Question

Simplify completely quantity 4 x squared minus 32 x plus 48 all over quantity 3 x squared minus 17 x minus 6

Answer 1

I factored the top to 4(x-2)(x-6) but idk how to factor the bottom... @phi

Answer 2

I don't like when the leading x^2 term has a number not = 1

but we can do this:
the 3 (from 3x^2) forms pairs 1,3
that means the factors will be
(1x )(3x )

now, instead of using -6 (the last number) we find the pairs for
3*6 =18

1,18
2,9
3,6

the -6 means different signs
the -17x means the larger one is -, and they add to -17
1, -18 is the pair that works

now we have to undo the 3*6 (if that makes sense)
divide one of the pair by 3: -18 can be divided. we get -6
we get
(x-6)(3x+1)

Answer 3

the other way to find the factors is test if either of the factors in the top divide into the bottom ... going on the theory that one or the other will "cancel"

Answer 4

How do you factor 2x^2+13x+20?

Answer 5

@phi

Answer 6

the 2 from 2x^2 means the factors will be
(2x ) (x )

now, look at the last number 20 times the 2= 40
list pairs of 40
1,40
2,20
4,10
5,8

+20 means same sign
+13x means largest is + (so both are plus)
which pair adds to 13 ?

Answer 7

5 and 8

Answer 8

now we "undo" the multiply by 2 (when we did 2*20 to get 40)
divide the 8 by 2 to get 4
the pair we want is 5,4

the last thing to do is figure out where the 5 and 4 go

Answer 9

we want to put the 4 in the factor so it gets multiplied by 2x (to get 8x)
(2x +5)(x+4)