Q: A projectile's height in meters is modeled by $$h(t) = t^2$ - 7t - 18. At $$what times does the projectile reach ground level?

$$t = 9$$ \, \text{seconds}$$ or t = -2$ \, \text{seconds}$$

Q: If $$x$$ represents the number of years since a medication was introduced, and its effectiveness is modeled by $$5x^2 = 25$, after how many years is the effectiveness at its maximum?

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

Question 1

Which of the following is the correct solution to the equation $$x^2 - 7x - 18 = 0$ by factoring?

Accepted Answer

$$x = 9 or$$ $$x = -2$$

Question 2

What are the roots of the equation $$4x^2 = 36x$ when solved by factoring?

Accepted Answer

$$x = 0 or$$ $$x = 9$$

Question 3

Solve $$5x^2 = 25$ by factoring. What are the solutions?

Accepted Answer

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

Question 4

A projectile's height in meters is modeled by $$h(t) = t^2$ - 7t - 18. At $$what times does the projectile reach ground level?

Accepted Answer

$$t = 9$$ \, 	ext{seconds}$$ or t = -2$ \, 	ext{seconds}$$

Question 5

If the area of a square is given by $$A = 5x^2$ and equals 25$, what are the possible values for x$?

Accepted Answer

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

Question 6

Which of the following represents the correct factorization of $$x^2 - 7x - 18$?

Accepted Answer

$$(x - 9)(x + 2)$$

Question 7

A company models its profit with $$P(x) = 4x^2$ - 36x. $$For what values of $$x is $$the profit zero?

Accepted Answer

$$x = 0 or$$ $$x = 9$$

Question 8

Which of the following is the correct factorization for $$4x^2 - 36x$?

Accepted Answer

$$4x(x - 9)$$

Question 9

If $$x$$ represents the number of years since a medication was introduced, and its effectiveness is modeled by $$5x^2 = 25$, after how many years is the effectiveness at its maximum?

Accepted Answer

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

Question 10

Which of the following is the correct factorization for $$5x^2 - 25$?

Accepted Answer

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

Question 11

A quadratic equation $$x^2 - 7x - 18 = 0$ models the population growth of a species. What are the possible population values (roots) after factoring?

Accepted Answer

$$x = 9 or$$ $$x = -2$$

Question 12

Which step is necessary to solve $$4x^2 = 36x$ by factoring?

Accepted Answer

Rewrite as $$4x^2 - 36x = 0$ and factor out 4x$

Question 13

If $$x is $$the length of a rectangle and $$5x^2 = 25$ represents its area, what are the possible values for x$?

Accepted Answer

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

Question 14

Which of the following is a correct method to solve $$x^2 - 7x - 18 = 0$?

Accepted Answer

Factor as $$(x - 9)(x + 2) = 0$$ and set each factor to zero

Question 15

A chemical reaction is modeled by $$4x^2 = 36x$. What are the possible concentrations (x$) at equilibrium?

Accepted Answer

$$x = 0 or$$ $$x = 9$$

Question 16

Which of the following is the correct solution to $$5x^2 = 25$?

Accepted Answer

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

Question 17

If $$x^2 - 7x - 18 = 0$ models the break-even point for a business, what are the possible values for x$?

Accepted Answer

$$x = 9 or$$ $$x = -2$$

Question 18

Which of the following is the correct factorization for $$4x^2 - 36x$?

Accepted Answer

$$4x(x - 9)$$

Question 19

A quadratic equation $$5x^2 = 25$ is used to model the spread of a virus. What are the possible values for x$?

Accepted Answer

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

College Algebra: Solving Quadratic Equations by Factoring

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