Question 30435: Please explain how to factor the following problem by grouping to solve the equation. x^3+3x^2-4x-12=0
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Please explain how to factor the following problem by grouping to solve the equation.
LET F(X)= x^3+3x^2-4x-12=0
TRY PUTTING X=0,1,-1,2,-2..ETC..TO GET A ZERO
WE FIND AT X=2..F(2)=2^3+3*2^2-4*2-12=8+12-8-12=0...SO X-2 IS A FACTOR.DIVIDE F(X) WITH X-2 NOW
2...|1..........3..........-4.........-12
....|0..........2..........10..........12
..................................................
.....1..........5...........6...........0
HENCE X^2+5X+6 IS THE QUOTIENT
=X^2+2X+3X+6=X(X+2)+3(X+2)=(X+2)(X+3)
HENCE F(X)=(X-2)(X+2)(X+3)
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