Question

Please help me factor the following equation

x^3+x^2-2=0

Answer 1

\[x^3+x^2-2=0\]

Answer 2

One way to solve cubic and higher order equations is to try out a few small values of x such as: 1, -1, 2, -2, etc.

If I try x = 1 in x^3+x^2-2 it become 0
that means (x - 1) is a factor.

Do synthetic division and figure out the quotient. It will be a quadratic expression which may be able to factor further.

Answer 3

ok i understand how (x-1) is a factor.

but what do you mean by 'do synthetic division and figure out the quotient'?

Answer 4

(x - 1) is a factor means:
The original expression x^3+x^2-2 = (x - 1){ some lower order expression }

We have to figure out what the lower order expression is.
So divide (x^3+x^2-2) by (x - 1) to figure out the lower order expression.

This division you can do either the long division or if you are familiar with synthetic division you can use that method.

Answer 5

ok thanks

Answer 6

you are welcome.