Question

Use the remainder theorem to find the remainder, when

(2x – 1)
³+ 6(3 + 4x)
²

is divided by 2x + 1

​

Answer 1

We know that the remainder theorem states that if a polynomial f(x) is divided by (x−a), the remainder is f(a).

Here, we have the polynomial f(x)=3x

3

+7x

2

−5x+1 which is divided by (x+3), therefore, by remainder theorem, the remainder is:

R=f(−3)=3(−3)

3

+7(−3)

2

−5(−3)+1=(3×−27)+(7×9)+15+1=−81+63+15+1=79−51=3