Question

Hey (: I need help figguring out the process for an equation!! please help??
5. Factor completely 21x3 + 35x2 + 9x + 15.

(3x − 5)(7x2 − 3)
(3x − 5)(7x2 + 3)
(3x + 5)(7x2 − 3)
(3x + 5)(7x2 + 3)

Answer 1

factor by grouping

Answer 2

\(\bf 21x^3 + 35x^2 + 9x + 15\\
(21x^3 + 35x^2)+(9x + 15)\\
7x^2(3x+5)+3(3x+5)\impliedby \textit{take common factor of it}\)

Answer 3

okay!! not to certain how to properly do that!! i know the answer and i have the process. i just need to know how it all works!! how do you add a picture to this??

Answer 4

\(\bf 21x^3 + 35x^2 + 9x + 15\\
(21x^3 + 35x^2)+(9x + 15)\\
7x^2{\color{blue}{ (3x+5)}}+3{\color{blue}{ (3x+5) }}\impliedby \textit{see any common factors?}\)

Answer 5

yeah!!! how do you start with the equation what was your first step??

Answer 6

as acxbox22 said, by grouping
then take any common factors from the groups

Answer 7

you have 4 terms
1 2 3 4
then we grabbed

(1 2) (3 4)
then common factors of them

Answer 8

yeap, that's correct

Answer 9

okay!! (: did you get the picture??
y

Answer 10

\(\bf 21x^3 + 35x^2 + 9x + 15\\
(21x^3 + 35x^2)+(9x + 15)\\
7x^2{\color{blue}{ (3x+5)}}+3{\color{blue}{ (3x+5) }}
\\ \quad \\
(7x^2+3)(3x+5)\)

Answer 11

yes

Answer 12

i see you got the same thing as she did!!! so lets see you took the numbers and put them into perethesis....

Answer 13

then you took the numbers and found the greatest common multipul??

Answer 14

yeap

Answer 15

okay after that then what did you do??

Answer 16

\(\bf 21x^3 + 35x^2 + 9x + 15
\\ \quad \\

(21x^3 + 35x^2)+(9x + 15)\impliedby grouping
\\ \quad \\

7x^2{\color{blue}{ (3x+5)}}+3{\color{blue}{ (3x+5) }}\impliedby \textit{common factor on each group}
\\ \quad \\
(7x^2+3)(3x+5)\impliedby \textit{common factor on the terms}\)

Answer 17

once you take the common factor on each group
what's left inside from the 1st group, is "common" with what's left inside the 2nd group
then you take common factor of that

Answer 18

ah!!! I think i get it now!!!(: thanks so so much to both of you. is there a way to give both of you medals??XD

Answer 19

yw

Answer 20

yw??

Answer 21

that's okay!! Just thanks so so much!!! and see you both later!!! (: