Question

Why do we let a function equal 0 when factoring?

Answer 1

I was just told to... now i'm being asked why...

Answer 2

It might be because when you're factoring, you're finding the points where x is equal to zero.

Answer 3

Well....... to be really picky, you set an EXPRESSION =0 when you are SOLVING an equation. Solving the equation may or may not involve factoring as one of the techniques used.

Answer 4

You are "finding points where x is equal to zero" when you're factoring. You are just... factoring when you're factoring, lol.

Answer 5

@Tauist628 is correct with what she is saying because it is supposed to be equal to zero because on a graph the the factoring shows you the intercept of where the graph would pass the x-axis

Answer 6

I would like to point out that I'm a male, and thank you.

Answer 7

When you set an expression = 0 to SOLVE it, you are finding the x's for which y=0. Not "finding points where x is =0". All you do for that, is set x=0 and evaluate.

Answer 8

my bad @Tauist628

Answer 9

this is confusing

Answer 10

Isn't it possible that it could be an f(y)=x function?

Answer 11

So the problem:

Factor \(\Large x^2-3x-4\) is just a factoring problem. Factor the trinomial.

The probelm:
Solve the equation \(\Large x^2-3x-4=0\) is an equation. You are looking for the x's that make the expression = 0. And as was mentioned above, IF those are real numbers, then they are also x-intercepts, e.g., they tell you where the graph crosses the x-axis.

Answer 12

I meant to say f(y)=y

Answer 13

All my assignment questions are f(x)= something and to solve (factor) I replace the f(x) with 0 like I was told...

Answer 14

Right... because what you really have is y=f(x)={some expression involving x}

You put an x in, you get a y out.

That is just "function notation" for an equation, like \(\Large y=x^2-3x-4\)

we write as \(\Large f(x)=x^2-3x-4\)
to emphasize that y is a FUNCTION of x (not all equations are functions).

Answer 15

But understand, there is a difference between "factoring" and "solving an equation".

solving an equation means to find all the x-values that make the equation true.

Factoring means... well... factoring, lol, which is really to "undo" multiplication. In the case of trinomials (which is what you are probably dealing with, judging by your question), factoring is "undoing" the FOIL multiplication of the two binomial that give you the trinomial.

Answer 16

But how they are related is THIS, and maybe this is what your question is really getting at:

If you have a PRODUCT = 0 , then there is a principle called the Zero FActor Property that says at least ONE Of the factors must be =0. E.g.:

If A*B=0 then A=0 or B=0

Answer 17

So in solving \(\Large x^2-3x-4=0\), when I factor the trinomial, I get:

\(\Large (x-4)(x+1)=0\)

And since now I have a PRODUCT=0, I know that ONE of the factors is =0:

\(\Large (x-4)=0\) or \(\Large (x+1)=0\)

THOSE I can solve!

So that's why we set = 0. Because of the zero factor property. A sum = 0 doesn't help us solve, but a product = 0, does. :)

Answer 18

Well put

Answer 19

That makes a lot of sense, thanks guys!!!

Answer 20

You're welcome. :)