Question

step by step factor x^3 - x^2 - 4x + 4

Answer 1

Use the order of operations

Answer 2

you could also use grouping

Answer 3

ok not sure how that works with so many terms
is why i am asking how to factor this

Answer 4

Or you could find one factor in that equation then use synthetic division to solve it

Answer 5

looking for real zeroes and yand x ints and end behavior

Answer 6

ty for assistance just dont have my brain wrapped around this

Answer 7

1) It's a cubic expression. It will only be luck if you can factor it.

2) Look around for common factors in various chunks.

x^2 is common in the first two terms.
-4 is common in the last two terms.

Factor those and reassess.

Answer 8

I guess I would group the first two and the last two terms?

Answer 9

That does look promising. Let's see what you get.

Answer 10

ok going to try

Answer 11

Find the factors of the constant and the factors of the leading coeffiecient. So you'll have +/- 1, 2, 4 so plug one of those factors in the place of the x and see what factors out to =0 and once you have that you can use synthetic division to find out your other factors. Even though they are already given to you once you have the factors of 4 since there are only 3 factors and the leading exponent is saying there are 3 possible factors. Hope this helps, idk what level of math you're at though.

Answer 12

college algebra just started learning synthetic division

Answer 13

You didn't learn this in high school?

Answer 14

No need. The problem statement WANTS you to factor it. Just stick with the grouping.

Answer 15

when I graduated in 1983 ( Not to date myself LOL ) it wasn't required.

Answer 16

Oh haha got ya, yeah not something you really need to remember in the real world but it's super easy anyways yeah just factor it simply and you got it, it's not a hard problem c:

Answer 17

is for me

Answer 18

I got x^2 ( X-1) - 4 (x+1)

Answer 19

I know I need to go further but how

Answer 20

Close. The last one should be (x-1). Try that part again.

Answer 21

just saw that
: )

Answer 22

More factoring. You;ve a common factor of (x-1) in both of those remaining terms.

Answer 23

so that (x-1) ^2

Answer 24

would that be x^2 - 4 (x-1)^2 so far

Answer 25

How did you get that?

\(x^{2}(x-1) - 4(x-1) = (x^{2} - 4)(x-1)\)

Answer 26

The \(x^{2}\) didn't magically square when you factored it out of the first two terms.

The \(-4\) didn't magically square when you factored it out of the first two terms.

Why would the \((x-1)\) square when you factored it out of the two remaining terms?

Answer 27

I shouldnt have combined the terms lol

Answer 28

You have to get this property stuck in your brain.

\(a\cdot(b+c) = ab + ac = ba + ca = (b+c)\cdot a\)

It works both ways.

Answer 29

I set it up like this (x^3 - x^2) - (4x+4)

Answer 30

then pulled out x^2 from the first set

Answer 31

then 4 from the second set

Answer 32

leaving me with x^2 (x-1) - 4(x-1)

Answer 33

Okai you're making it harder than it is. first things first. The highest exponent is telling you how many factors there are going to be. So there are 3 factors. you take the factors of the constant which is 4. Then you take the factors of the leading coefficient. In this case that is 1. so your factors are +/- 1,2,4.
Try one of the factors. I chose 1. so the problem will look like this (1)^3-(1)^2-4(1)+4
that equals 1-1-4+4=0 so there you have your first factor.

Answer 34

and I am lost from tht point

Answer 35

Then you're going to use synthetic division which is gonna look like this...