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)

 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)

    D

10) x² - 25

    a = √x² = x        

    b = √25 = 5

    Factors: (x - 5)(x + 5)

    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)

    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

    D

the correct answer is b) histograms can be used to exhibit the shape of distributions. this is because histograms count the frequency of each possible answer, so one is able to see which results are more common and which are less common.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80