Question 1

Which of the following correctly applies the properties of exponents to simplify the expression $$ (2x^3$y^2)^2$ $$?

Accepted Answer

$$ 4x^6$y^4$$ $

Question 2

A biologist is modeling the population of bacteria in a lab using the polynomial $$ P(t) = 3t^2$ + 2t + 5 . If $$the population at time $$ t = 4 $$ hours is needed, what is $$ P(4) $$?

Accepted Answer

$$ 61 $$

Question 3

Which of the following is the result of subtracting $$ (4x^2$ - 3x + 7) $$ from $$ (6x^2$ + 2x - 5) $$?

Accepted Answer

$$ 2x^2$ + 5x - 12 $$

Question 4

A rectangular garden has a length of $$ (2x + 3) $$ meters and a width of $$ (x - 1) $$ meters. What is the area of the garden, expressed as a polynomial?

Accepted Answer

$$ 2x^2$ + x - 3 $$

Question 5

Which of the following is the correct factorization of $$ x^2$ - 9 $$?

Accepted Answer

$$ (x + 3)(x - 3) $$

Question 6

Solve the quadratic equation $$ x^2$ + 5x + 6 = 0  by $$factoring.

Accepted Answer

$$ x = -2, x = -3 $$

Question 7

Which of the following is the greatest common factor (GCF) of $$ 12x^3$y $$ and $$ 18x^2$y^2$$ $?

Accepted Answer

$$ 6x^2$y $$

Question 8

A company’s profit in thousands of dollars is modeled by $$ P(x) = -2x^2$ + 8x + 10 $$, where $$ x  is $$the number of units sold in hundreds. What is the profit when $$ x = 3 $$?

Accepted Answer

$$ 16 $$

Question 9

Which of the following is the result of multiplying $$ (x + 2) $$ and $$ (x - 5) $$?

Accepted Answer

$$ x^2$ - 3x - 10 $$

Question 10

Factor the polynomial $$ 6x^2$ + 11x + 3 $$ using the AC method.

Accepted Answer

$$ (2x + 3)(3x + 1) $$

Question 11

Which of the following is the result of adding $$ (3x^2$ + 2x - 5) $$ and $$ (x^2$ - 4x + 7) $$?

Accepted Answer

$$ 4x^2$ - 2x + 2 $$

Question 12

A projectile is launched and its height in meters after $$ t $$ seconds is given by $$ h(t) = -5t^2$ + 20t + 1 . $$After how many seconds does it reach its maximum height?

Accepted Answer

$$ 2 $$

Question 13

Which of the following is the correct factorization by grouping for $$ x^3$ + 3x^2$ + 2x + 6 $$?

Accepted Answer

$$ (x^2$ + 2)(x + 3) $$

Question 14

Which of the following is the simplified form of $$ (x^2$y^3)^2$ \cdot (xy)^3$ $$?

Accepted Answer

$$ x^7$y^9$$ $

Question 15

A quadratic equation $$ x^2$ - 8x + 16 = 0 $$ models the area of a square garden. What is the length of one side of the garden?

Accepted Answer

$$ 4 $$

Question 16

Which of the following is the correct factorization of $$ 4x^2$ - 25 $$?

Accepted Answer

$$ (2x + 5)(2x - 5) $$

Question 17

A chemist mixes two solutions. The volume of the first is $$ (3x^2$ + 2x)  mL $$and the second is $$ (x^2$ - x)  mL. $$What is the total volume?

Accepted Answer

$$ 4x^2$ + x $$

Question 18

Which of the following is the correct solution to the quadratic equation $$ 2x^2$ - 3x - 2 = 0 $$?

Accepted Answer

$$ x = 2, x = -0.5 $$

Question 19

Which of the following is the result of multiplying $$ (x - 4)  by$$ $$ (x^2$ + 2x + 1) $$?

Accepted Answer

$$ x^3$ - 2x^2$ - 7x - 4 $$

Question 20

A rectangular field has an area given by $$ 3x^2$ + 11x + 6 . $$Which of the following could represent its possible dimensions?

Accepted Answer

$$ (3x + 2) $$ and $$ (x + 3) $$

Exponents, Polynomials, and Polynomial Functions: Key Concepts and Techniques

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