Question

Can anyone help with some factoring ? /:

Answer 1

I don't need the answer but I need someone to help me guide through this , its confusing me /:

Answer 2

it is confusing to me too, all this verbiage.
but we can try "factor by grouping" for \[2x^2 + 13x + 15 \]

Answer 3

okay.

Answer 4

we will break the middle term in to two pieces
lets try \(12x+x\) if it works great, if not we will change it

Answer 5

yeah i'll help you with some factoring ;)

Answer 6

wait what did u just do ?

Answer 7

\[2x^2+12x+x+15\] is our first start
then from \(2x+12x\) we can factor out a \(2x\) to get
\[2x(x+6)+x+15\] but you see that the second possible factor is \(x+15\) which is not equal to \(x+6\) so lets try again

Answer 8

i looked at \{13x\) and broke it in to two parts as \(13x=12x+x\)

Answer 9

but that didn't work, often the first guess is wrong

Answer 10

lets try \(13x=10x+3x\)

Answer 11

then we write
\[2x^2+10x+3x+15\] and factor \(2x\) out of the first two terms, that is, factor \(2x\) out of \(2x^2+10x\)

Answer 12

you get
\[2x^2+10x+3x+15=2x(x+5)+3x+15\]
are you okay to this step?

Answer 13

you don't have to solve it , you just have to explain how a trinomial of the form 2x2 + 13x + 15 can be turned into a four term polynomial suitable for factoring by grouping.

Answer 14

for part 1 , and then part 2 we can make up our own problem .

Answer 15

you can turn it in two a four term polynomial by rewriting it as
\[2x^2+10x+3x+15\]

Answer 16

that is because \(2x^2+10x\) has a common factor of \(2x^2\) and \(3x+15\) has a common factor of \(3\)

Answer 17

ohh alright now I see it

Answer 18

so you can factor as
\[2x^2+13x+15=2x^2+10x+3x+15=2x(x+5)+3(x+5)\]\[=(2x^2+3)(x+5)\]

Answer 19

oops typo there, last line should be
\[(2x+3)(x+5)\] sorry

Answer 20

its fine haha :] thanks for your help
wanna help me with part 2?

Answer 21

to answer part 2, you can make up your own polynomial that factor by first writing it in factored form
say you pick \((3x+1)(x+2)\)

Answer 22

then when you multiply it out you would get
\[3x^2+6x+x+2=3x^2+7x+2\]and since you started with the factored form you know that
\[3x^2+7x+2\] will factor

Answer 23

when you multiplied that you foiled it right ?
im just trying to make sure I understand what you did there .