Question

What must be subtracted or added to p(x)=8x4+14x3−2x2+8x−12 so that 4x2+3x−2 is a factor of p(x). pls send fast and genuine questions. proper answers will be marked brainliest and improper will be reported..

Answer 1

Answer:

Hola‼..............✌

The general principle underlying the answer to this question is this:

If p(x) is a polynomial of degree n and d(x) is a polynomial of degree m, where m is less than or equal to n, you can divide d(x) into p(x) — similar to long division of numbers — and get a quotient polynomial q(x) of degree n-m and a remainder polynomial r(x) of degree less than m.

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 we divide

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

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

we get q( x) = 2x^2 +2x & r(x) = 12x -12

Then,p'(x) = p(x) -r(x) = 8 x^4 +14x^3 +2x^2 -4x

So, when you divide p' (x) by d(x) you get a quotient of 2x^2 & no reminder so that d(x) is the factor of p'(x).

Hope it's helpful....... ☺