Question

One of the factors of $4x^2-36$ is:

• A. x+3
• B. x-3
• C. x+5
• D. x - 15

Answer 1

Answer: (A), (B)

The correct options are
A

x+3

B

x-3

The expression $4x^2-36$ can be written as

$(2x{)}^2-(6{)}^2$.....(i)

Comparing (i) with the identity $a^2-b^2=(a+b)(a-b)$, we get

$a^2=(2x{)}^2\Rightarrow a=2x$

$b^2=6^2\Rightarrow b=6$

$4x^2-36$

$=(2x{)}^2-(6{)}^2$

$=(2x+6)(2x-6)$

$=2(x+3)2(x-3)$

$=4(x+3)(x-3)$.

Therefore, the factors of $(2x{)}^2-(6{)}^2$ are (2x+6) and (2x-6) or 4, (x + 3) and (x - 3).