how do you factor trinomials

- anonymous

how do you factor trinomials

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- schrodinger

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- anonymous

you can use pascal's triangle or the binomial theorem or by factoring the first two and the second two and seeing if a common factor emerges...its kind of hard to explain

- anonymous

I know my teacher cant even do it

- anonymous

haha do you have a specific problem?

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## More answers

- anonymous

yeah I just dont know how to do exponents on the computer

- anonymous

you can use the equation button down on the left of just do shift 6 its the ^ which means exponent

- anonymous

2x squared- 14x - 36
we have to do polynomials in the x squared+ bx +c

- anonymous

ok so you have \[2x ^{2} - 14x - 36 =0\]

- anonymous

no we have to pull the lowest number and the lowest variable then divide each term by that so I know its @ because they all dont have a common variable then divide each term by 2

- anonymous

sorry the @ is suppose to be 2

- anonymous

ok so notice all the coefficients can be factored out a 2 so you have\[ (x ^{2} - 7x - 16) = 0\]

- anonymous

yeah good

- anonymous

oops its \[2 (x ^{2} - 7x - 18) = 0\]

- anonymous

yeah thats what I got but then I have to find the factors of 18 and then im lost

- anonymous

yeah ok. so the trick is to find two numbers that add up to -7 but when multiplied together equal -18

- anonymous

so it would be 2 and 9

- anonymous

so look at 9 and 2. 9*2 = 18 but you want one to be negative so you have -18 and you want them to add to -7. so try -9*2 = -18 and -9 + 2 = -7

- anonymous

yeah good job

- anonymous

but then what do you do?

- anonymous

something like ( x-9) ( x+2)

- anonymous

ok so now you factor them you know one is -9 and one is 2 so you subtract them from x. you get
(x-2)(x+9)=0 and by FOILing you get x^2 -7x -18 = 0

- anonymous

oops
YES

- anonymous

haha sorry i mean that

- anonymous

you are correct

- anonymous

then you have your roots, x=2, x=-9

- anonymous

does it matter which one goes where can I switch them and get the samething

- anonymous

so whats the answer

- anonymous

no it does matter
if you had what i put you'd have (x-2)(x+9) = 0 and you get x^2 + 7x - 18 which is not correct.
the answer is x =-2, x = 9

- anonymous

those are your roots

- anonymous

in the back of the book its 2(x+2) (x-9)

- anonymous

oh you were just factoring? sorry i thought you were solving.
yeah we factored out the 2 remember? we have to bring it back in
so mulitply it by what you told me
and its the answer

- anonymous

I was solving two but I got as far as the last part. Do you mind helping me on another?

- anonymous

sure

- anonymous

-x^3+6x^2+16x I have to solve and factor

- anonymous

I got x(-x^2+6x+16) is that right?

- anonymous

yeah you could do that but it might be easier to factor out a negative. just so its a little simpler to look at. so you could just have -x(x^2 -6x - 16)

- anonymous

so are the factors then -2 and 8

- anonymous

are you sure? 8 + -2 = 6

- anonymous

yeah isnt it?

- anonymous

no switch the signs. then you have -8 and 2 which -8*2 = -16 and -8 + 2 = -6 which is what we want

- anonymous

oh we need -6

- anonymous

so how do you pull a number or variable from 4y-45+y^2

- anonymous

ok you can't since you have to see that there is no coefficient on y^2

- anonymous

thats what I thought but in the back of the book it says (y-5) (y+9)

- anonymous

think of some basic multiples of 45 ...one to try is 5 since 45 ends in 5

- anonymous

rearrange the polynomial...its really y^2 + 4y - 45

- anonymous

so all you have to do is factor in a problem like that

- anonymous

yeah thats it

- anonymous

so are you doing the same thing with x^2-72+6x

- anonymous

yeah exactly the same. sometimes if it helps you to see it you should rewrite it in the form ax^2 + bx + c to see it. if you can already see it then it doesnt matter.

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