Answer:
Let ax + b be subtracted from p(x)=x
3
−6x
2
−15x+80
so that it is exactly divisible by x
+x−12.
∴s(x)=x
−15x+80−(ax+b)
=x
−(15+a)x+(80−b)
Dividend = Divisor × quotient + remainder
But remainder will be zero.
∴ Dividend = Divisor × quotient
⇒s(x)=(x
+x−12)×quotient
⇒s(x)=x
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
+x−12
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Answers & Comments
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