Question

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Answer 1

Question :

Divide $x^{4} - 5x^{2} - 4x$ by $x+3$ . Find the remainder by Remainder Theorem. Verify by finding the remainder using synthetic division.

Solution :

By remainder theorem

Dividend polynomial $p(x)$ = $x^{4} - 5x^{2} - 4x$

Divisor = $x + 3$

$x = -3$

=> take $x = -3$

$p(-3) = -3^{4} - 5(-3)^{2} - 4(-3) \\ => 81 + 225 + 12 \\ => 318$

=> remainder = 318