Question

If the polynomial 6^4−9^3−2^2+ax−b is exactly divisible by the polynomial 3x^2−4, then find the values of a and b.

Answer 1

Step-by-step explanation:

Given polynomial

p(x)=6x

4

+8x

3

−5x

2

+ax+b

And g(x)=2x

2

−5

So,

On divide p(x) to g(x) and we get,

Quotient =3x

2

+4x+5

Reminder=(20+a)x+(25+b)

Given that,

The polynomial 6x

4

+8x

3

−5x

2

+ax+b is exactly divisible by the polynomial 2x

2

−5.

Hence,

(20+a)x+(25+b)=0

⇒20+a=0

⇒a=−20

And 25+b=0

b=−25