Question

SOMEONE PLEASE HELP (factoring)

Answer 1

what do you need to factor?

Answer 2

15q^3+40q^2+3q+8

Answer 3

i dont understand factoring at all ive tried all day to learn but i couldnt understand the steps

Answer 4

You have 4 terms, so let's try to factor this by grouping

Answer 5

you start off by grouping up the terms into pairs

15q^3+40q^2+3q+8

(15q^3+40q^2)+(3q+8)

what can you factor from (15q^3+40q^2) ?

Answer 6

you know what factoring is, right ?

Answer 7

isnt factoring basically grouping them? @hartnn

Answer 8

i dont understand what you mean? so you factor each group alone? @jim_thompson5910

Answer 9

ignore the variables for now

let's focus on factoring single numbers

what do you get when you factor 15 ?

Answer 10

okay im sorry for sounding so stupid but what do you mean by " factor 15"

Answer 11

its opposite to distributing

\(\large ☻(☺+♥) = ☻☺+☻♥ \\ \text {this is distributing}\)

\(\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}\)
now is it clear, what factor basically means ?

Answer 12

thats what someone on here was trying to explain that its distributing but in reverse

Answer 13

factoring is writing a number as a product of 2 or more numbers

Answer 14

for example,

10 = 2*5

Answer 15

so 5 x 3

Answer 16

good

Answer 17

40 = 5*8, so we can see that 40 and 15 have a common factor of 5

this is the greatest common factor (the largest factor they share)

Answer 18

one more example :

\(abc+adc\)
what is common from both terms?
'a' and 'c' , right ??
so i factor it out from the expression.
in first term, 'b' remains
and in 2nd term, 'd' remains
so i will have
\(ac (b+d)\)
see if you get this.
you will be applying this in your problem

Answer 19

ohhhh that helped actually, thanks!! @hartnn

and so we're finding the gcf, right? @jim_thompson5910

Answer 20

what do we do with the exponents then? and the variables?

Answer 21

exactly, so let's say we had something like

20x + 30y

first we factor 20 and 30

20 = 2*10 = 2*2*5
30 = 3*10 = 3*2*5

we see that 2*5 or 10 is the GCF between 20 and 30

so we factor that out

to go from

20x + 30y

to

10(2x + 3y)

notice how if you distributed the 10 back in you'd get 20x + 30y again

Answer 22

ohhh that makes total sense now!

Answer 23

Here's a way to visualize factoring 20x + 30y