Factor problems 9 - 12 by using the difference of squares method.

9. x^2 – 4

AThis polynomial cannot be factored by using the difference of squares method.
B(x – 2)(x – 2)
C(x – 2)(x – 1)
D(x – 2)(x + 2)
E (x – 1)(x – 4)
F (x + 2)(x + 2)

10. x^2 – 25

A(-x – 5)(x - 5)
BThis polynomial cannot be factored by using the difference of squares method.
C(-x + 5)(x + 5)
D(x – 5)(x + 5)
E (x + 5)(-x - 5)
F (x – 5)(x - 5)

11. 36x^4 – 4x^2

A(6x^2 – 2x)(6x^2 - 2x) = 4x^2(3x - 1)(3x - 1)

B(6x^2 + 2x)(6x^2 + 2x) = 2x^2(3x + 1)(2x + 1)

CThis polynomial cannot be factored by using the difference of squares method.

D(-6x^2 – 2x)(-6x^2 - 2x) = 4x^2(-3x - 1)(-3x - 1)

E (6x^2 – 2x)(6x^2 + 2x) = 4x^2(3x - 1)(3x + 1)

F (-6x^2 + 2x)(6x^2 - 2x) = 2x^2(-3x + 1)(3x - 1)

12. x^2 + 100

A(x + 10)(x – 10)
B(-x + 10)(x – 10)
C(x + 10)(x + 10)
DThis polynomial cannot be factored by using the difference of squares method.
E (x - 10)(x – 10)
F (-x + 10)(-x – 10)

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tramserran tramserran · Answer 1 · 2020-03-21T17:57:18+01:00

Answer: 9) D 10) E 11) E 12) D

Step-by-step explanation:

Notes: The difference of squares is a² - b² = (a - b)(a + b)

To solve, take the square root of the first term and the square root of the last term. The factors are the sum and difference of those values.

9) x² - 4

a = √x² = x

b = √4 = 2

Factors: (x - 2)(x + 2)

Answer: D

10) x² - 25

a = √x² = x

b = √25 = 5

Factors: (x - 5)(x + 5)

Answer: E

11) 36x⁴ - 4x²

Factor out the common term (4x²) --> 4x²(9x² - 1)

a = √9x² = 3x

b = √1 = 1

Factors: 4x²(3x - 1)(3x + 1)

Answer: E

12) x² + 100

The plus (+) sign means this is not in the form of a² - b²

so it cannot be factored over the Real #s using this method

Answer: D