Question

which is $x^2 - 36$ factored?

a $(x + 6)(x - 6)$

b this is not factorable.

c $(x + 9)(x - 4)$

d $(x - 6)(x - 6)$

e $(x - 6)(x + 7)$

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

Substitute \(a = x\) and \(b = 6\) into the difference of squares formula: \(x^2 - 6^2=(x + 6)(x - 6)\).

Step3: Check Other Options

• Option B: Incorrect, as we just factored it.
• Option C: \((x + 9)(x - 4)=x^2 + 5x - 36

eq x^2 - 36\).

• Option D: \((x - 6)(x - 6)=x^2 - 12x + 36

eq x^2 - 36\).

• Option E: \((x - 6)(x + 7)=x^2 + x - 42

eq x^2 - 36\).

Answer:

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