Question

solve by factoring:

5x^2 + 9x - 72 = 0

Answer 1

@jim_thompson5910 can you help? I just cant figure out the factors that would sum up to 9

Answer 2

this might be a bit ugly

Answer 3

5*(-72) = -360

Answer 4

you need to find two numbers that

a) multiply to -360

AND

b) add to 9

Answer 5

15 & 24!

Answer 6

so you would list out the ways to multiply to -360 (ie factor it)

-1*360
-2*180
-3*120
...
...
etc etc

then add up each factor pair

-1+360 = 359 ...is that equal to 9? no, so move on
-2+180 = 178...is that equal to 9? no, so move on
-3+120 = 117...is that equal to 9? no, so move on
etc etc

Answer 7

15+24 = 39 not 9

Answer 8

however

24 + (-15) = 9

Answer 9

5x^2 + 9x - 72

5x^2 + 24x - 15x - 72

now factor by grouping

Answer 10

5x^2 + 9x - 72 = 0
I suppose we could use the quadratic formula?
\[\frac{ -9\pm \sqrt{9^{2}-4(5)(-72)} }{ 2(5) }\]

Answer 11

Wouldn't it be... (5x + 24)(x - 15)

Answer 12

I mean we can find the zeroes and then just group them?

Answer 13

5x + 24 = 0
5x = -24
x = -24/5

x - 15 = 0
x = 15

Answer 14

yes you could use the quadratic formula to find the zeros/roots

then you use that to find the factorization

that's probably the most efficient method

Answer 15

Exactly.

Answer 16

but here's how you factor it by grouping

5x^2+9x-72


5x^2+24x-15x-72


(5x^2+24x)+(-15x-72)


x(5x+24)+(-15x-72)


x(5x+24)-3(5x+24)


(x-3)(5x+24)



---------------------------------------------------------------------------

So


5x^2+9x-72


completely factors to


(x-3)(5x+24)

Answer 17

actually its x = 3 and x = -24/5

Answer 18

^ @angelina22309

Answer 19

ok I get it, How do you know when you need to factor by graphing? Why woulnt have mine worked?

Answer 20

Could you also help with

3x^2 + 19x - 50 - 0

Answer 21

your method only works when the leading coefficient is 1

Answer 22

example

x^2 + 5x + 6

factors to

(x+3)(x+2)

since 3+2 = 5 and 3*2 = 6

Answer 23

oh ok. thanks!! I need to keep that in mind

Answer 24

@jim_thompson5910
Please let me know if I did this correctly.

3x^2 + 19x - 50 = 0

3x^2 + 25x - 6x - 50

(3x^2 + 25x) + (-6x - 50)

x(3x + 25) + (-6x - 50)

x(3x + 25) -2(4x + 25)

(x - 2)(4x + 25)

Answer 25

@some_someone could you check this please ^

Answer 26

3x^2+19x-50


3x^2+25x-6x-50


(3x^2+25x)+(-6x-50)


x(3x+25)+(-6x-50)


x(3x+25)-2(3x+25)


(x-2)(3x+25)



---------------------------------------------------------------------------


3x^2+19x-50


completely factors to


(x-2)(3x+25)

Answer 27

so the only mistake you made was writing 4x instead of 3x on this line

x(3x + 25) -2(4x + 25)

Answer 28

thanks @jim_thompson5910

Answer 29

yw