Question

what must be subtracted from the polynomial 4x^4 + 2x^3-8x^2 +3x -7 so that the resulting polynomial is exactly divided by 2x^2 +x-2.

my answer was comming (x-5)
but when I checked the answer at the end it was written 5x-11. so someone please help me to solve it.​

Answer 1

Given:-

P(x)=0

→4x⁴+2x³-8x²+3x-7

q(x)=2x²+x-2

$\rule{200}{1}$

To Find:-

The Remainder =r(x)?

$\rule{200}{3}$

Answer:-

•Formula to be used↓•

→p(x)=q(x)×g(x)+r(x)

→$\frac{p(x)}{q(x)}$=g(x)+r(x)

•Putting the Values•

→$\frac{4x^{4}+2x^{3}-8x^{2}+3x-7}{2x^{2}+x-2}$ =g(x)+r(x)

→$\frac{\cancel{4x^{4}+2x^{3}-8x^{2}+3x-7}}{\cancel{2x^{2}+x-2}}$=2x²-2+5x+11

→g(x)=2x²-2

→r(x)=5x+11

★Check Attachment for Division★

♦Hence 5x+11 is to b subtracted by p(x),so that p(x) is completely divisible by q(x).

$\rule{200}{8}$

Answer 2

Step-by-step explanation:

The given answer is correct.