Question

I need help factoring x squared minus 12x + 3

Answer 1

You need to find two numbers that multiply to 3 and add to 12

Answer 2

oops meant -12

Answer 3

-1, 0 ??

Answer 4

No

Answer 5

-3, -6?

Answer 6

No, (-3)*(-6) = 18, but we want 3

Answer 7

1,-3

Answer 8

closer, but 1*(-3) = -3, and we want positive 3

Answer 9

1 and 3?

Answer 10

better, but there's a problem, does 1 and 3 add to -12?

Answer 11

no

Answer 12

so it's not 1 and 3. The same can be said about -1 and -3

Answer 13

-4 and -3?

Answer 14

no because -4 times -3 is NOT 3

Answer 15

we've basically run out of options because the only factors of 3 are 1 and 3


so because we've exhausted everything and still haven't found the two numbers, this means that x^2-12x+3 can't be factored

Answer 16

hmmm I have to solve this equation (x-4) squared equals 2x squared minus 4x+19

Answer 17

correct, kind of like 0 lol

Answer 18

and solve for x

Answer 19

what do you get when you expand out (x-4)^2

Answer 20

x squared + 16

Answer 21

is that right?

Answer 22

close, but there should be a middle x term

Answer 23

x squared -4x+16?

Answer 24

I get stuck on the middle x term when I'm expanding

Answer 25

Complete steps and answer for expanding (x-4)^2:


(x-4)^2 = (x-4)(x-4)


(x-4)^2 = x(x-4)-4(x-4)


(x-4)^2 = x*x+x*(-4)-4*x-4*(-4)


(x-4)^2 = x^2 - 4x - 4x + 16


(x-4)^2 = x^2 - 8x + 16


So (x-4)^2 expands out to x^2 - 8x + 16

Answer 26

So


(x-4)^2 = 2x^2 - 4x+1


turns into


x^2 - 8x + 16 = 2x^2 - 4x + 1

Answer 27

Let me know if that helps or not.

Answer 28

ya that helped. so now the equation would be 2x^2 - 4x - 8x+16+19?

Answer 29

well if it were an equation, there'd be an equal sign somewhere...not sure where you placed yours in that last expression.

Answer 30

oh it's 0 equals that equation

Answer 31

so now I just need to factor that equation, so I can solve for x

Answer 32

You should have


x^2 - 8x + 16 = 2x^2 - 4x+19


0 = 2x^2 - 4x+19 - x^2 + 8x - 16


0 = x^2 + 4x + 3

Answer 33

so then x is -1 and -3

Answer 34

you nailed it

Answer 35

thanks so much for your help

Answer 36

you're welcome

Answer 37

could you check if I did this right? I have (v+5)^2 which needs to be expanded. I got v^2+50x+25

Answer 38

and if I didn't could you explain what I did wrong?

Answer 39

you have the middle term incorrect

Answer 40

try thinking of (v+5)^2 as (v+5)(v+5)

Answer 41

then expanding that to get v(v+5)+5(v+5)

Answer 42

would the middle term be 10v?

Answer 43

bingo

Answer 44

so now I have to factor out 0 equals 2v^2 + 14v+29+10v+25

Answer 45

so combine like terms on the right side, what do you get when you do that?

Answer 46

2v^2+24v+54

Answer 47

the gcf is 6 I believe

Answer 48

no, 6 does not go into 2v^2

Answer 49

then is it 2?

Answer 50

yes

Answer 51

factor out 2 to get???

Answer 52

so I have (v+4) (2v+)

Answer 53

if you factor out a 2, you'll go from 2v^2+24v+54 to 2(v^2+12v+27)

Answer 54

so you can focus on factoring v^2+12v+27

Answer 55

(v+9)(v+3)

Answer 56

good, so the complete factorization is 2(v+9)(v+3)

Answer 57

that didn't work...when I entered the answers, it came out wrong

Answer 58

what was the original problem

Answer 59

(v+5)^2=2v^2+14v+29

Answer 60

oh i see where you went wrong, you somehow added 10v to 14v when you should have subtracted 10v from 14v

Answer 61

ohhh

Answer 62

same with 29+25, it should be 29-25

Answer 63

which makes -4v

Answer 64

so now I have 2v^2-4v+4

Answer 65

the stumbling block you're dealing with is taking v^2+10v+25=2v^2+14v+29 and converting it into 0 = v^2 + 4v + 4

Answer 66

ya

Answer 67

this is where your mistake occurred

Answer 68

the key is to get everything to one side

Answer 69

to do that, we subtract v^2 from both sides, then we subtract 10v from both sides, finally we subtract 25 from both sides

Answer 70

ok

Answer 71

why all those subtractions? I did all that to make the left side equal to 0

Answer 72

so now I have to factor out v^2-4v+4

Answer 73

more like v^2+4v+4 since 14v-10v = 4v

Answer 74

I see what I did wrong

Answer 75

that's great

Answer 76

would (w-1)^2 be expanded as w^2 +2w+2?

Answer 77

close, it should be w^2-2w+1

Answer 78

(w-1)^2 = (w-1)(w-1) = w(w-1) - 1(w-1)

Answer 79

my online math program logged out and now it changed my problem. I now have to expand (w+6)^2, and expanding that got me x^2+36w+36

Answer 80

the middle term is off

Answer 81

I don't know why expanding is so hard for me

Answer 82

(w+6)^2 = (w+6)(w+6)

Answer 83

is the middle term 12w?

Answer 84

yes

Answer 85

I just solved the problem

Answer 86

that's great, glad you're getting the hang of this

Answer 87

4