Question

can I factor 7a^2+48a-7?

Answer 1

yes

Answer 2

you can factor any polynomial. It might not be pretty or easy to see right away, but you can

Answer 3

You can not factor all polynomials...at least not over the Real numbers which is usually meant by factoring.

Answer 4

allowing the imaginary number you can.

and i disagree that the real number plane is what is "meant by factoring"

Answer 5

For example \[x^2+1\] is not "factorable" (at least not over the Real Numbers)

Answer 6

Really ... I would assume that most individuals in here are not in math courses where they say factor and do not assume it to be over the Rational Numbers.

Answer 7

would I find the common factor then do it?

Answer 8

It is rare to see the term factor used for anything other than Rational Factoring in any course until Algebra 2 or Pre-Calc and then it is qualified as to what number set the factoring is to be over. @Euler271

Answer 9

Yes mspare that is factorable in the commonly intended way.

Answer 10

im so horrible at math its not even funny! sorry so many questions

Answer 11

Let me make a suggestion about factoring...Can I show a way I like to use for multiplying binomials? It helps with factoring.

Answer 12

yes please. Ill take any help i can get at this point

Answer 13

@irania that is not quite it.

Answer 14

ok mspare you will have to bare with me...

Answer 15

First instead of using foil we will line the binomials up in an up and down way.
So for
(x+5)(2x-3)

We will actually write it like this...

Answer 16

Now there are 5 steps to multiplying this way.
1) Multiply straight down the front.
2) Multiply criss
3) Multiply cross
4) Multiply straight down the back
5) Combine any like terms (usually the criss and the cross)...

I'll show you on the drawing in a second

Answer 17

Now in step five notice that the criss and cross term are like terms (x terms) so they can be combined
so \[2x^2-x+10x-5=2x^2+9x-5\] so \[( x+5)(2x-1)=2x^2-9x-5\]

Answer 18

Does this make sense? @mspare

Answer 19

Because if it does then we can move on to factoring.

Answer 20

yes it does

Answer 21

Ok so here are my rules of factoring: (1) Always factor out commmon factors if you can.

Answer 22

so for \[7a^2+48a-7\] are there any common factors?

Answer 23

7 would be common right? but then again that doesn't seem right because its not common for 48

Answer 24

so no 7 doesnyt wor k bc its not divisible in every term.

Answer 25

So now we do what I call unmultiply

Answer 26

ok?

Answer 27

First figure what are the possible terms that will make the first term...\[7a^2\]

Answer 28

So what times what will give you \[7a^2\]?

Answer 29

@mspare

Answer 30

7a(a) or a(7a)?

Answer 31

right either way it is 7a and a ... That pair is the only possible pair so that is good. Now let's focus on the last term...what are the possible factors of 7?

Answer 32

1 and 7

Answer 33

Correct again it is good because there is only one pair that works...now we will focus on the signs that we will choose.

Look at the equation... \[7a^2+48a-7\]

Answer 34

Look at the last term ... it is subtraction (negative). How do you multiply 2 numbers together and get a negative number?

Answer 35

a positive and a neg

Answer 36

-1(7)

Answer 37

Correct so we know one of the signs is + and one is - we will just pick one and figure it out later.

Now the last step is guess and check using the criss cross multiply method.

Answer 38

so let's just pick a combination of our possibilities and check them.