Given question:
If a polynomial leaves a remainder of $5$ when divided by $x − 3$ and a remainder of $−7$ when divided by $x + 1$,
what is the remainder when the polynomial is divided by $x^2 − 2x − 3$?
Solution:
We observe that when we divide by a second degree polynomial the remainder will generally be linear. Thus
the division statement becomes
$p(x) = (x^2 − 2x − 3)q(x) + ax + b $
Can someone please explain at a PRE-CALCULUS level? Thanks
Best Answer
Because by definition the quotient and the remainder of the division of a polynomial $p_1(x)$ by a polynomial $p_2(x)$ are polynomials $q(x)$ (the quotient) and $r(x)$ (the remainder) such that
In particular, if $p_2(x)$ is a quadratic polynomial, then the degree of $r(x)$ will be at most $1$.