PLEASE HELP :)! i have a whole worksheet on factoring and i dont know how to do it! here are some of them! please explain and help me work them out.

Question

anonymous · Answer

$$a ^{2}-5a+6$$

hartnn · Answer

what are the 2 numbers whose product is 6 and sum = -5 ?

anonymous · Answer

$$a ^{2}-8a-9$$

anonymous · Answer

hmm 2 numbers whose product is 6 are 3 and 3?

hartnn · Answer

but sum is not -5
wait! 3*3 is not 6 :P

anonymous · Answer

haha thought you meant plus :p okay so -3 and 2 ?

hartnn · Answer

-3*2 is -6
not +6

hartnn · Answer

hint: both are  negative

anonymous · Answer

ergggg i dont know im sorry

hartnn · Answer

try -2 and -3 ??
is product 6 ? is sum -5 ?

anonymous · Answer

Your product, 6 is positive, and the sum, -5, is negative, so the two numbers which are factors of 6 wil both be negative.  Your factors have to both be negative, otherwise you could not get a -5 sum from two positive numbers.

anonymous · Answer

@tcarroll010 oh okay so could you show me how to properly write that?

anonymous · Answer

Well, @hartnn did give you the right numbers.  The factoring form is (a +- some number)(a +- the other number)

anonymous · Answer

okay so, (a-2)(a-3) ?

hartnn · Answer

yup

anonymous · Answer

Yes!  But to verify that and to consolidate your understanding, you should try going in the other direction and multiplying it out.  Do this in the beginning with these types of problems.  If you go backward and forward, you will gain a lot of understanding and insight.

anonymous · Answer

thankyou so much guys! so just one more example to make sure i got it lol. if i had n^2-2n-24  it would be (n+4)(n-6) @hartnn @tcarroll010

hartnn · Answer

yup, correct!

anonymous · Answer

thankyou!

hartnn · Answer

welcome ^_^

anonymous · Answer

does it matter if i were to write it vice versa? like (n-6)(n+4)

hartnn · Answer

DOES NOT MATTER.