Question

Let f(x) be ax2 + bx – 6 and g(x) be bx2 + ax. If (x – 2) divides f (x) completely but leaves remainder –12 when it divides g(x), then f(x) + g(x) + 2x2 is _____



answer for 65 pts.

Answer 1

Step-by-step explanation:

f(x)=ax2+bx+2 and 

g(x)=bx2+ax+1

x−2 is a factor of f(x)

∴ By factor theorem,

f(2)=0

⇒a(2)2+b(2)+2=0

⇒4a+2b+2=0

By dividing both sides by 2,

⇒2a+b+1=0…(i)

Also given that, g(x) divide dby (x−2), leaves remainder −15

∴ By remainder theorem,

g(2)=−15

⇒b(2)2+2a+1=−15

⇒4b+2a+1+15=0

⇒4b+2a+16=0...(ii)

Now, subtracting equation (i) from equation (ii), we get

(4b+2a+16)–(2a+b+1)=0–0

⇒4b+2a+16−2a−b−1=0

⇒3b+15=0

⇒3b=−15

⇒b=−315=−5

Substituting this value in equation 

Answer 2

Step-by-step explanation:

the answer According to the question must be (x^2-x-6)

I have also given the factors along with it.

hope it helped.

pls mark it as the brainliest answer

thanks