Factoring question

[MathGuy1999]

Hey, guys I just have a quick math question that I need help on, it goes like this:

f(x)=(−3x^3+9x^2+14x−8)

We can partial factor to write f(x)=A(x−4)+B, where deg(B)<deg(x−4)

I am looking for the A and B values, any help is greatly appreciated thanks!

 

[Steven G]

Use synthetic division--divide f(x) by (x-4).

 

[lex]

[MATH](−3x^3+9x^2+14x−8)=A(x-4)+B[/MATH]Note, what you call A is actually a quadratic polynomial.
In this particular case, you can substitute in [MATH]x=4[/MATH], to find B, which turns out to be 0.
So in fact [MATH](−3x^3+9x^2+14x−8)=(ax^2+bx+c)(x-4)[/MATH]and you could fill in a, b, c easily 'by inspection': a=?, c=? and then b=?
(In general the solution is as @Jomo has rightly said).