Unit 8 Quiz 3 Review

Factor completely: (x² + 8x + 12)

• (x + 2)(x + 6)

• (x + 4)(x + 3)

• (x + 6)(x + 2)

• (x + 4)(x + 2)

Answer explanation

To factor completely, find two numbers that multiply to 12 and add to 8. The numbers are 4 and 3, so the correct factorization is (x + 4)(x + 3).

Factor completely: (x² + 5x - 36)

• (x + 9)(x - 4)

• (x - 9)(x + 4)

• (x + 6)(x - 6)

• (x + 12)(x - 3)

Answer explanation

To factor completely, find two numbers that multiply to -36 and add to 5. The numbers are 9 and -4, so the correct factorization is (x + 9)(x - 4).

Factor completely: (2x² + 26x + 44)

• 2(x² + 13x + 22)

• 2(x + 11)(x + 2)

• (x + 22)(2x + 2)

• Cannot be factored

Answer explanation

The correct factorization of (2x^2 + 26x + 44) is 2(x + 11)(x + 2), which is the second answer choice.

Factor completely: (x³ - 2x² - 15x)

• x(x - 5)(x + 3)

• x(x - 3)(x + 5)

• x(x² - 2x - 15)

• x(x² - 3x + 5)

Answer explanation

To factor completely, factor out the common factor x from each term, then factor the resulting quadratic expression. The correct factorization is x(x - 3)(x + 5).

Factor completely: (3x³- 9x² - 54x)

• 3x(x² - 3x - 18)

• 3x(x - 3)(x + 6)

• 3(x³ - 3x² - 18x)

• 3x(x - 6)(x + 3)

Answer explanation

To factor completely, first factor out the common factor 3x. Then factor the quadratic expression (x^2 - 3x - 18) to get 3x(x - 3)(x + 6), which is the correct choice.

Factor completely: (5x² + 10x)

• 5x(x + 2)

• 5(x² + 2x)

• 5x(x + 10)

• x(5x + 10)

Answer explanation

To factor completely, factor out the greatest common factor, which is 5x. This leaves (x^2 + 2x), so the correct choice is 5(x^2 + 2x).

How many solutions would you expect to have for the equation (2x² - 32x = 0)?

• 0

• 1

• 2

• Infinite

Answer explanation

The equation is a quadratic equation, so it would have 2 solutions according to the fundamental theorem of algebra.

Tags

CCSS.HSA-REI.B.4B

How many solutions would you expect to have for the equation (3x³ - 9x² - 54x = 0)?

• 1

• 2

• 3

• Infinite

Answer explanation

The given equation is a cubic equation, so it would be expected to have 3 solutions according to the fundamental theorem of algebra.

Tags

CCSS.HSA-REI.B.4B

How many solutions would you expect to have for the equation (x² - 10x - 24 = 0)?

• 0

• 1

• 2

• Infinite

Answer explanation

The given equation is a quadratic equation, and a quadratic equation can have 2 solutions, so the correct answer is 2.

Tags

CCSS.HSA-REI.B.4B

Factor (if necessary) and then solve using ZPP: (x(2x+1)(x - 4) = 0)

Answer explanation

To solve the equation, set each factor equal to zero: x = 0, 2x+1 = 0 (x = -1/2), x - 4 = 0 (x = 4). Therefore, the correct answers are x = 0, x = 1/2, x = 4.

Tags

CCSS.HSA-REI.B.4B