Question

Factoring polynomials by grouping?

Answer 1

Can anyone explain this step by step? Please!! :)

Answer 2

@phi @mathstudent55 anyone?

Answer 3

Something like 7x^3 – 28x^2 + 3x – 12 that doesn't have a GCF

Answer 4

\[ 7x^3 – 28x^2 + 3x – 12= (7x^3 – 28x^2) + (3x – 12)\]

Answer 5

factor the two groups in parenthesis

Answer 6

that makesss... 7x^2(x-4)+3(x-4) right?

Answer 7

yes

Answer 8

And where do we go from there?

Answer 9

you have a common factor of x-4...factor that out

Answer 10

wait like x-4(7x^2(x-4)+3(x-4)?

Answer 11

no

Answer 12

How?

Answer 13

ac+bc=(a+b)c

Answer 14

\[a=7x^2\]
\[b=3\]
\[c=x-4\]

Answer 15

Oh so (7x^2+3)x-4?

Answer 16

close the x-4 in parenthesis

Answer 17

but with the communitive property of multiplication we can write it as (x-4)(7x^2+3) right?

Answer 18

yes

Answer 19

Oh I see, so we group the terms and force a common factor between the two!

Answer 20

if possible ...yes

Answer 21

and if not, its prime?