x2−5x+9

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , perform the indicated operation. - f(x)=(2x6−15x3−14),g(x)=(4x6−18x3+4)f(x)=\left(2 x^{6}-15 x^{3}-14\right), g(x)=\left(4 x^{6}-18 x^{3}+4\right)f(x)=(2x6−15x3−14),g(x)=(4x6−18x3+4) Find f(x)−g(x)f(x)-g(x)f(x)−g(x) .

Find a quadratic equation with integer coefficients that has the given solution set. - {6,10}\{6,10\}{6,10}

Determine which factoring technique is appropriate for the given polynomial. - 8x3−1258 \mathrm{x}^{3}-1258x3−125

Factor completely. If the polynomial cannot be factored, write "prime." - 3x3+15x2−18x3 x^{3}+15 x^{2}-18 x3x3+15x2−18x

Factor completely. If the polynomial cannot be factored, write "prime." - 216−343t3216-343 t^{3}216−343t3

Factor completely. If the polynomial cannot be factored, write "prime." - 2x2+2xy+y22 x^{2}+2 x y+y^{2}2x2+2xy+y2

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - z−7z−3\frac{z^{-7}}{z^{-3}}z−3z−7​

Evaluate the given function - f(x)=x7,f(b3)f(x)=x^{7}, f\left(b^{3}\right)f(x)=x7,f(b3)

Find a quadratic equation with integer coefficients that has the given solution set. - {−7,−10}\{-7,-10\}{−7,−10}

(x3−4x2+23x)−(6x2−6x+10)\left(x^{3}-4 x^{2}+23 x\right)-\left(6 x^{2}-6 x+10\right)(x3−4x2+23x)−(6x2−6x+10)

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , perform the indicated operation. - f(x)=4x3−6x2+3x−10,g(x)=x3+12x2−5f(x)=4 x^{3}-6 x^{2}+3 x-10, g(x)=x^{3}+12 x^{2}-5f(x)=4x3−6x2+3x−10,g(x)=x3+12x2−5 Find f(x)−g(x)f(x)-g(x)f(x)−g(x) .

(x−4)(−4x+6)(x-4)(-4 x+6)(x−4)(−4x+6)

Evaluate the polynomial - b2b^{2}b2 - 4ac for a=4,b=−6a=4, b=-6a=4,b=−6 and c=3c=3c=3

Perform the indicated calculation. Express your answer using scientific notation. - (9.3×10−4)÷(3.1×107)\left(9.3 \times 10^{-4}\right) \div\left(3.1 \times 10^{7}\right)(9.3×10−4)÷(3.1×107)

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - x−3x−8\frac{x^{-3}}{x^{-8}}x−8x−3​

Convert the given number to scientific notation -0.000426

Factor the GCF out of the given expression. - 4wx−4wy−10wz4 w x-4 w y-10 w z4wx−4wy−10wz

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - (x−2y6)−2\left(x^{-2} y^{6}\right)^{-2}(x−2y6)−2

x2+14x+49=0\mathrm{x}^{2}+14 \mathrm{x}+49=0x2+14x+49=0

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{2}-5 x+9$

For the given functions $f(x)$ and $g(x)$ , perform the indicated operation. - $f(x)=\left(2 x^{6}-15 x^{3}-14\right), g(x)=\left(4 x^{6}-18 x^{3}+4\right)$ Find $f(x)-g(x)$ .

Find a quadratic equation with integer coefficients that has the given solution set. - $\{6,10\}$

Determine which factoring technique is appropriate for the given polynomial. - $8 \mathrm{x}^{3}-125$

Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{3}+15 x^{2}-18 x$

Factor completely. If the polynomial cannot be factored, write "prime." - $216-343 t^{3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $2 x^{2}+2 x y+y^{2}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac{z^{-7}}{z^{-3}}$

Evaluate the given function - $f(x)=x^{7}, f\left(b^{3}\right)$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{-7,-10\}$

$\left(x^{3}-4 x^{2}+23 x\right)-\left(6 x^{2}-6 x+10\right)$

For the given functions $f(x)$ and $g(x)$ , perform the indicated operation. - $f(x)=4 x^{3}-6 x^{2}+3 x-10, g(x)=x^{3}+12 x^{2}-5$ Find $f(x)-g(x)$ .

$(x-4)(-4 x+6)$

Evaluate the polynomial - $b^{2}$ - 4ac for $a=4, b=-6$ and $c=3$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(9.3 \times 10^{-4}\right) \div\left(3.1 \times 10^{7}\right)$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac{x^{-3}}{x^{-8}}$

Factor the GCF out of the given expression. - $4 w x-4 w y-10 w z$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(x^{-2} y^{6}\right)^{-2}$

$\mathrm{x}^{2}+14 \mathrm{x}+49=0$