Question

The graph of y= 12x^3 - 41x^2 + 13x + 6 passes through the point (3,0).
Completely factor the polynomial 12x^3 - 41x^2 + 13x + 6.
how do i factor?

Answer 1

@johnweldon1993

Answer 2

Just doing it out on paper first :)

Answer 3

ok ^^

Answer 4

Oh boy this one is annoying lol

Answer 5

xD im sorry! i missed a day of school and now i'm clueless D:

Answer 6

Alright...alright..

think I got it...need to breathe again! haha

Okay first...do you know how to do polynomial long division?

Answer 7

its a hit and miss, im wrong the majority of the time

Answer 8

Lol well lets see how we do this time ;P

So we are GIVEN a factor of the polynomial already...it states that (3,0) is a point...that means when x = 3..y = 0...hence....we have a factor of

(x - 3) because when you plug in 3 there...you get 0
okay?

Answer 9

ok

Answer 10

So we need to divide that annoying little polynomial up there...by this factor...it will make it smaller and much easier to deal with lol

Answer 11

Alright...so now..first

How many times does 'x' go into 12x^3?

Answer 12

2 times i believe cause x multiplied by x^2 = x^3

Answer 13

Close....

So you would need to multiply x by 12....to make 12x right?

Well to make 12x^2 .....we would need to multiply x by 12 (to make the 12) and THEN multiply it by x as well! because x times x = x^2

SO!

to make 12x^3 we multiply x....by 12....and by x^2 because

x times 12 = 12x

and 12x times x^2 = 12x^3

Make sense? kinda? sorta? :D

Answer 14

So very close!!! just 1 mistake it

-41x^2 - (-36x^2)

is

-41x^2 + 36x^2

which is

-5x^2 not 5x^2

Try 1 more time? :)

Answer 15

ok, ill try ^^