Verify the division algorithm for the polynomials
$p (x) = 2 x^{4} - 6 x^{3} + 2 x^{2} - x + 2$ and $g (x) = x + 2$ .

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Solution

$Q u o t i e n t = 2 x^{3} - 10 x^{2} + 22 x - 45 V e r i f i c a t i o n D i v i s o r \times Q u o t i e n t + R e m a i n d e r = (x + 2) \times (2 x^{3} - 10 x^{2} + 22 x - 45) + 92 = 2 x^{4} - 10 x^{3} + 22 x^{2} - 45 x + 4 x^{3} - 20 x^{2} + 44 x - 90 + 92 = 2 x^{4} - 6 x^{3} + 2 x^{2} - x + 2 = D i v i d e n t H e n c e p r o v e d$

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p (x)

g (x)

p (x) = 2 x^{2} - 9 x + 9; g (x) = x - 3

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

f(x) = $2 x^{4} - 6 x^{3} + 2 x^{2} - x + 2$ , g(x) = x + 2

P(x) =2x⁴-6x³+2x²-x+2

G(x)=x+2

Find remainder by long division.

f (x) = 2 x^{4} - 6 x^{3} + 2 x^{2} - x + 2

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