Question

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

Answer 1

Answer:

(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)

Answer 2

Answer:

Let f(x) = x3 + 2x2 – x – 2 Constant term = -2 Factors of -2 are ±1, ±2 Let x – 1 = 0 ⇒ x = 1 Put the value of x in f(x) f(1) = (1)3 + 2(1)2 – 1 – 2 = 1 + 2 – 1 – 2 = 0 So, (x – 1) is factor of f(x) Let x + 1 = 0 ⇒ x = -1 Put the value of x in f(x) f(-1) = (-1)3 + 2(-1)2 – 1 – 2 = -1 + 2 + 1 – 2 = 0 (x + 1) is a factor of f(x) Let x + 2 = 0 ⇒ x = -2 Put the value of x in f(x) f(-2) = (-2)3 + 2(-2)2 – (-2) – 2 = -8 + 8 + 2 – 2 = 0 (x + 2) is a factor of f(x) Let x – 2 = 0 ⇒ x = 2 Put the value of x in f(x) f(2) = (2)3 + 2(2)2 – 2 – 2 = 8 + 8 – 2 – 2 = 12 ≠ 0 (x – 2) is not a factor of f(x) Hence f(x) = (x + 1)(x - 1)(x + 2)