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Factor Theorem

Find the valu...

Question

Find the value of $a$ and $b$ so that $x^{4} + x^{3} + 8 x^{2} + a x + b$ is divisible by $x^{2} + 1$ .

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Solution

$x^{4} + x^{3} + 8 x^{2} + a x + b$ is exactly divisible by $x^{2} + 1$
$(a - 1) x + (b - 7) = 0$
If $a = 1, b = 7$ then the remainder will be $0$
Hence $a = 1, b = 7$

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