Question

How do you use the remainder theorem to find the remainder of `(x^3 - 5x^2 + 7x +3) ÷ (x-2)`?

Answer 1

Put 2 as the value of `x` in the dividend

Explanation:

The remainder theorem states that every polynomial,
For Ex - p( `x` )= `x^2 + x + 1`
if divided by a polynomial of the form - ( `x - a` )
will give remainder as p(`a`) = (In this case) `a^2 + a + 1`

Here:
p(`x`) = `(x^3 - 5x^2 + 7x + 3)`
g(`x`) = `(x-2)`

So,
p(`2`) = `(2^3 - 5*2^2 + 7*2 + 3)`
= `(8-20+24 + 3)`
= `15`
Remainder = 15