Question

4x^2-9x+5/4x^2+7x-15. They'll factor into?

Answer 1

First break each of the numerator and denominator into its factors....

Answer 2

(4x )(x ) and same for the second one, but then what?

Answer 3

it is possible that it is (2x+..)(2x+...) also

Answer 4

Whether it's 2x and 2x or just 4x in the end ill have the same answer

Answer 5

I'm afraid that is not true

Answer 6

Like, the \[4x ^{2}-9\] will break into (4x-5)and (x-1)....then after completely breaking them into their factors, if they do not cancel out...keep them like that...

Answer 7

@Sourav12084 and for the other one (The denominator) do i use 1 and 15 or 3 and 5?

Answer 8

Hey...(4x-5) is a common factor in the numerator and denominator...in the denominator, break 7x into 12x-5x...

Answer 9

After that factorise it....

Answer 10

@Sourav12084 Got A. Thank you.

Answer 11

In THIS case both expressions factorise as (4x+a)(x+b)

but PLEASE be aware that (2x+a)(2x+b) is a possible factorisation - and will NOT give the same answer

Answer 12

@MissyMartinez : Glad I could help...

Answer 13

@MrNood Maybe not all the time.

Answer 14

@MissyMartinez

The point I am trying to make is a general point about factorising:

You saw "4x^2" and IMMEDIATELY decided it MUST be (4x )(x )

This will lead you into difficulties if you do not realise that the number in front of the "x^2" term can factorise as well.

For example

\[4x ^{2}+20x+21 = (2x+7)(2x+3)\]
The only values that a & b can be are 1 & 21 or 7 & 3 (because we need a*b = 21)

(4x+a)(x+b) is not a valid factorisation for either of those pairs (to give "20x")