Question

Given that (x-2) and (x+1) are factors of x^3 + 3x^2 + ax + b, calculate the values of a and b and hence find the remaining factor

Answer 1

x³+3x²+ax+b
substitute x=2 and x=-1
Because, x-2=0. , x+1=0
x=2. , x=-1
2³+3(2)²+a(2)+b=0
8+3(4)+2a+b=0
8+12+2a+b=0
2a+b=-20–––––(1)

Now,x=-1
(-1)³+3(-1)²+a(-1)+b=0
-1+3(1)-a+b=0
-1+3-a+b=0
-a+b=-2––––––(2)
comparing equations (1) and (2),we get
2a+b=-20
-a+b=-2
(+) (-). (+)
———————
3a-0=-18
a=-18/3
a=-6
substitute a value in any equation to get b value
-a+b=-2
-(-6)+b=-2
6+b=-2
b=-2-6=-8
1 3 -6 -8
x=2. 0 2 10 8
——————————————————
1 5 4 0
x=-1 0 -1 -4
—————————————————
1. 4. 0
x=-4. 0 -4
—————————————————
1 0
Therefore, (x+4) is the remaining factor

(x+4) is the remaining factor
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