Question

What must be subtracted on added to p(x)=8x4+14x3-2x2+8x-12 and 4x2+3x-2 is the factor of p(x)

Answer 1

Answer:

Step-by-step explanation:

If you subtract r(x) from p(x) — that is, add -r(x) to p(x) — and divide the result p’(x) = p(x) - r(x) by d(x), then the quotient will be q(x) and there will be no remainder.

In the given example, if you divide

p(x) = 8x^4 + 14x^3 + 2x^2 + 8x - 12 by

d(x) = 4x^2 + 3x - 2,

you get q(x) = 2x^2 + 2x and r(x) = 12x - 12.

Then p’(x) = p(x) - r(x) = 8x^4 + 14x^3 + 2x^2 - 4x.

When you divide p’(x) by d(x) you get a quotient of 2x^2 + 2x and no remainder, so that d(x) is a factor of p’(x).

Answer 2

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