Question

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

Answer 1

(q - 6)(q-3)

Answer 2

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

Answer 3

could you explain how to do this

Answer 4

Your first two automatics are the q's

Answer 5

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

Answer 6

ok

Answer 7

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

Answer 8

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

Answer 9

so what are some factors of 18

Answer 10

-6 and -3

Answer 11

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+?).

Answer 12

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.

Answer 13

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

Answer 14

@manutdd30 , Well, now he knows them. But how about this ?

i.e: 2x^2 - 18 x + 40 @mitu12

Answer 15

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

Answer 16

Work up. your brian.

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

^ What do you think you should do next?

Answer 21

the two factors are -6 and -3

Answer 22

Yes… then what?

Answer 23

then i think you plug them into the parenthesis

Answer 24

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…
\(\\\color{darkblue}{Give~a~man~a~fish,~he~eats~for~a~day.}\)
\(\\\color{pink}{Teach~a~man~to~fish,~he~eats~for~a~lifetime.}\)

Answer 25

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

Answer 26

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.

Answer 27

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

Answer 28

Thanks :)

Answer 29

Nice job @Aureyliant :).

Answer 30

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

Answer 31

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

Answer 32

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)

Answer 33

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

Answer 34

Yes.. good job.

Answer 35

thank you

Answer 36

same method i use just forgot