Question

The HCF of $3(x^2-9)(x+4)and12(x-3{)}^2$ is:

• A. $3(x-3)$
• B. $3(x-3)(x+4)$
• C. $3(x-3{)}^2$
• D. $3(x-3)$

Answer 1

The correct option is A $3(x-3)$

$3(x^2-9)(x+4)=3\times (x+3)\times (x-3)\times (x+4)$.
$12(x-3{)}^2=2^2\times 3\times (x-3{)}^2$.
Hence, the common irreducible factors between $3(x^2-9)(x+4)and12(x-3{)}^2$ are 3 and (x-3).
The least exponents of these factors are respectively 1 and 1.
Hence, the HCF = $3^1\times (x-3{)}^1=3(x-3)$.