Question

what must be subtracted or added to p(x) = 8x4+14x3-2x2+8x-12 so that4x2+3x-2 is the factor of p(x)

Answer 1

Therefore 15x-4 is to be added

Answer 2

Answer:

15x-14

Step-by-step explanation:

$Dividend = 8x^4+14x^3-2x^2+8x-12$

$Divisor=4x^2+3x-2$

Since we know that :

$Dividend = (Divisor \times Quotient)+Remainder$

So, $8x^4+14x^3-2x^2+8x-12 = (4x^2+3x-2 \times 2x^2)+(8x^3+2x^2+8x-12)$

$8x^4+14x^3-2x^2+8x-12 = (4x^2+3x-2 \times 2x^2+2x)+(-4x^2+12x-12)$

$8x^4+14x^3-2x^2+8x-12 = (4x^2+3x-2 \times 2x^2+2x-1)+(15x-14)$

So, Remainder is 15x-14

So, 15x-14 should be subtracted form $8x^4+14x^3-2x^2+8x-12$ so that $4x^2+3x-2$ is the factor of p(x).