Question

I don't understand factoring, so I'm so confused on this.

Find the zeros of the function f(x) = x^2 - 5x - 6 by factoring.

Answer 1

\(Basically, \\ \large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}\)

Answer 2

It shows nothing but question marks? @hartnn

Answer 3

refrsh your page :)

Answer 4

Oh! Ahh fixed I see it!! So the two xs would be out and left with the negative six?

Answer 5

factoring trinomials doesn't exactly work that way.

We split the middle term first and then factor out whatever we can from the 2 pairs of terms we get after splitting...
let me give you an example :)

Answer 6

te reason why we use factoring to fin zeros is because if you multiply 2 numbers together and the answer is zero, then at least ONE of those numbers must be zero

That is
if a x b = 0 then either a=0, OR b=0 (or a and b are BOTH zero)

SO

If you star with the equation and want to find its zeros then it would be good if we can write the equation as (M) x (N)

Note that not ALL quadratics can be factorised.

so - the equation has x^2 in it so it must be made up of (x) x (x)
the equation also has a constant term without any x in it which must be made up of multiplying two constant terms


so we start with the assumption that your equation can be re written as

(x+a)(x+b) = 0


If oyu expand those brackets you get

x^2 + x(a+b) + ab = 0

and you can see that comparing this to your equation

a+b = -5
ab= 6

so you need to work out a & b so those two things are true.

so if ab = 6

then a & b could be:

1,6
6,1
-1, -6
-6, -1
3,2
2,3
-2,-3
-3-2

these are the only options

so now look at those and find which pair ADD up to -5

Answer 7

Thats a lot of possible answers @MrNood

Answer 8

\(x^2+6x+8\)

We find 2 numbers whose sum is +6 and product is +8

Such 2 numbers are easy to find, here, +4 and +2

so we split the middle term like
+6x= +4x+2x

Thats the first step of splitting...

Answer 9

Those are the [possible ways of getting 6 from multiplying two numbers

Just take a SIMPLE look at them, and firn WHICH pair adds up to -5

There is only 1

Answer 10

But couldn't it be others as well? How do you find the right one?? @hartnn

Answer 11

as I said - those are the ONLY ways of multiplying two numbers together to make 6, and ONLY one of them adds up to -5

Take a look, and find which pair adds up to -5

Answer 12

-3,-2 @MrNood

Answer 13

OOPs - sorry - the number we want is -6, not 6

the options are:

-1,6
-6,1
-3,2
-2,3

sorry - same issue find the ones that add to -5

Answer 14

Okay I semi get it. I'll try the next one with this system. Thanks @MrNood & @hartnn