Question

Match the polynomials with their respective factors.

• A. $x-1$
• B. $x-7$
• C. $x-5$
• D. $x-3$

Answer 1

According to the factor theorem, if $(x-a)$ is a factor of a polynomial f($x$), then f(a) = 0.

For $f\left(x\right)=x^2-3x+2$
$f\left(1\right)=1^2-3\times 1+2=0$.
Hence, $(x-1)$ is the factor of $x^2-3x+2.$

For $f\left(x\right)=x^2-7x+12$
$f\left(3\right)=3^2-7\times 3+12=0$.
Hence, $(x-3)$ is the factor of $x^2-7x+12.$

For $f\left(x\right)=x^2-11x+30$
$f\left(5\right)=5^2-11\times 5+30=0$.
Hence, $(x-5)$ is the factor of $x^2-11x+30.$

For $f\left(x\right)=x^2-15x+56$
$f\left(7\right)=7^2-15\times 7+56=0$.
Hence, $(x-7)$ is the factor of $x^2-15x+56.$