SOLUTION: Find b so that (x-3) is a factor of f(x)=x^3+bx^2-7x+12. Should x-3 replace the x's in the problem and then solve for b? I've been trying that, but end up with a huge mess for

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find b so that (x-3) is a factor of f(x)=x^3+bx^2-7x+12. Should x-3 replace the x's in the problem and then solve for b? I've been trying that, but end up with a huge mess for       Log On


   

Question 21920: Find b so that (x-3) is a factor of f(x)=x^3+bx^2-7x+12.
Should x-3 replace the x's in the problem and then solve for b? I've been trying that, but end up with a huge mess for a answer! Hope you can help. Thanx.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Find b so that (x-3) is a factor of f(x)=x^3+bx^2-7x+12.
THERE IS THEOREM CALLED REMAINDER THEOREM WHICH SAYS THAT IF F(X)IS DIVIDED BY X-A,WE GET F(A)AS REMAINDER..IT IS VERY USEFULL THEOREM AND EASY TO PROVE,UNDERSTAND AND USE...IF YOU WANT THE PROOF COME BACK AND I WILL TELL YOU..FOR THE PRESENT LET US USE THE THEOREM
HERE F(X)IS DIVIDED BY X-3...SO F(3) IS THE REMAINDER.BUT IT IS GIVEN THAT X-3 IS A FACTOR. THAT IS X-3 DIVIDES WITHOUT REMAINDER THAT IS REMINDER IS ZERO..THAT IS F(3)=0
F(X)=X^3+BX^2-7X+12
F(3)=3^3+B*3^2-7*3+12=0
27+9B-21+12=0
9B=21-27-12=-18
B=-18/9=-2