#### Question

If x^{3} + ax^{2} + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.

#### Solution

Leftf(x)=`x^3+ax^2+bx+6`

`x-2=0`⇒ x=2

Since, x-2 is a factor, remainder=0

∴ f(2)=0

`(2)3+a(2)^2+b(2)+6=0`

`8+4a+2b+6=0`

`2a+b+7=0` .........(1)

On dividing f(x)by x-3, it leavvves a remainder 3.

∴ f(3)=3

`(3)^3+a(3)^2+b(3)+6=3`

`27+9a+3b+6=3`

`3a+b+10` ...........(2)

Subtracting (1) from (2), we get,

a+3=0

a=-3

Substituting the value of a in (1), we get,

-6+b+7=0

b=-1

Is there an error in this question or solution?

Solution If X3 + Ax2 + Bx + 6 Has X – 2 as a Factor and Leaves a Remainder 3 When Divided by X – 3, Find the Values of a and B. Concept: Remainder Theorem.