Question

f(x)=(x^3)+3(x^2)-9x+5 in factored form (step by step)

Answer 1

Using synthetic division:So, -5 is a zero and (x + 5)r with a quadratic leftover:

x^2 - 2x + 1
which can be factored:

(x - 1)^2

So, your factoring is:

(x + 5)(x - 1)^2

Answer 2

Oh okay I see. But why did you use -5 and not 1

Answer 3

(x + 5)r is supposed to be:

(x + 5) is a factor

Openstudy lags and truncates typing sometimes, but I'm sure you probably already know that.

Answer 4

Your possible *rational* factors are going to be +-1 and +-5 I was going to try them all but I hit on -5 right away.

Answer 5

ohh

Answer 6

so you have to try all of them..?

Answer 7

The rational factors will be the factors the last term divided by the coefficient of the first term (when written descending in power). But since the coefficient of the first term is "1", that simplified things.

Answer 8

Yes, you try all of them. But we only had 4 to try so this was a rather "contained" problem.

Answer 9

ahh I see

Answer 10

1 can work too right

Answer 11

Yes, and that was the "double" root from (x - 1)^2

Answer 12

but when I use 1 I get (x+5)(x-1)

Answer 13

Yes, but (x - 1) is a factor twice. You'll see this when you multiply out:

(x + 5)(x - 1)^2

Answer 14

If you look at the results of my synthetic division, you'll see a quadratic"

x^2 - 2x + 1

factored as (x - 1)^2

Answer 15

I do not really understand that part

Answer 16

x^2 - 2x + 1

appears as the result of my synthetic division. Do you see that? Is that the part where you are foggy?

Answer 17

yea

Answer 18

Ok so I got this