Question

2x3+11x2-7x-6(factorize)

Answer 1

2x^3+11x^2 -7x-6
let q(x)=x-1
so x=1
now,
p(x)= 2x^3+11x^2 -7x-6
p(1)= 2*1^3+11*1^2 -7*1-6
[let p(x) = 0]
0=2=11-7-6
0=13-13
0=0
so,(x-1) is one factor of 2x^3+11x^2 -7x-6
now,
divide 2x^3+11x^2 -7x-6 by x-1 
which is 
= 2x^2 + 13x +6 
now,
 p(x)=(2x^2 + 13x +6) (x-1)    
0=(2x^2+13x+6)(x-1)    
0=(2x^2+x+12x+6)(x-1) ......[made parts of 13 which on multiplication give 12 ,the product of 2 and 6]
0=[x(2x+1)+6(2x+1)](x-1) 
0=(2x+1)(x+6)(x-1) 
factors are (2x+1)(x+6)(x-1)