Question

If the polynomial f(x)=2x³-ax²+4x-1, leaves remainder -37 when divided by x+2, then the value of a is ​

Answer 1

Answer:

        a = 3

Step-by-step explanation:

By the Remainder Theorem, the remainder when f(x) is divided by x+2 is f(-2).

Thus...

    Dividing f(x) by x+2 leaves a remainder of -37

⇒  f(-2)  =  -37

⇒  2×(-2)³ - a×(-2)² + 4×(-2) - 1  =  -37

⇒  -16 - 4a - 8 - 1  =  -37

⇒  4a  =  37 - 16 - 8 - 1

⇒  4a  =  12

⇒  a = 3