$$x = 1$$ \, \text{or} \, x = -5$

Question 1

Which of the following is the correct factorization of the quadratic expression $$3x^2 - 9x$?

Accepted Answer

$$3x(x - 3)$$

Question 2

Given the equation $$x^2 + 4x - 5 = 0$, which of the following shows the correct steps to factor and solve for x$?

Accepted Answer

Factor as $$(x + 5)(x - 1) = 0$$, so $$x = -5 or$$ $$x = 1$$

Question 3

A rectangular garden has an area of $$x^2 + 4x - 5$ square meters. Which set of possible dimensions (in meters) could the garden have?

Accepted Answer

$$(x + 5)$$ and $$(x - 1)$$

Question 4

Which of the following is the correct way to factor $$y^2 - 10y$?

Accepted Answer

$$y(y - 10)$$

Question 5

If $$x^2 + 4x - 5$ is rewritten by grouping, which is the correct grouping before factoring?

Accepted Answer

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

Question 6

Solve for $$x$$: $$x^2 - 16 = 0$

Accepted Answer

$$x = 4 or$$ $$x = -4$$

Question 7

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

Accepted Answer

$$(a + 5)(a - 5)$$

Question 8

A company’s profit, in dollars, is modeled by $$P(x) = x^2$ - 5x - 6. $$What is the break-even point(s) for the company?

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 9

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

Accepted Answer

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

Question 10

If $$x^2 + 4x - 5$ represents the area of a rectangle, and one side is x + 5$, what is the length of the other side?

Accepted Answer

$$x - 1$$

Question 11

Which of the following expressions is equivalent to $$x^2 - 10x + 25$?

Accepted Answer

$$(x - 5)^2$

Question 12

A chemical reaction requires the product of two consecutive integers to be 56. Which equation models this scenario?

Accepted Answer

$$x(x + 1) = 56$$

Question 13

Which of the following is the correct factorization of $$x^2 + 10x + 25$?

Accepted Answer

$$(x + 5)^2$

Question 14

If $$y^2 - 16 = 0$, what are the solutions for y$?

Accepted Answer

$$y = 4 or$$ $$y = -4$$

Question 15

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

Accepted Answer

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

Question 16

A rectangular field has a length of $$x + 4$$ meters and a width of $$x - 5$$ meters. What is the area of the field in terms of $$x$$?

Accepted Answer

$$x^2 - x - 20$

Question 17

Which of the following is the correct factorization of $$x^2 - 4x - 21$?

Accepted Answer

$$(x - 7)(x + 3)$$

Question 18

If $$x^2 + 4x - 5 = 0$ models the height (in meters) of a ball thrown upward after x$ seconds, when does the ball hit the ground?

Accepted Answer

$$x = 1$$ \, 	ext{or} \, x = -5$

Question 19

Which of the following is the correct factorization of $$x^2 + 6x + 9$?

Accepted Answer

$$(x + 3)^2$

Question 20

A rectangular parking lot has an area of $$x^2 - 10x$ square meters. If the width is x$ meters, what is the length?

Accepted Answer

$$x - 10$$

Factoring Polynomials and Quadratic Expressions

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