Exam 5: Exponents, Polynomials, and Factoring Polynomials

For the given quadratic equation, one of its solutions has been provided. Use it to find the other solution. - $15 x^{2}+29 x+12=0, x=-\frac{4}{3}$

(Multiple Choice)

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Question 41

Simplify. (A ssume all variables are nonzero.) - $\frac{(4 x-10)^{10}}{(4 x-10)^{5}}$

(Multiple Choice)

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Question 42

Factor the GCF out of the given expression. - $5 x+15$

(Multiple Choice)

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Question 43

$-10 x y^{7}\left(5 x y^{7}+2 y^{3}+5\right)$

(Multiple Choice)

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Question 44

If a projectile is launched upward from the ground with an initial velocity of 64.5 feet per second, its height $h$ in feet $t$ seconds later is given by the function $h(t)=-16 t^{2}+64.5 t$ . After how many seconds does the projectile land on the ground?

(Multiple Choice)

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Question 45

Factor completely. If the polynomial cannot be factored, write "prime." - $9 x^{2}+24 x+16$

(Multiple Choice)

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Question 46

Perform the indicated calculation. Express your answer using scientific notation. - $\left(3 \times 10^{9}\right)\left(8 \times 10^{9}\right)$

(Multiple Choice)

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Question 47

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) -2- 4

(Multiple Choice)

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Question 48

Evaluate the polynomial or polynomial function for the given value of the variable. - $-3 x^{2}-2 x-10$ for $x=-2$

(Multiple Choice)

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Question 49

Factor completely. If the polynomial cannot be factored, write "prime." - $-24 x^{2}+20 x-4$

(Multiple Choice)

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Question 50

Factor the GCF out of the given expression. - $9 x(x-4)-(x-4)$

(Multiple Choice)

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Question 51

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(n^{9}\right)^{-2}$

(Multiple Choice)

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Question 52

Choose the one alternative that best completes the statement or answers thequestion. - $m^{17} \cdot m^{21}$

(Multiple Choice)

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Question 53

$-9 x^{3} y^{4}\left(3 x^{9} y^{8}-10 y^{6}+2 x\right)$

(Multiple Choice)

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Question 54

Find the GCF. -34, 85

(Multiple Choice)

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Question 55

Factor completely. If the polynomial cannot be factored, write "prime." - $24 x^{2}+18 x-20 x-15$

(Multiple Choice)

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Question 56

$-7 x^{2} \cdot 2 x^{5}$

(Multiple Choice)

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Question 57

Find the GCF. -50, 60

(Multiple Choice)

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Question 58

Choose the one alternative that best completes the statement or answers thequestion. - $\left(x^{3}\right)^{4}\left(x^{3}\right)^{5}$

(Multiple Choice)

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Question 59

Factor completely. If the polynomial cannot be factored, write "prime." - $w^{4}-s^{4}$

(Multiple Choice)

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Question 60

For the given quadratic equation, one of its solutions has been provided. Use it to find the other solution. - $15 x^{2}+29 x+12=0, x=-\frac{4}{3}$

Simplify. (A ssume all variables are nonzero.) - $\frac{(4 x-10)^{10}}{(4 x-10)^{5}}$

Factor the GCF out of the given expression. - $5 x+15$

$-10 x y^{7}\left(5 x y^{7}+2 y^{3}+5\right)$

If a projectile is launched upward from the ground with an initial velocity of 64.5 feet per second, its height $h$ in feet $t$ seconds later is given by the function $h(t)=-16 t^{2}+64.5 t$ . After how many seconds does the projectile land on the ground?

Factor completely. If the polynomial cannot be factored, write "prime." - $9 x^{2}+24 x+16$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(3 \times 10^{9}\right)\left(8 \times 10^{9}\right)$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) -2- 4

Evaluate the polynomial or polynomial function for the given value of the variable. - $-3 x^{2}-2 x-10$ for $x=-2$

Factor completely. If the polynomial cannot be factored, write "prime." - $-24 x^{2}+20 x-4$

Factor the GCF out of the given expression. - $9 x(x-4)-(x-4)$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(n^{9}\right)^{-2}$

Choose the one alternative that best completes the statement or answers thequestion. - $m^{17} \cdot m^{21}$

$-9 x^{3} y^{4}\left(3 x^{9} y^{8}-10 y^{6}+2 x\right)$

Find the GCF. -34, 85

Factor completely. If the polynomial cannot be factored, write "prime." - $24 x^{2}+18 x-20 x-15$

$-7 x^{2} \cdot 2 x^{5}$

Find the GCF. -50, 60

Choose the one alternative that best completes the statement or answers thequestion. - $\left(x^{3}\right)^{4}\left(x^{3}\right)^{5}$

Factor completely. If the polynomial cannot be factored, write "prime." - $w^{4}-s^{4}$

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

For the given quadratic equation, one of its solutions has been provided. Use it to find the other solution. - 15x2+29x+12=0,x=−4315 x^{2}+29 x+12=0, x=-\frac{4}{3}15x2+29x+12=0,x=−34​

Simplify. (A ssume all variables are nonzero.) - (4x−10)10(4x−10)5\frac{(4 x-10)^{10}}{(4 x-10)^{5}}(4x−10)5(4x−10)10​

Factor the GCF out of the given expression. - 5x+155 x+155x+15

−10xy7(5xy7+2y3+5)-10 x y^{7}\left(5 x y^{7}+2 y^{3}+5\right)−10xy7(5xy7+2y3+5)

If a projectile is launched upward from the ground with an initial velocity of 64.5 feet per second, its height hhh in feet ttt seconds later is given by the function h(t)=−16t2+64.5th(t)=-16 t^{2}+64.5 th(t)=−16t2+64.5t . After how many seconds does the projectile land on the ground?

Factor completely. If the polynomial cannot be factored, write "prime." - 9x2+24x+169 x^{2}+24 x+169x2+24x+16

Perform the indicated calculation. Express your answer using scientific notation. - (3×109)(8×109)\left(3 \times 10^{9}\right)\left(8 \times 10^{9}\right)(3×109)(8×109)

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) -2- 4

Evaluate the polynomial or polynomial function for the given value of the variable. - −3x2−2x−10-3 x^{2}-2 x-10−3x2−2x−10 for x=−2x=-2x=−2

Factor completely. If the polynomial cannot be factored, write "prime." - −24x2+20x−4-24 x^{2}+20 x-4−24x2+20x−4

Factor the GCF out of the given expression. - 9x(x−4)−(x−4)9 x(x-4)-(x-4)9x(x−4)−(x−4)

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - (n9)−2\left(n^{9}\right)^{-2}(n9)−2

Choose the one alternative that best completes the statement or answers thequestion. - m17⋅m21m^{17} \cdot m^{21}m17⋅m21

−9x3y4(3x9y8−10y6+2x)-9 x^{3} y^{4}\left(3 x^{9} y^{8}-10 y^{6}+2 x\right)−9x3y4(3x9y8−10y6+2x)

Find the GCF. -34, 85

Factor completely. If the polynomial cannot be factored, write "prime." - 24x2+18x−20x−1524 x^{2}+18 x-20 x-1524x2+18x−20x−15

−7x2⋅2x5-7 x^{2} \cdot 2 x^{5}−7x2⋅2x5

Find the GCF. -50, 60

Choose the one alternative that best completes the statement or answers thequestion. - (x3)4(x3)5\left(x^{3}\right)^{4}\left(x^{3}\right)^{5}(x3)4(x3)5

Factor completely. If the polynomial cannot be factored, write "prime." - w4−s4w^{4}-s^{4}w4−s4

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

For the given quadratic equation, one of its solutions has been provided. Use it to find the other solution. - $15 x^{2}+29 x+12=0, x=-\frac{4}{3}$

Simplify. (A ssume all variables are nonzero.) - $\frac{(4 x-10)^{10}}{(4 x-10)^{5}}$

Factor the GCF out of the given expression. - $5 x+15$

$-10 x y^{7}\left(5 x y^{7}+2 y^{3}+5\right)$

If a projectile is launched upward from the ground with an initial velocity of 64.5 feet per second, its height $h$ in feet $t$ seconds later is given by the function $h(t)=-16 t^{2}+64.5 t$ . After how many seconds does the projectile land on the ground?

Factor completely. If the polynomial cannot be factored, write "prime." - $9 x^{2}+24 x+16$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(3 \times 10^{9}\right)\left(8 \times 10^{9}\right)$

Evaluate the polynomial or polynomial function for the given value of the variable. - $-3 x^{2}-2 x-10$ for $x=-2$

Factor completely. If the polynomial cannot be factored, write "prime." - $-24 x^{2}+20 x-4$

Factor the GCF out of the given expression. - $9 x(x-4)-(x-4)$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(n^{9}\right)^{-2}$

Choose the one alternative that best completes the statement or answers thequestion. - $m^{17} \cdot m^{21}$

$-9 x^{3} y^{4}\left(3 x^{9} y^{8}-10 y^{6}+2 x\right)$

Factor completely. If the polynomial cannot be factored, write "prime." - $24 x^{2}+18 x-20 x-15$

$-7 x^{2} \cdot 2 x^{5}$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(x^{3}\right)^{4}\left(x^{3}\right)^{5}$

Factor completely. If the polynomial cannot be factored, write "prime." - $w^{4}-s^{4}$