Question

factor each polynomial:
h^3-10h

Answer 1

\(\color{blue}{please\ show\ work}\)

Answer 2

I'll help you out.

Do you see anything that \[h^{3} = h*h*h\]and\[10h\]have in common?

Answer 3

h?

Answer 4

Correct, so if I factor out the h:\[h^{3} - 10h = h(...)\]what's left in the brackets?

Answer 5

(h^2-10)

Answer 6

Great! That's your answer

Answer 7

ok thanks:) and i have one more question, is that fine?

Answer 8

Sure

Answer 9

same instructions:
2x^3-x^2-162x+81

Answer 10

\[2x^3-x^2-162x+81\]

Answer 11

Okay, this one wont be so obvious. Are you familiar with The Factor Theorem? (I believe some people call if The Remainder Theorem also)

Answer 12

call it*

Answer 13

no i just learned this today

Answer 14

Okay well in that case, we'll try something different.

Can you see anything that any of the terms of the expression share? It doesn't have to be something that all of the terms share, 2 or 3 works

Answer 15

2

Answer 16

and which 2 share that?

Answer 17

2 and -162

Answer 18

That is correct, but if you look closely you'll see that the 2 terms related to those share even more than that

Answer 19

-162\2=-81
and then there's x

Answer 20

Correct, I was pointing out that they also share x, so you can see that the common factor between these 2 terms is 2x

If we move them to the front, and factor out 2x we get\[2x(...) -x^{2}+81\] fill in the brackets

Answer 21

\[2x(x-81)\]

Answer 22

Very close, but not quite, can you see why its\[2x(x^{2}-81)\] instead of what you got?

Answer 23

oh i forgot the exponent was three

Answer 24

No problem, happens all the time.

So now we have\[2x(x^{2}-81)-x^2+81\]
Can you see what these terms share? This one is a bit harder to spot.

Answer 25

how did we get the -x^2+81

Answer 26

Those are the other 2 terms in our expression, remember I just moved the other 2 to the front

Answer 27

oh ok, then the terms that are shared are: 81 and 2x

Answer 28

Not quite. Can you see how\[-x^{2} + 81 = -1(x^2-81)?\]

I just factored -1 from the last 2 terms

Answer 29

yes

Answer 30

Okay so our original expression is now\[2x(x^{2}-81)-1(x^{2}-81)\]Can you see what the common factor is now?

Answer 31

yes it is: x^2-81

Answer 32

ok i got it is the answer: (2x-1)(x-9)(x+9)?

Answer 33

Yes indeed. Are you sure you even needed help? ;)

Answer 34

well the last part i know to factor the rest, its just getting started i needed help with, also just sorting the stuff out:)

Answer 35

Well good work at any rate. Take care