Question

Factor: x^4+5x^2-36

Answer 1

do you know how to do synthetic division

Answer 2

Not off the top of my head.

Answer 3

I think you can break the middle term first. That way, you can factor it easier.
You'll get (x^2 + a)(x^2 + b) for x^4 +5x - 36
Expand (x^2 + a)(x^2 + b)
(x^2 + a)(x^2 + b)
= x^4 + (a+b) x^2 + ab

So, a+b = 5 and ab = -36
Can you solve a and b first?

Answer 4

this is an equation reducible to a quadratic... let u = x^2

so the problem is u^2 + 5u - 36

which can be factorised

Answer 5

It's actually not an equation.

Answer 6

at a guess its (u + 9)(u - 4)

so it becomes (x^2 +9)(x^2 - 4)

Answer 7

so for the final answer.. x^2 + 9 won't factor but x^2 - 4 does factor because its the difference of 2 squares.

so the answer would be (x^2 +9)(x - ?)(x+ ?)

just find ?

Answer 8

i confirm campbell's way is the easiest lol

Answer 9

For ab= -36 and a+b = 5 would be a -4 and 9, correct? I get that much..

Answer 10

a is -4 and b is 9
That's why you get
x^4 +5x -36
= (x^2 -4)(x^2+9)

Answer 11

Note that (x^2 - 4) can be further factored as it is difference of two squares

Answer 12

Okay, so all of that makes it (x^2-4)(x^2+3)

Would that factor that into (x+2)(x-2)(x^2+3)?

Or can the (x^2+3) Be factored? It looks like it cannot be factored to me at this point.

Answer 13

well its x^2 + 9... not x^2 + 3

Answer 14

Shoot, I mean the 9, not three, so that can be factored to (x+3)(x-3) then?

Answer 15

no it won't factorise... leave it as it is

Answer 16

Understood, so now I have (x^2-4)(x^2+9)

So then the (x^2-4) goes to (x+2)(x-2)(x^2+9)? Why does the last one stay as is?

Answer 17

because it isn't the product of binomials.... i.e. can't be factored.

Answer 18

Would that have to do with the number or the addition and subtraction sign? I am trying to completely understand this, I came across this earlier..

Answer 19

well it has 2 terms and a plus sign... so can't be factored...

Answer 20

Gotcha, thank you!