Question

For the polynomial P(x) = 4x + 7x + 8 and c = 1, find P(c) by (a) direct substitution and (b) the remainder theorem

Answer 1

SOLUTIONS

For the polynomial P(x) = 4x^2 + 7x + 8 and c = 1

`P(x)=4x^2+7x+8`

where c = 1

(a) By direct substitution

`\begin{gathered} P(c)=P(1) \\ P(x)=4x^2+7x+8 \\ P(1)=4(1)^2+7(1)+8=4+7+8=19 \\ P(1)=19 \end{gathered}`

(b) The Remainder Theorem states that when we divide a polynomial

P(x) by x - c the remainder R equals P(c)

`4x^2+7x+8/ x-1`

From the remainder theorem , the remainder = 19