Question

@johnweldon1993 I need help factoring again > . <

Answer 1

lol yes? :)

Answer 2

One sec, writing em on sketchtoy. I have two problems :P

Answer 3

haha okay :P

Answer 4

http://www.sketchtoy.com/40506599

Answer 5

Hang on ...taking time to load for me...

Answer 6

Okay...well that one is fairly simple...

what are the factors of 15?
and what are the factors of 2?

Answer 7

ACTUALLY!!! want to do the quadratic formula??? :) I know you asked me about it earlier...

Answer 8

Let's do regular first, then quadratic. ^_^

Answer 9

Factors of 15 are 3 and 5 and factors of 2 are 1 and 2

Answer 10

well ...the full factors are

15 = 1 , 3 , 5 , 15 ...but yes you chose the only 2 important ones here lol
and yes
2 = 1, 2

so

we know we need 2x² not just x² ...so there will not just be

(x 3)(x 5)

instead we will have

(2x + 3)(x + 5)

*we want positives because we have both positive numbers....so that's it...that's your factorization

Answer 11

Do you want to solve for the zeros?

Answer 12

What do you mean, the zeros?

Answer 13

Here...the quadratic formula solves for the zeros of the function...so I'm sure that's what you wanted

Answer 14

>.< uh ok

Answer 15

So we have

(2x + 3)(x + 5) = 0

right?

we can break that up

2x + 3 = 0
x + 5 = 0

solve for x in each equation

Answer 16

Lol you seem to be very confused based on that face lol....let me start over...

you have

2x² + 13x + 15 = 0 to start with right?

Answer 17

Yes

Answer 18

Okay...well see how it is set to = 0? that means we want to find out what values of 'x' make that equation = 0 okay? This is done by factoring! *this is what I meant when I said find the zeros

Answer 19

So....We factored....and now we are able to figure out exactly what values of 'x' make that equation = 0

(2x + 3)(x + 5) = 0

we know that with either of the parenthesis...we only need 1 to = 0 in order for everything to = 0 right?

(0)(x + 5) = 0 because anything times 0 = 0 right?

so

we can split this into 2 equations

2x + 3 = 0
and
x + 5 = 0

can you solve for 'x' in each of those equations?

Answer 20

Both x's would be 0, right? > _ <

Answer 21

Not quite...

2x + 3 = 0

if 'x' = 0 then you would have

2(0) + 3 - 0
0 + 3 = 0

3 = 0

is this correct?

Answer 22

Ohhh, you have to have it equal 1... right?

Answer 23

Here I'll do this one for you

2x + 3 = 0

you want to subtract 3 from both sides to get 2x by itself

2x + 3 = 0
-3 -3

2x = -3

divide both sides by 2 to completely isolate x...

2x = -3
--------
2 2

x = -3/2

This is one "zero" meaning...if you plugged in (-3/2) into your original equation...you would get 0 which is what you want...

so now

x + 5 = 0

what does x = ?

Answer 24

-5 ?

Answer 25

Did you want to use the quadratic formula? If so you need to have an equation, something with an equal sign, What you have written is an expression, it can be factored, but there is no zeros unless itself is equal to zero.

Answer 26

I think I already have one factored enough. Can you help me with the second one?

Answer 27

*I only saw one. The first one factored to (x+5)(2x+3)

Answer 28

What does the second one look like?

Answer 29

@unheard do you have a second one?

Answer 30

Good luck with your studies.

Answer 31

@jim_thompson5910 can you help me with 5x^2-2x-7 ?

Answer 32

What are the factors of \(5x^2\)?
What are the factors of 7?

Answer 33

another way to factor is to first solve 5x^2-2x-7 = 0 for x (use the quadratic formula)

once you have the roots, you can use them to factor

Answer 34

The factors of 7 are 1 and 7 and the factors of 5 are 1 and 5. I don't know about the x^2 part >.<

Answer 35

@eSpeX ?

Answer 36

@jim_thompson5910

Answer 37

what do you get when you solve 5x^2-2x-7 = 0 for x

Answer 38

Can you break the problem up so it makes it easier for me to work it out. > . <

Answer 39

are you familiar with the quadratic formula?

Answer 40

Kinda. It's really hard.

Answer 41

5x^2-2x-7 = 0

a = 5
b = -2
c = -7

Answer 42

the discriminant is

D = b^2 - 4ac

D = (-2)^2 - 4(5)(-7)

D = ???

Answer 43

4 - (-140)

Answer 44

keep going

Answer 45

144

Answer 46

since that is a perfect square, this means that you'll get 2 rational solutions

this means the original expression can be factored

Answer 47

if you didn't get a perfect square, then it couldn't be factored and you can move on and not bother to try to factor it

Answer 48

anyways, you then take the square root of this to get sqrt(144) = 12

Answer 49

you will then have

x = (-b+sqrt(D))/(2a)

x = (-(-2)+sqrt(144))/(2*5)

x = (2+12)/(10)

x = (14)/(10)

x = 7/5

that's one solution

Answer 50

the other solution is

x = (-b-sqrt(D))/(2a)

x = (-(-2)-sqrt(144))/(2*5)

x = (2-12)/(10)

x = (-10)/(10)

x = -1

Answer 51

Thanks for taking it over @jim_thompson5910 !

Answer 52

now that you know the two solutions are x = 7/5 and x = -1, we can do this

x = 7/5 or x = -1

5x = 7 or x = -1

5x - 7 = 0 or x +1 = 0

(5x - 7)(x + 1) = 0

Answer 53

so this shows that 5x^2-2x-7 = 0 turns into (5x - 7)(x + 1) = 0

which means 5x^2-2x-7 factors to (5x - 7)(x + 1)

Answer 54

Thanks!

Answer 55

yw