Question

x^3 + 2x^2 - x-2 factotise it by factor theorm​​

Answer 1

:

(x+1)(x+2)(x-1)

Step-by-step explanation:

p(x)=x³+2x²-x-2

Factors of -2 are ±1,±2.

p(1)=1+2-1-2=0

By trial and error, 1 is a zero of p(x).

So by factor theorem, x-1 is a factor of p(x).

p(x)=x³+2x²-x-2

=x³-x²+3x²-3x+2x-2

=x²(x-1)+3x(x-1)+2(x-1)

=(x²+3x+2)(x-1)

=(x²+2x+x+2)(x-1)

=[x(x+2)+1(x+2)](x-1)

=(x+1)(x+2)(x-1)

To factorise cubic polynomial we use herons method after reducing it by the remaining coefficient we set a quadratic polynomial as shown and then factorise

HOPE YOU UNDERSTAND