Question

1. find the factors of $x^2 - 36$

a. $(x - 2)(x + 12)$
b. $(x - 3)(x + 6)$
c. $(x + 6)(x - 6)$
d. $(x + 36)(x - 36)$

Explanation:

Step1: Recall Difference of Squares

The expression \(x^2 - 36\) is a difference of squares, which follows the formula \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = x\) and \(b = 6\) (since \(6^2 = 36\)).

Step2: Apply the Formula

Substituting \(a = x\) and \(b = 6\) into the difference of squares formula, we get \(x^2 - 36=(x + 6)(x - 6)\). We can also check the other options by expanding them:

• Option A: \((x - 2)(x + 12)=x^2+12x - 2x - 24=x^2 + 10x - 24

eq x^2 - 36\)

• Option B: \((x - 3)(x + 6)=x^2+6x - 3x - 18=x^2 + 3x - 18

eq x^2 - 36\)

• Option D: \((x + 36)(x - 36)=x^2-36x + 36x - 1296=x^2 - 1296

eq x^2 - 36\)

Answer:

C. \((x + 6)(x - 6)\)