Question

how do i factor x^2-9x+10?

Answer 1

find two numbers that multiply to 10 and add to -9

Answer 2

so -10 and 1?

Answer 3

notice how -10 times 1 = -10 though

Answer 4

but we want them to multiply to +10 or just 10

Answer 5

-10 and -1? but then doesnt that equal -11?

Answer 6

yes so we get +10 when they multiply but -11 when they add

Answer 7

so then how do you get -9?

Answer 8

the only other factors besides 1 and 10 are 5 and 2 but that equals 7

Answer 9

well it turns out that there are no two whole numbers that both

a) multiply to 10

AND

b) add to -9

at the same time


so this all means that x^2-9x+10 CANNOT be factored

Answer 10

so we say x^2-9x+10 is prime

Answer 11

oh! ok so next i have 4y^2-49 how would i do that?

Answer 12

hint: difference of squares

Answer 13

so would i need to find the square root of both numbers or just one?

Answer 14

sorry im horrible at math... :/

Answer 15

of both, so what is the square root of 4y^2?

Answer 16

the square root of 8 is 2.82

Answer 17

and 49 is 7

Answer 18

4y^2 is the same as (2y)^2

you take the square root of 4 to get 2
you take the square root of y^2 to get y

so that's how I got 2y

Answer 19

so

4y^2 - 49

turns into

(2y)^2 - 7^2

Answer 20

now you use the difference of squares formula

Answer 21

so it would be 2^2-7^2?

Answer 22

the difference of squares formula is

a^2 - b^2 = (a-b)(a+b)

Answer 23

so in this case

a = 2y
b = 7

Answer 24

oh! so it's (2-7) (2+7)

Answer 25

very close, but you're missing the y

Answer 26

it should be

(2y-7) (2y+7)

Answer 27

ok! im sorry but i have two more i dont understand. can you help me real quick?

Answer 28

sure

Answer 29

ok so there's 4n^2-20n+25

Answer 30

have you learned about perfect square trinomials?

Answer 31

my teacher just went over what a trinomial was but i dont know what to do.

Answer 32

would you just find the square root of 4 and 25?

Answer 33

yes what is the square root of each?

Answer 34

2 and 5

Answer 35

notice how 2*5 = 10

and if you double that, you get 2*10 = 20

Answer 36

because this is equal to the middle coefficient (ignore the negative), this means we have a perfect square trinomial

Answer 37

so it would be (2+5) (2+5)?

Answer 38

i mean (2n+5)(2n+5)

Answer 39

close, but the middle coefficient is negative, so you have to change all the + signs to - signs

so it should be (2n-5)(2n-5)

Answer 40

ok and now there's 100-w^2

Answer 41

would this be common factoring? because i have to also place them in either trinomial, difference of squares or common factoring

Answer 42

this is another difference of squares

Answer 43

100 is a perfect square (100 = 10^2)

w^2 is a perfect square

Answer 44

so it would be (10-w)(10-w)?

Answer 45

yep, you nailed it

Answer 46

oh wait, sorry

Answer 47

it's actually

(10-w)(10+w)

the signs should alternate

Answer 48

wow i suck haha

Answer 49

since it's a difference of squares and the rule is

a^2 - b^2 = (a-b)(a+b)

Answer 50

no you don't, get that idea out of your head, it's definitely not true and not helpful

Answer 51

you just made a silly typo

Answer 52

so it's (w-10)(w+10)?

Answer 53

no you just needed to change one sign so it's (10-w)(10+w)

Answer 54

100 - w^2 = 10^2 - w^2

100 - w^2 = (10-w)(10+w)

Answer 55

ok so how do i figure out if one of them is common factoring because i also have 2x^2-8x, x^2-9x, 2m^2-9m+4, and 4x^2+x

Answer 56

if you don't know, that's fine

Answer 57

2x^2 and -8x have a 2x in common, so you factor that out to get

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

Answer 58

so 2x(x-4) would be the answer?

Answer 59

yes after factoring 2x^2-8x

Answer 60

notice how if you distributed that 2x back through, you'd get 2x^2-8x back again

Answer 61

oh so 2x(x-4) is the factored answer?

Answer 62

yes

Answer 63

im sorry i keep asking you questions but for 2m^2-9m+4 would i just find the common factor of 2 and 4?

Answer 64

hmm this is pretty complicated, so one sec

Answer 65

ok

Answer 66

ok the steps are pretty long and drawn out, so I had to post them elsewhere (I was able to post a table and use different colors and such, so that's why I posted it there)


anyways, it's posted here

http://www.algebra.com/algebra/homework/equations/Equations.faq.question.787996.html


let me know what you think and feel free to ask questions on any step you have

Answer 67

ok :)

Answer 68

you're a genius!

Answer 69

thanks lol

Answer 70

sounds like things are clicking now, which is great

Answer 71

you should literally be my algebra 2 teacher. i learn more from you hahaha

Answer 72

I'm glad you are learning, but I'm sure you learned stuff from your teacher too

Answer 73

im pretty sure i can do the last two by myself but i just have one last quick question. would x^2-9x and 4x^2+x be difference of squares or common factoring?

Answer 74

x^2-9x would be common factoring (they have x in common)

so is 4x^2 + x (this also has x in common)

Answer 75

so x^2-9x would be x(x-3)?

Answer 76

close, but it's really x^2 - 9x = x(x-9)

Answer 77

to check, distribute that x back through and you will get x^2 - 9x again

Answer 78

oh ok i get it now. so that makes 4x^2+x= 4x(x+x)?

Answer 79

4x^2 and x do NOT have 4 in common

Answer 80

they have x in common so it would be x(x+4x)?

Answer 81

actually it should be 4x^2 + x = x(4x + 1)

Answer 82

is that because having the x where the 1 is would make it x^2?

Answer 83

instead of just x?

Answer 84

well it's because x is also x*1

Answer 85

so that means

4x^2 + x

x*4x + x*1

x(4x + 1)

Answer 86

see how that works?

Answer 87

yup! well that's all of my homework for tonight. thank you so much again! you don't understand how much you've helped me :)

Answer 88

you're welcome, I'm glad to be of help