Question

what will be the remainder if a polynomial f(x) is divided by (ax+b).​

Answer 1

Answer:

the ans is

A more general theorem is: If f(x) is divided by ax + b (where a & b are constants and a is non-zero), the remainder is f(-b/a).

Answer 2

What will be the remainder if a polynomial f(x) is divided by (ax+b).​

Given:$(ax+b)$

• The remainder of the polynomial can be found by using remainder theorem.
• First equating $ax+b$ to zero we get the value of $x$,

Calculation:

$ax+b = 0\\ax = -b\\x = -b/a$

• According to the remainder theorem,

Remainder is $f(-b/a)$ when divided by $ax+b$.

Polynomial remainder theorem

• In algebra, the polynomial remainder theorem or little Bezout's theorem is an application of Euclidean division of polynomials.
• It states that the remainder of the division of a polynomial $f(x)$ by a linear polynomial {\displaystyle ${\displaystyle x-r}$} is equal to {\displaystyle $f(r)$}.