how do you factor these quadratic functions?

Question

hello i'm in 9th grade in Algebra 2. I need help on these if possible!

How do you factor the expressions completely:

1) 9y^2 - 16


2) 15w^2 - 2w - 24


3) 2m^3n + 5m^2n^2 + 2mn^3


please show steps!! you don't have to answer all if you don't know =P

Answer 1

1... x^2 - y^2 = (x+y)(x-y)
if you look closely enough, you'll see the pattern....

2... (ax + b)(cx + d) How would you do this? Now, think how you can undo it. This is all to do with having enough practice so you can recognize the pattern. Try combinations that you think they'll work. Eventually, you'll find one that actually work!

3.... do you see anything common that you can group and take it out side?

do you see there is at least one "n" in every term? Take it out.
What about "m" can you take it out? Make use of parenthesis...

I'm not going to do them for you. You need to figure this out and have enough practice, so you'll recognize them.

Answer 2

1) 9 can be rewritten as 3^2 and 16 as 4^2 so we get
(3y)^2 - 4^2
then just use the form (ax + c) (bx - d) for perfect binomials
(3y + 4)(3y - 4)

2) This one is kinda just guess-n-check...
(15w - 12 ) (w + 2 ) no
(15w - 8 ) (w + 3 ) no
... not gonna work with 15
(5w - 8 ) (3w + 3 ) no
(5w - 6 ) (3w + 4 ) no but close
(5w + 6 ) (3w - 4 ) there we go
You just have to look at the numbers and guess

3) First we can factor out mn
mn( 2m^2 + 5mn + 2n^2 )
this is a trinomial with *gasp* 2 squares
so we factor as follows.. (have to use a bit of guessing)
mn( 2m + 2n )( m + n ) no
mn( 2m + n )( m + 2n ) no but close...
mn( 2m - n )( m - 2n ) there!

Answer 3

1) 9y^2 - 16
(3y-4)(3y+4)=0
y=+/- (4/3)

2) 15w^2 - 2w - 24
(5w+6)(3w-4)=0
w = -6/5 or w = 4/3


3) 2m^3n + 5m^2n^2 + 2mn^3

Answer 4

f(x)=3x^2+16x+5 f(x)=(3x1)(x+5) x intercepts would be making x=0 and giving y fee which may well be 5 yet i assume you fairly need y intercepts 0=3x+one million 3x=-one million x=-one million/3 x=-5 f(x)=6x^2+5x+one million f(x)=(3x+one million)(2x+one million) lower back x intercept would be one million yet i nonetheless assume you like y 0=3x+one million 3x=-one million x=-one million/3 2x+one million=0 2x=-one million x=-one million/2

Answer 5

BRAIN CRAMP!