Homework Help; Math-Polynomials

[acidvoodoo]

hey guys, i'm just doing work for my advanced high school math class.

i came across a question that asks

"The Cubic polynomial x^3 + ax^2 + bx -8 , where a and b are constants, has factors (x+1) and (x+2). Find the values of a and b."

i'm unsure what to do. i have the answers, a=-1 b=-10 from the book, but don't know where to start. i'm thinking there must be a missing factor? I tried combining the existing factors and then sticking in (ax + b), because the 2 factors on there own don't make a cubed x. But the above ends up giving a's and b's on both sides so i can't equate constants to get my answers. Any one have any guidance?

 

[notfred]

(x+1)(x+2) = x^2+3x+2
(x^2+3x+2)(x-4) = x^3 - 4x^2 + 3x^2 - 12x + 2x - 8 = x^3 - x^2 - 10x - 8

Where did I get (x-4) from? 2 * -4 = -8

 

[maziwanka]

do what u just said:

(x+1)(x+2)=x^2+3x+2, then

(x^2+3x+2)(cx+d)=cx^3+(3c+d)x^2+(2c+3d)x+2d

then by the above:

2d=-8 -> d=-4
c=1 (from the coeff of x^3),

therefore:

3c+d=-1 and 2c+3d=-10.