Question

How do I factor (x^3-5x+4)?

Answer 1

r u sure its x^3 and not x^2

Answer 2

solution = (x-1)(x^2 +x - 4)

Answer 3

It's x^3. My textbook factored it out as (x-1)(x^2+x-4), but I don't know how to get that answer.

Answer 4

@engstat How did you get that answer?

Answer 5

To factor cubic expressions you can use the trial and error method.

Try putting in a few small values for x and see if the expression becomes zero. A few values to try are: 1, 2, -1, -2, etc.

Once you find a value of x, say x = a, for which the expression becomes zero then it means (x - a) is a factor. Divide the original expression by (x - a) and you will get a quadratic expression which you know how to factor.

Answer 6

If I put x = 1 in (x^3-5x+4), I get (1 - 5 + 4) = 0
This means (x - 1) is a factor.
Divide (x^3-5x+4) by (x - 1)
You can use long division or synthetic division.
You will get a quadratic expression which may or may not be factorable.
If it is not factorable you just leave it as it is.

Answer 7

Thanks @ranga, that was really helpful! My calculus textbook didn't explain this step, so I was confused on how they factored it. Thanks!

Answer 8

Glad to help.

Answer 9

Use synthetic division.

Answer 10

I find synthetic division to be really easy