Question

Use the remainder theorem to find P(-2) for P(x)=x4+2x° -6x²+9.Specifically, give the quotient and the remainder for the associated division and the value of P(-2).OlaQuotient0Х?Remainder0P(-2) = 0

Answer 1

Given data:

$P(x)=x^4+2x^3-6x^2+9$

Now, by using remainder theorem we simply write out the coefficients in a line we get

$\begin{gathered} (-2)\text{ 1 2 -6 0 9} \\ \text{ -2 0 }12\text{ -24} \\ \text{ }1\text{ 0 -6 12 -15} \end{gathered}$

The remainder theorem says that the last term we get that is -15 is the remainder.

P(-2) = 16 - 16 - 24 + 9

= -15

Quotient is (x + 2)