Algebra Factoring?

Question

I have really big test tomorrow and i need your help. I can not figure out these 3 problems
10 pts best answer

1) xsquared + 33x - 108

2)18 - 9x - 35xsquared

3) 6 + 7 - 20xsquared

Answer 1

Take a deep breathe first before reading this... Did you? Okay... now 'read' slowly to absorb what I'm saying...

Problem 1...

x^2 + 3x - 108...

in factoring you know the FOIL method... you use that method to get what you have above as the answer...

the only difference here is that you are doing the problem 'backwards'... THEY give you what the result was when you multiply two numbers... and now you have to find out the two quantities that were multiplied...

remember the FOIL method?... it goes something like...

first multiply "F"irst two terms....

then multiply "O"uter two terms...

then multiply "I"nner two terms...

then multiply "L"ast two terms...

soo....remembering the FOIL method... you are 'trying' to find two number that when multipled together will equal -108.... a NEGATIVE 108....

and according to FOIL method... these SAME two number ALSO have to add up to +33...

so what two numbers when multiplied together will equal -108,... and when added together will equal +33?

to find that out... what is 108 divisible by? 3? let me see... 108 divide by 3 is...? 36! YES! sooo... now see if 3 and 36, using various + and -'s... what combination will add up to 33.... you KNOW that one has to be - and the other to get + to get a -108.... you ALSO know that the BIGGER number has to be + to get a POSITIVE 33... so what works???

Yup... +36 and -3.... (+36)*(-3) = -108... and +36 + -3 = +33...

so you now get...

x^2 + 3x - 108.... is the same as (x+36)(x-3)...

you FOIL method to 'check' if you are right and you factor right... multiply 'f'irst 2 terms, 'o'uter two terms, 'i'nner terms, and 'l'ast 2 terms... get it? F - O - I - L.... that's why it's called FOIL method...

does (x+36)(x-3) = x^2 + 3x - 108? If you do the math and multiplication of the two () quantities.. you SHOULD get the given problem...

Okay... Problem 2...

18 - 9x - 35x^2...

well... for this problem.. put it into x^2 + x + number order.... order it like that.... so that you can apply the FOIL method thinking....

so 18 - 9x - 35x^2 becomes -35^2 - 9x +18.... do you see what I did? in ordering the terms? higher powers to lower powers.... x^3...next x^2... next x which is same as x^1... and then whole number...

soo... now we are working with -35x^2 - 9x +18

how can you break this up ('factor') so that FOIL will work...?

well this problem is a bit more challenging... because you don't have x^2 like the first... you have this -35 hanging around... so... how can you factor -35x^2 so that when you 'multiply' you 'will' get -35x^2???

well... figure out what 35 is divisible by first... 7 and 5 when 'multiplied' will give you 35... right? Okay... and you know that each of them have an 'x'... right? Okay...so 7x and 5x....BUT... 'one' of them has to be NEGATIVE to get -35x^2... MINUS 35x^2... right? Okay...

so it's either the combo +7x and -5x or it's the combo -7x and +5x... sooo... which is it???... well... at this point you 'don't' know.... you need to find 'other clues'.... but at least you know that it is one of two combinations... at least for the first two terms in the () () when you finally factored.

Look at the last term of what I had rewritten...

-35^2 - 9x +18... so the last two numbers in the ()() have to multiply to equal POSITIVE 18... it could be 1 and 18 .... or -1 and -18 (because 2 negative multiplied equal a positive)... it could be 2 and 9 ... or -2 and -9... it could be 3 and 6 ... or -3 and -6...

you have to find out what combinations... by trial and error (no one can really teach you have to do trial and error... but you have to try out all the possible combinations... when you do.... you should get...

-35^2 - 9x +18 is the same as saying (-5x+3)(7x+6) because when you multiply the ()() result... what do you get using FOIL?

first multiply "F"irst two terms....

then multiply "O"uter two terms...

then multiply "I"nner two terms...

then multiply "L"ast two terms... and then add the 4 terms together...

you get...(-5x+3)(7x+6) = (-5x * 7x) + (-5x * +6) + (3 * 7x) + (+3 * +6)

which equals... -35x^2 + (-30x) + (21x) + 18...

combine all like terms... and you get -35x^2 -9x + 18...

Is that what you were given? Yup... just the given was written with the terms in a different order... but the order doesn't matter....

Phew!... and here is the LAST problem...

uhh... I don't know how the answerer after me solved that... because I think you are missing an 'x' somewhere... 6x? or 7x?... because what you gave is equal to 13 - 20x2... and there is nothing to factor here....

but if you give me the problem as written... I will be happy to work it out for you so that you can do well on your test tomorrow....

2 and 3 are the harder of the three problems you gave, because they require a lot more thought...

things to be factored with just x^2... are the easiest problems to solve and factor... things with a number in front of the x^2 are much harder... because they are much harder and challenging (even for an adult...LOL)... expect to see at least one of those on the test... maybe more... because that is how the teacher can 'know' that you really mastered the skill of factoring.... it's being able to solve Prob 2 and prob 3... that will separate you from the rest of the people in your class. It's not enough just to know how to solve only ones like Problem 1. So what I would do... is go through your textbook and do TONS of ones like the last two problems... because if you can solve those... then you can solve ANYTHING.... I promise you.... you will.... but you have to master doing Problem 1 first.... because without the understanding of the 'process' or factoring... you won't be able to attack the last two problems... it would be all in vain, to say it nicely....

I'll be checking on you to see your last problem correctly written... I'm going to eat dinner now... and will be back...

Answer 2

ok always think this when doing quadratic trinomials
#1

the 33x means to number have to add to 33
and the 108 means the two numbers have to multiply to get 108

108/3 is 36 so 36-3 can make 33
so now just plug it in and try it out
(x- 3 ) (x+ 36 )
another tip
if you want postive 33(or 36-3)then the big number goes in the second one. if its negtive you want to get(like -33) then its the opposite!!


sorry, for the other 2, im not going to try because i dont trust myself and dont want to give you wrong answers

but number 1 i am sure of

Answer 3

1. (x+36)(x-3)


2. (-5x+3)(7x-6)

3. (-4x+3)(5x+2)