how do you factor trinomials

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how do you factor trinomials

Mathematics
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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
I know my teacher cant even do it
haha do you have a specific problem?

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yeah I just dont know how to do exponents on the computer
you can use the equation button down on the left of just do shift 6 its the ^ which means exponent
2x squared- 14x - 36 we have to do polynomials in the x squared+ bx +c
ok so you have \[2x ^{2} - 14x - 36 =0\]
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
sorry the @ is suppose to be 2
ok so notice all the coefficients can be factored out a 2 so you have\[ (x ^{2} - 7x - 16) = 0\]
yeah good
oops its \[2 (x ^{2} - 7x - 18) = 0\]
yeah thats what I got but then I have to find the factors of 18 and then im lost
yeah ok. so the trick is to find two numbers that add up to -7 but when multiplied together equal -18
so it would be 2 and 9
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
yeah good job
but then what do you do?
something like ( x-9) ( x+2)
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
oops YES
haha sorry i mean that
you are correct
then you have your roots, x=2, x=-9
does it matter which one goes where can I switch them and get the samething
so whats the answer
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
those are your roots
in the back of the book its 2(x+2) (x-9)
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
I was solving two but I got as far as the last part. Do you mind helping me on another?
sure
-x^3+6x^2+16x I have to solve and factor
I got x(-x^2+6x+16) is that right?
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)
so are the factors then -2 and 8
are you sure? 8 + -2 = 6
yeah isnt it?
no switch the signs. then you have -8 and 2 which -8*2 = -16 and -8 + 2 = -6 which is what we want
oh we need -6
so how do you pull a number or variable from 4y-45+y^2
ok you can't since you have to see that there is no coefficient on y^2
thats what I thought but in the back of the book it says (y-5) (y+9)
think of some basic multiples of 45 ...one to try is 5 since 45 ends in 5
rearrange the polynomial...its really y^2 + 4y - 45
so all you have to do is factor in a problem like that
yeah thats it
so are you doing the same thing with x^2-72+6x
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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