Question

what must be subtracted from x cube minus x square minus 15 X + 84 that the result is exactly divisible by X square + X - 12​

Answer 1

Answer:

Let ax + b be subtracted from p(x)=x

3

−6x

2

−15x+80

so that it is exactly divisible by x

2

+x−12.

∴s(x)=x

3

−6x

2

−15x+80−(ax+b)

=x

3

−6x

2

−(15+a)x+(80−b)

Dividend = Divisor × quotient + remainder

But remainder will be zero.

∴ Dividend = Divisor × quotient

⇒s(x)=(x

2

+x−12)×quotient

⇒s(x)=x

3

−6x

2

−(15+a)x+(80−b)

Hence, x(4−a)+(−4−b)=0,x



=0

⇒4−a=0 & (−4−b)=0

⇒a=4 and b=−4

Hence, if in p(x) we subtract 4x - 4 then it is exactly divisible by x

2

+x−12