Factoring Trinomials Review

Factor:
x² + 7x - 30

• (x + 10)(x - 7)

• (x - 10)(x + 3)

• (x + 10)(x + 3)

• (x + 10)(x - 3)

Answer explanation

To factor x² + 7x - 30, we look for two numbers that multiply to -30 and add to 7. The correct pair is 10 and -3. Thus, the factors are (x + 10)(x - 3).

Factor
x² + 9x - 36

• (x + 12)(x - 3)

• (x + 9)(x - 4)

• (x - 12)(x + 3)

• (x - 9)(x - 4)

Answer explanation

To factor x² + 9x - 36, we look for two numbers that multiply to -36 and add to 9. The numbers 12 and -3 fit this, leading to the factors (x + 12)(x - 3). Thus, the correct answer is (x + 12)(x - 3).

Factor
n² + 5n - 6

• (n - 2)(n - 3)

• (n - 1)(n + 6)

• (n + 1)(n - 6)

• (n + 2)(n - 3)

Answer explanation

To factor n² + 5n - 6, we look for two numbers that multiply to -6 and add to 5. The correct pair is -1 and 6. Thus, the expression factors to (n - 1)(n + 6), which is the correct answer.

What is the GCF of the trinomial?
3x² - 9x -120

• 3

• 2

• 6

• 9

Answer explanation

To find the GCF of the trinomial 3x² - 9x - 120, we look for the largest number that divides all coefficients. The GCF of 3, -9, and -120 is 3, making it the correct choice.

What is the GCF?

5x² + 20x

• 5

• x

• 5x

• 20x

Answer explanation

The GCF of 5x^2 and 20x is found by identifying the highest common factors. Both terms share a factor of 5 and x, making 5x the greatest common factor.

What is the GCF?

16x⁵ + 12x⁴ - x³

• x⁵

• 12x

• 6x³

• x³

Answer explanation

To find the GCF of 16x^5, 12x^4, and -x^3, we take the lowest power of x, which is x^3. The coefficients 16, 12, and -1 have a GCF of 1. Thus, the GCF is x^3.

Factor
9x²-6x-8

• (3x+2)(3x-4)

• (3x+2)(3x+4)

• (3x-2)(3x-4)

• (x-1)(9x+8)

Answer explanation

To factor 9x² - 6x - 8, we look for two numbers that multiply to -72 (9*-8) and add to -6. The numbers -12 and 6 work. Thus, we can rewrite and factor as (3x+2)(3x-4), which is the correct choice.

Factor
4n²-17n-15

• (n-10)(6n+1)

• (4n-5)(n-3)

• (n-5)(4n-3)

• (n-5)(4n+3)

Answer explanation

To factor 4n² - 17n - 15, we look for two numbers that multiply to -60 (4*-15) and add to -17. The numbers -20 and 3 work. Thus, we can factor it as (n-5)(4n+3), which is the correct choice.

Factor
2x² - 13x - 70

• (2x-7)(x+10)

• (7x+5)(x+2)

• (2x+7)(x-10)

• 2(x+7)(x+10)

Answer explanation

To factor 2x² - 13x - 70, we look for two numbers that multiply to -140 (2 * -70) and add to -13. The correct factors are (2x + 7)(x - 10), which can be verified by expanding.

x² - 25

• ( x + 5 ) ( x - 5 ) 

• ( x - 5 ) ( x - 5 ) 

• ( x + 5 ) ( x + 5 ) 

• Prime

Answer explanation

The expression x² - 25 is a difference of squares, which factors as (x + 5)(x - 5). This is the correct choice, as it represents the two binomials that multiply to give the original expression.

Tags

CCSS.HSA.APR.C.4