Question

What must be subtracted from $x^2-7x+19$ so that $x-3$ is a factor.

• A. 7
• B. -7
• C. 8
• D. -8

Answer 1

The correct option is A 7

Let $f\left(x\right)$= $x^2-7x+19$

By Remainder theorem, if $f\left(x\right)$ is divided by $x-3$, the remainder is equal to $f\left(3\right)$.

Plugging $x=3$ in $f\left(x\right)$, we get:
$f\left(3\right)=(3{)}^2-7(3)+19$
$f\left(3\right)=7$

So, 7 must be subtracted from $x^2-7x+19$ to make $f\left(3\right)$ zero, so that $x-3$ is a factor.