xplain, in complete sentences, how you would factor 27x^4-90x^2+75

Question

myininaya · Answer

Okay first it easier to look at 
$$27u^2-90u+75$$
and the way we can do that is making the substitution
$$u=x^2$$
so first we ask ourselves what is the gcf of 27,90,75?

anonymous · Answer

I will stare at it and keep staring and then write $ 3 \left(3 x^2-5\right)^2 $

myininaya · Answer

so fool just mentioned the gcf which is 3

mr.math · Answer

stare at it and keep staring! LOL!

anonymous · Answer

ok

myininaya · Answer

$$3(9u^2-30u+25)$$
now we look at the inside (the thing in the grouping symbols)
$$9u^2-30u+25$$
note we will bring the 3 down later

ok so a=9,b=-30, c=25
We need to find two factors of a*c that have product a*c and have sum b.

$$a \cdot c=9(25)=45(5)=15(15)=-15(-15)$$
b=-15+(-15)=-15-15 (whatever!)

so Then we replace bu with -15u-15u

$$9u^2-30u+25=9u^2-15u-15u+25$$
Then we factor by grouping
$$3u(3u-5)-5(3u-5)=(3u-5)(3u-5)=(3u-5)^2$$
so we have (remember to bring down mr.3 )
$$3(3u-5)^2$$
we should probably put this back in terms of x
so recall
we let
$$u=x^2$$
so replacing u in $$3(3u-5)^2$$
with $$x^2$$
we get 
$$3(3x^2-5)^2$$
which is what Fool had

turingtest · Answer

Bravo myin, determined to explain it :)

myininaya · Answer

lol