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Factor Theorem

If the G.C.D ...

Question

If the G.C.D of the polynomials $x^{3} - 3 x^{2} + p x + 24$ and $x^{2} - 7 x + q$ is $(x - 2),$ find the value of $(p + q)$

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Solution

Remainder $= 24 - 2 p + 4 = 0$
$\Rightarrow - 2 p = - 28$
$\Rightarrow p = 14$
Again when $x^{2} - 7 x + q$ is divided by $x - 2$
the remainder $= q - 10 = 0$
$∴ q = 10$
Hence $p + q = 14 + 10 = 24$

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