Quadratic Factoring UNW Assessment - for Advanced Algebra

Factor the expression x²+x-6

• (x + 2)(x - 3)

• (x - 3)(x + 2)

• (x + 1)(x - 6)

• (x + 3)(x - 2)

Answer explanation

To factor x² + x - 6, we look for two numbers that multiply to -6 and add to 1. The numbers 3 and -2 fit this, so the expression factors to (x + 3)(x - 2). Thus, the correct answer is (x + 3)(x - 2).

Factor the expression x² - 5x + 6

• (x - 1)(x - 6)

• (x + 2)(x + 3)

• (x - 2)(x - 3)

• (x + 1)(x - 6)

Answer explanation

To factor x² - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 fit this, so the expression factors to (x - 2)(x - 3). Thus, the correct choice is (x - 2)(x - 3).

Factor the expression x² + 4x + 3

• (x + 2)(x + 2)

• (x - 1)(x - 3)

• (x - 2)(x + 3)

• (x + 1)(x + 3)

Answer explanation

To factor x² + 4x + 3, we look for two numbers that multiply to 3 and add to 4. The numbers 1 and 3 fit this, so the expression factors to (x + 1)(x + 3). Thus, the correct choice is (x + 1)(x + 3).

Factor the expression x² - x - 12

• (x - 4)(x + 3)

• (x + 4)(x - 3)

• (x - 6)(x + 2)

• (x + 6)(x - 2)

Answer explanation

To factor x²- x - 12, we look for two numbers that multiply to -12 and add to -1. The numbers -4 and 3 fit this, so we can write the expression as (x - 4)(x + 3). Thus, the correct choice is (x - 4)(x + 3).

Completely factor the expression 2x²+18x

• 2x(x - 9)

• x(2x + 18)

• 2(x² + 9x)

• 2x(x + 9)

Answer explanation

To factor 2x² + 18x, first factor out the greatest common factor, which is 2x. This gives us 2x(x + 9). The correct choice is 2x(x + 9).

Factor the expression x² + 7x + 10

• (x - 2)(x - 5)

• (x + 2)(x + 5)

• (x - 1)(x + 10)

• (x + 1)(x + 10)

Answer explanation

To factor x² + 7x + 10, we look for two numbers that multiply to 10 and add to 7. The numbers 2 and 5 fit this, so the expression factors to (x + 2)(x + 5).

Completely factor the expression 3x² - 12x

• x(3x - 12)

• 3x(x - 4)

• 3x(x + 4)

• 3(x² - 4x)

Answer explanation

To factor 3x² - 12x, first factor out the greatest common factor, which is 3x. This gives 3x(x - 4). The correct choice is 3x(x - 4), as it is fully factored.

Factor the expression x² - 16

• (x - 4)(x - 4)

• (x + 16)(x - 1)

• (x - 16)(x + 1)

• (x + 4)(x - 4)

Answer explanation

The expression x² - 16 is a difference of squares, which factors as (x + 4)(x - 4). This is because a² - b² = (a + b)(a - b) where a = x and b = 4.

Tags

CCSS.HSA.APR.C.4

Completely factor the expression 4x² - 20x

• 2x(2x + 10)

• x(4x - 20)

• 4(x² - 5x)

• 4x(x - 5)

Answer explanation

To factor 4x² - 20x, first factor out the greatest common factor, which is 4x. This gives us 4x(x - 5). The correct choice is 4x(x - 5), as it is fully factored.

Factor the expression x² + 6x + 8

• (x - 1)(x + 8)

• (x + 2)(x + 4)

• (x - 2)(x - 4)

• (x + 1)(x + 8)

Answer explanation

To factor x² + 6x + 8, we look for two numbers that multiply to 8 and add to 6. The numbers 2 and 4 fit this, so the expression factors to (x + 2)(x + 4). Thus, the correct choice is (x + 2)(x + 4).