How do you use the remainder theorem to see if the $p - 2$ $p-2$ is a factor of $p^{4} - 8 p^{3} + 10 p^{2} + 2 p + 4$ $p^4-8p^3+10p^2+2p+4$ ?

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Answer 1 · 2016-09-28T17:42:06

The remainder = 0, which means that $(p - 2)$ $(p-2)$ is a factor of the expression.

Let $f (p) = p^{4} - 8 p^{3} + 10 p^{2} + 2 p + 4$ $f(p) = p^4-8p^3+10p^2+2p+4$

If $p - 2 = 0 \to p = 2$ $p-2 = 0 " "rarr p = 2$

Find $f (2)$ $f(2)$ which will give the remainder.

$f (2) = 2^{4} - 8 {(2)}^{3} + 10 {(2)}^{2} + 2 (2) + 4$ $f(2) = 2^4-8(2)^3+10(2)^2+2(2)+4$

$f (2) = 16 - 64 + 40 + 4 + 4 = 0$ $f(2) = 16-64+40+4+4 =0$

The remainder = 0, which means that $(p - 2)$ $(p-2)$ is a factor of the expression.

How do you use the remainder theorem to see if the p−2p-2 is a factor of p4−8p3+10p2+2p+4p^4-8p^3+10p^2+2p+4?