Question

What must be added to x - 3x² - 12x + 19 so that the result is exactly divisibly by x² + x - 6 ?​

Answer 1

Let p(x) = x3 - 3x2 -12x +19 and q(x) = x2 + x -6.

By division algorithm, when p(x) is divided by q(x), the remainder is a linear expression in x

So, let r(x) = ax +b is added to p(x) so that p(x) + r(x) is divisible by q(x).

(more answer in the image)

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