Question

If the polynomial x4 + 2x3 + 8x2 + 12x+18 is divided by another polynomial x2 + 5,the remainder comes out to be p x + q ,find the value of p and q.

Answer 1

So, remainder is 2x+3
So, by comparing with px+q
we got p=2 and q=3.

Answer 2

Answer:

p(x)=q x g(x) + r         [p(x) =polynomial, q= quotient, r= remainder]

Step-by-step explanation:

by formula:-

x4+2x³+8x²+12x+18= (x²+5)q + r

x4+2x³+8x²+12x+18 divided by x²+5 =q+r

Now divide:-

                  x²+2x+3

x²+5         )x4+2x³+8x²+12x+18

                -x4        -5x²

                   2x³ +3x² +12x +18

                  -2x³          -10x

                         3x² +2x +18

                         -3x²        -15

                                 2x +3

So after dividing we get 2x+3

Hence, px+q = 2x+3

So p=2 and q=3