Question

Use the remainder theorem to find the value of F(x). Find F(-3). F(X)=2x^2 - 5x-8

Answer 1

well, the remainder theorem states that for an expression of  x + a dividing a polynomial say f(x), will gives some remainder, well that remainder is exactly the same value as if we simply just take f(-a).

so, let's take a peek, we're given f(-3), that means that x = -3,  which we can write as x + 3 = 0.

that means that if we divide f(x) by x + 3, we'll get the same value as if we simply solve for f(-3), let's check, let's divide 2x² - 5x - 8 by x + 3, using synthetic division.

$\bf x + 3 = 0\implies x = \boxed{-3}~~\leftarrow \textit{our divisor for the synthetic division} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{r|rrrr} -3&2&-5&-8\\ &&-6&33&\\\cline{1-5} &2&-11&\underline{25}&\leftarrow remainder \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2x^2-5x-8\implies f(-3)=2(-3)^2-5(-3)-8\implies f(-3)=\underline{25}$