Question

let A and B the remainder when the polynomials y³ + 2y² - 5ay - 7 and y³ + ay² - 12y + 6 divided by y + 1 and y - 2 if 2 A + B = 6 find a​

Answer 1

y ^3 +2y^2 −5ay−7 leaves a remainder A, when divided by y+1.

So, plugging in y=−1 in the above polynomial, we can find remainder A.

A=−1+2+5a−7=5a−6

y^3+2y^2−5ay−7 leaves a remainder B, when divided by y−2.

So, plugging in y=2 in the above polynomial, we can find remainder A.

B=8+4a−24+6=4a−10

Given, 2A+B=6

10a−12+4a−10=6

14a−22=6

14a=28

a=2