Question

LOOK AT THE ATTACHMENT ABOVE AND ANSWER!! Plz

Answer 1

f(x) = x^3 + ax^2 -21x +b
It is divisible by (x+6)
f(-6) = -216 + 36a +126 +b
According to the question,
36a + b + 90 = 0......(1)
Now,
When f(x) is divided by x-2 it leaves remainder -8
f(2) = -8
4a +b -42 +b = -8
4a +b = 26.......(2)
From (1) and (2)
a = 2
b = 18
So,
f(x) = x^3 +2x^2 -21x +18
Now, when f(x) is divided by x+6 by division method, we get x^2-4x+3 as quotient
factorising our quotient,
x^2-4x+3
= x^-x-3x+3
= (x-1)(x-3)