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Question
If a polynomial p(x) = x2 – 5x – 14 is divided by another polynomial q(x) we get `(x - 7)/(x + 2)`, find q(x)
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Solution
p(x) = x2 – 5x – 14
= (x – 7) (x + 2)
By the given data
`("p"(x))/("q"(x)) = ((x - 7))/(x + 2)`
`((x - 7)(x + 2))/("q"(x)) = ((x - 7))/(x + 2)`
q(x) × (x – 7) = (x – 7) (x + 2) (x + 2)
q(x) = `((x - 7)(x + 2)(x + 2))/((x - 7))`
= (x + 2)2
q(x) = x2 + 4x + 4
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