Question

on dividing the polynomial 9x⁴-4x² + 5 by another polynomial 3x²+x-1 square + X - 1, the remainder comes out to be ax-b. find a and b​

Answer 1

Answer:

The remainder is -x+5.

So a = -1 and b = -5.

Hope this helps.

Step-by-step explanation:

9x⁴-4x² + 5 = (3x²+x-1) (cx²+dx+e) + ax - b

Coefficients of x⁴: 9 = 3c  =>  c = 3

Coefficients of x³:  0 = 3d + c  =>  d = -c/3 = -1

Coefficients of x²:  -4 = 3e + d - c  =>  3e = c-d-4 = 3+1-4 = 0  =>  e = 0

Coefficients of x:  0 = -d + e + a  =>  a = d - e = -1

Coefficients of 1:   5 = -e - b  =>  b = -e - 5 = -5