mitu12
  • mitu12
Factor the following polynomials correctly q^2-9q+18
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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TrojanPoem
  • TrojanPoem
(q - 6)(q-3)
sweetburger
  • sweetburger
what 2 values multiply to equal 18 and add to equal -9... alright nm
mitu12
  • mitu12
could you explain how to do this

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anonymous
  • anonymous
Your first two automatics are the q's
anonymous
  • anonymous
so we have (q+-?)(q+-?)
mitu12
  • mitu12
ok
TrojanPoem
  • TrojanPoem
@sweetburger , that's how I do it. You could complete the square.
anonymous
  • anonymous
Next thing you have to do is find what multiplies to =18
anonymous
  • anonymous
so what are some factors of 18
mitu12
  • mitu12
-6 and -3
sweetburger
  • 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
  • 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
  • sweetburger
@TrojanPoem I do actually know how to do these kind of problems so you dont have to tell me...
TrojanPoem
  • TrojanPoem
@manutdd30 , Well, now he knows them. But how about this ? i.e: 2x^2 - 18 x + 40 @mitu12
TrojanPoem
  • TrojanPoem
@sweetburger , I was telling you I do it the same. BUt complete the square is for mitu12
TrojanPoem
  • TrojanPoem
Work up. your brian.
sweetburger
  • sweetburger
The question in your example you just apply the quadratic or use the rational root theorem and then use the remainder theorem
TrojanPoem
  • TrojanPoem
-,- , Not for you @sweetburger , it's for @mitu12.
anonymous
  • 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
  • anonymous
^ What do you think you should do next?
mitu12
  • mitu12
the two factors are -6 and -3
anonymous
  • anonymous
Yes… then what?
mitu12
  • mitu12
then i think you plug them into the parenthesis
anonymous
  • 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
  • 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
  • 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
  • sweetburger
I know you were limiting them for clarification but just putting that out there.
anonymous
  • anonymous
Thanks :)
sweetburger
  • sweetburger
Nice job @Aureyliant :).
anonymous
  • anonymous
@mitu12 What do you believe you should do for step 4? Recall factoring by grouping.
mitu12
  • mitu12
yes and you will get q(q-6)-3(q-6)
anonymous
  • 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
  • mitu12
then you will get (q-3)(q-6)
anonymous
  • anonymous
Yes.. good job.
mitu12
  • mitu12
thank you
mitu12
  • mitu12
same method i use just forgot

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