Please I need to know how to factorise this quadratic expression!
Please solve it for me and show me the correct and right method to solving these kind of questions.
(xcubed + 2xsquared - 5x - 6)
Please help
and Thanks alot
$\displaystyle P(x)=x^3+2x^2-5x-6$
Well , are you familiar with the factor theorem ?
If not , note that for a polynomial P(x),(x-a) is a factor of P(x) if and only if P(a)=0 .
Notice that the constant term for the equation above is -6 .
Hence if (x-a) were to be a factor of P(x) , then a must be a factor of -6.
a=+/-1,+/-2,+/-3,+/-6
Substitute :
If x=1 , P(1)=1+2-5-6=-8 , hence (x-1) is NOT a factor .
If x=-1,P(-1)=-1+2+5-6=0 , hence (x+1) IS a factor .
Try doing this for all values of a stated above and you should get all the factors for this equation .
$\displaystyle
1 ------x^3+2x^2-5x-6)
$
$\displaystyle
2-----x^3+x^2+x^2+x-6x-6
$
$\displaystyle
3------x^2*(x+1)+x*(x+1)-6*(x+1)
$
$\displaystyle
4------(x^2+x-6)*(x+1)
$
$\displaystyle
5------(x^2+3x-2x-6)*(x+1)
$
$\displaystyle
6------(x*(x+3)-2*(x+3))*(x+1)
$
$\displaystyle
7------(x-2)*(x+3)*(x+1)
$