Unit 4 (Part 1) Test Review #2

If the area of a rectangle is given by x² - 49y², then the product of the width and length can be expressed as:

(Hint: Use Difference of Squares)

• (x - 7y)(x - 7y)

• (x - 7y)(x + 7y)

• (x + 7y)(x + 7y)

• (x - 49y)(x - y)

Answer explanation

Remember that Difference of Squares has a Difference.

Factor 4x² - 9y².

(Hint: Use Difference of Squares)

• (2x - 3y)(2x + 3y)

• (4x - y)(x - 9y)

• (2x - 3y)(2x - 3y)

• (2x + 3y)(2x + 3y)

Answer explanation

Remember that Difference of Squares has a Difference.

Which equation has the same solutions as  5x² - 11x - 12 = 0?

(Hint: Use the box method or Desmos.)

• (5x - 4)(x + 3) = 0

• (5x + 3)(x - 4) =0

• (5x + 4)(x - 3) = 0

• (5x - 3)(x + 4) = 0

Answer explanation

Remember that the solutions have the opposite signs from the factored form.

Which of the following is a factor of x² - 9x + 20?

(Hint: Use the Box Method to factor.)

• (x + 4)

• (x - 5)

• (x + 10)

• (x - 2)

Answer explanation

This is another way to do the Box Method.

Which of the following is a factor of x² + 5x - 24?

(Hint: Use the Box Method to factor.)

• (x - 12)

• (x - 8)

• (x - 3)

• (x + 2)

Answer explanation

This is another way to do the Box Method.

Solve (x – 6)(x + 5) = 0.

(Hint: Remember to change the signs.)

• x = – 6 or x = – 5

• x = 6 or x = 5

• x = – 6 or x = 5

• x = 6 or x = – 5

Answer explanation

Remember that the solutions have the opposite signs from the factored form.

If 2x is a factor of 2x² - 12x, what is the other factor?

(Hint: Use GCF Factoring.)

• (x² - 6)

• (x + 6)

• (x - 6)

• (x² - 6x)

Answer explanation

2x is the GCF, so that goes on the outside of the expression. The remainder is the other factor.

If 6x² is a factor of 6x³ + 18x², what is the other factor?

(Hint: Use GCF Factoring.)

• (x² + 3)

• (x + 3)

• (x² + 3x)

• (x - 3x²)

Answer explanation

6x² is the GCF, so that goes on the outside of the expression. The remainder is the other factor.

Which three functions have zeros of x = 5 and x = -3?

(Hint: Remember to change the signs. Factor or use Desmos.)

• f(x) = (x - 5)(x + 3)

• f(x) = (x + 5)(x - 3)

• f(x) = x² + 2x - 15

• f(x) = x² - 2x - 15

• f(x) = (x - 1)² - 16

Answer explanation

Remember that the solutions have the opposite signs from the factored form.

What are the zeros of the function f(x) = 24x² - 37x - 5.

(Hint: Use the box method or Desmos.)

Answer explanation

Remember that the solutions have the opposite signs from the factored form. Another word for solutions, roots or x-intercepts is zeros.