Question

I need help in factoring

Answer 1

what do you mean? like a method?

Answer 2

well for example a question is 9a^2+18-7 and the answer would look like (3a-1) (3a+7) and Im not sure how he arrived at that answer

Answer 3

ahh i saw this method once from another user... it goes like this...

9a^2 + 18a - 7

the first step is to split the middle term into two addends..one must have a common factor with the first term..the other must be a factor of the last term...you follow?

Answer 4

yes

Answer 5

now..the hard part is which of the addends...well if you notice..your first term is positive..the last term is negative..so your addends must have one negative and one positive...now..what are two numbers that when subtracted results to positive 18? first pair that comes to your mind...

Answer 6

3 and 21

Answer 7

nice! which would be the negative?

Answer 8

would it be 21?

Answer 9

but 3-21 is not equal to +18..it would result to a negative..remember your middle term is +18 your addends must equal that

Answer 10

oh that makes since! so it would have to be 3 so the 18 comes out positive?

Answer 11

yes! so now you have...

(9a^2 - 3a) + (21a - 7)

what do you think comes next?

Answer 12

factor them? so my teacher said under it to write 3*3*a*a-3*a+3*7*a and then eliminate the common numbers and letters. or is there a better way to do that do you think? This is where I general become lost. I know you factor them but I still get confused about which ones are used in the answer

Answer 13

hmm that method could work too...i'll try to use it and show you and maybe you'll understand..to make it easier work on one group at a time...

for the first group you have (9a^2 - 3a) -> (3)(3)(a)(a) - (3)(a)

3a is common so factor it out... 3a(3a - 1) because 3a is what's left from 9a^2 if 3a is taken out then \(\large \frac{3a}{3a}\) = 1

can you do the second group?

btw..do you have questions regarding the explanation?

Answer 14

This is where im lost. so the second group would be (21a-7) -> (3)(7)(a)-(7) so you would factor out the 7 but he is saying that the answer is (3a+7)

Answer 15

there is actually a factor such as 3a + 7..youll see it later on..for now..focus on this..what is 21a - 7 factored out?

Answer 16

(3)(7)(a)-(7)(1)

Answer 17

right! and what is that simplified further?

Answer 18

Can that be simplified further?

Answer 19

yes...factor out 7 like what i did earlier with 3a

Answer 20

would it just be 7?

Answer 21

it's 7(3a - 1) right? because you have (3)(7)(a) - 7..you're taking out 7 so it'll become

\( \large 7(\frac{21a}{7} - \frac{7}{7}) = 7(3a - 1)\)

do you understand that part now?

Answer 22

oh yeah so would you then distribute the 7 to the -1?

Answer 23

no..why would you do that? distributing is gonna bring you back to 21a - 7 which is the original values lol

Answer 24

well now you have ...

3a(3a - 1) + 7(3a - 1) right? notice how 3a - 1 is common to both terms...thus you can factor it out...try doing that..

Answer 25

oh! so when you factor them out it brings you to (3a+7)

Answer 26

\(\Huge \color{red}{\checkmark}\)

Answer 27

but remember it's (3a-1)(3a+7) not just the latter

Answer 28

right I know how we got (3a-1) I was just confused on the second part! thank you so much!! while your here would you mind if I asked you one more quick question on factoring?

Answer 29

sure

Answer 30

ok so another problem is 4x^2-13x+10 and the answer is (4x-5). I completely understand the process. At one point it comes to be (4x-5) (4x-5) and he writes it as x(4x-5) -2 (4x-5) does he do that so one of the (4x-5) goes away? because in the problem, when factoring, there is an extra x that isn't factored out so is that where the x outside of the parenthesis is coming from? and is the -2 there to get it back to -8? I f this is too much for tonight then that is ok! I just thought I would ask because I was a little confused and you helped me so much on the last one!!

Answer 31

hmm if i solve it step by step would it help? coz i dont get your question much...

Answer 32

yes thank you so much!!!

Answer 33

4x^2 - 13x + 10
4x^2 - 8x - 5x + 10
(4x^2 - 8x) + (-5x + 10)
4x(x - 2) + -5(x - 2)
4x(x-2) - 5(x-2)

(x-2)(4x-5)

Answer 34

That makes so much more since then the way he did it! Thank you so much!!! You helped a ton