Question

I have a factoring question:
x^4 − 17x^2 + 16. I need some assistance.

Answer 1

step 1:
Factor x4−17x2+16
x4−17x2+16
=(x+1)(x−1)(x+4)(x−4)

Answer 2

Any old chum can find the answer. I need the steps.

Answer 3

step 2: yo answer
(x+1)(x−1)(x+4)(x−4)

Answer 4

Since both terms are perfect squares, factor using the difference of squares formula, a 2 − b 2 = ( a + b ) ( a − b ) where a = x and b = 4 . ( x + 4 ) ( x − 4 ) ( x + 1 ) ( x − 1 )

Answer 5

does that help you at all bro

Answer 6

Let \(u = x^2\)

Answer 7

Then the expression becomes \(u^2 - 17u + 16\)

Answer 8

@Gdeinward

Answer 9

What method is that? I am unfamiliar with it

Answer 10

u-substitution

Answer 11

Technically, you don't have to use it, however, it enables you to factor the expression easier. You can put the \(x^2\) back after factoring.

Answer 12

I always enjoy easier methods, but I dont know what the teacher will think, seeing a method not introduced in the lesson. I did find how to solve it in that way, but I was worried about it. What are your thoughts? Should I play it safe, or proceed with the u-substitution method?

Answer 13

Proceed with the u-substitution. Just say you learned it trying to figure out how to factor it. No biggie. He or she can't dock points for you trying to learn. It's praiseworthy to try to figure out how to do something. Not something that is frowned upon.

Answer 14

That is true, I had those same thoughts and assumptions, but you can understand my concerns.

Answer 15

On that note, I can take it the rest of the way. Thanks for your assistance.

Answer 16

Trust me, you needn't worry no matter what the teacher says or thinks. Its a method that will help you later on in your math studies. If the teacher can't appreciate that, then he or she does not have your best interests in mind.

Answer 17

Thank you Hero and DC for your assistance.

Answer 18

your welcome bro