Question

Does the following function have any factors at all?
f(x) = -2x^4 + 7x^2 - 3

Answer 1

We suppose
x^2 = y

So we will get,

-2y^2 + 7y - 3

Can you factor now?

Answer 2

\[-2x^4+7x^2-3=-2x^4+6x^2+x^2-3\]\[=-2x^2(x^2-3)+(x^2-3)=(x^2-3)(-2x^2+1)\]

Answer 3

@joemath314159 , is my method correct as well?

Answer 4

yes. Your method makes it a little easier to see what to do. People are generally comfortable with quadratics.

Answer 5

i like joe's method more :P haha jk

Answer 6

HAHA @lgbasallote

Answer 7

Btw @joemath314159 , how are you? It's been long since you been here! :D

Answer 8

Im doing good :) only one more school week left in the semester. Things are winding down.

Answer 9

Cool. xD

Answer 10

Joe how did you get to that method?

Answer 11

it was something I learned here a while back. Its called the "a-c" method i think. when trying to factor something like:\[ax^2+bx+c\]you multiply a and c, and think of two numbers that multiply to ac, but add up to b. In our case, we needed to think of two numbers that multiply to 6, but add up to 7, which is 6 and 1. Notice how I split the 7x^2 into 6x^2+1x^2.

Answer 12

Got it. Thanks

Answer 13

But, there is one thing I do not understand.
When you have a composite function, is it correct to say that it its domain is determined by:

range(outer fcn) intersect domain(inner fcn)?

Answer 14

i think it might be the other way around. The range of the inner function intersect the domain of the outer...i think.

Answer 15

wait wait..but you have to watch the domain of the inner as well. hmm..