Factor the following polynomials correctly
q^2-9q+18

- mitu12

Factor the following polynomials correctly
q^2-9q+18

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- TrojanPoem

(q - 6)(q-3)

- sweetburger

what 2 values multiply to equal 18 and add to equal -9... alright nm

- mitu12

could you explain how to do this

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## More answers

- anonymous

Your first two automatics are the q's

- anonymous

so we have (q+-?)(q+-?)

- mitu12

ok

- TrojanPoem

@sweetburger , that's how I do it. You could complete the square.

- anonymous

Next thing you have to do is find what multiplies to =18

- anonymous

so what are some factors of 18

- mitu12

-6 and -3

- sweetburger

something interesting to note when the notation is like this ax^2-bx+c the final form will look like this (q+-?)(q+-?). if the form looks like ax^2-bx-c then the notation will look like this (q+-?)(q+?). And finally if it looks like this ax^2+bx+c the notation will look like this (q+?)(q+?).

- anonymous

correct and then once you get your factors plug them in for the ?'s and test and see if they work. To test it you simply multiply the sets in the parenthesis by each other.

- sweetburger

@TrojanPoem I do actually know how to do these kind of problems so you dont have to tell me...

- TrojanPoem

@manutdd30 , Well, now he knows them. But how about this ?
i.e: 2x^2 - 18 x + 40 @mitu12

- TrojanPoem

@sweetburger , I was telling you I do it the same. BUt complete the square is for mitu12

- TrojanPoem

Work up. your brian.

- sweetburger

The question in your example you just apply the quadratic or use the rational root theorem and then use the remainder theorem

- TrojanPoem

-,- , Not for you @sweetburger , it's for @mitu12.

- anonymous

Trying to factor by splitting the middle term
2.1 Factoring q^2-9q+18
The first term is, q^2 its coefficient is 1 .
The middle term is, -9q its coefficient is -9 .
The last term, "the constant", is +18
Step-1 : Multiply the coefficient of the first term by the constant 1 • 18 = 18
Step-2 : Find two factors of 18 whose sum equals the coefficient of the middle term, which is -9 .
-18 + -1 = -19
-9 + -2 = -11
-6 + -3 = -9 That's it

- anonymous

^ What do you think you should do next?

- mitu12

the two factors are -6 and -3

- anonymous

Yes… then what?

- mitu12

then i think you plug them into the parenthesis

- anonymous

lol no…
Please don't give out direct answers :) @TrojanPoem Instead, try engaging the asker so they can learn better and understand where your answer is coming from.
As the saying goes…
\(\\\color{darkblue}{Give~a~man~a~fish,~he~eats~for~a~day.}\)
\(\\\color{pink}{Teach~a~man~to~fish,~he~eats~for~a~lifetime.}\)

- anonymous

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -3
q^2 - 6q - 3q - 18

- sweetburger

Technically there are 3 more factors that should be included which are 18,1 2,9 and 3,6 due to the c value being positive.

- sweetburger

I know you were limiting them for clarification but just putting that out there.

- anonymous

Thanks :)

- sweetburger

Nice job @Aureyliant :).

- anonymous

@mitu12 What do you believe you should do for step 4? Recall factoring by grouping.

- mitu12

yes and you will get q(q-6)-3(q-6)

- anonymous

q2 - 6q - 3q - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
q • (q-6)
Add up the last 2 terms, pulling out common factors :
3 • (q-6)
Step-5 : Add up the four terms of step 4 :
(q-3) • (q-6)

- mitu12

then you will get (q-3)(q-6)

- anonymous

Yes.. good job.

- mitu12

thank you

- mitu12

same method i use just forgot

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