Question

The expression $2x^3+a{x}^2+bx+3$, where a and b are constants, has a factor of x-1 and leaves a remainder of 15 when divided by x+2. Find the value of a and b respectively.

• A. $-3,8$
• B. $3,-8$
• C. $-3,-8$
• D. $3,8$

Answer 1

The correct option is B $3,-8$

f(x)=$2x^3+a{x}^2-bx+3$
At x=2
f(2)=15
f(1)=0
f(x)=$2x^3+a{x}^2-bx+3$
f(1)= 2+a-b+3=0
a-b+5=0......A
f(x)= $2x^3+a{x}^2-bx+3$
f(2)=$2\left(2^3\right)+a\left(2^2\right)-2b+3=15$
4a-2b=-4
Multiply A by 2 and subtract from above equation
4a-2b=-4
2a-2b+10=0
2a-10=-4
2a= 6
a=3
From A
3-b+5=0
8-b=0
b=8
So a=3 and b=8