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# 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. - Mathematics

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#### Question

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.

#### 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?

#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 8: Remainder and Factor Theorems
Exercise 8(A) | Q: 11 | Page no. 109

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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.
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