Question

If x+1 is a factor of x^3-3x+a then factorize the latter.
Answer in my book=(x+1)(x+1)(x-2)

Answer 1

First we have to find the value of a.

Given that (x+1) is a factor of above equation.

x³ - 3x + a = 0

x = -1

(-1)³ - 3(-1) + a = 0

-1 + 3 + a = 0

a = -2

So the equation is

x³ - 3x - 2 = 0

Using synthetic division,

x³ - 3x - 2 = (x + 1) (x² - x - 2)

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

So the roots are (x + 1) (x - 2) (x + 1) of x³ - 3x + a = 0.

-WonderGirl