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Please show the solution to completely factoring w^2-15w+54; also,45g^2 + 12g -9.
Thank you for your time and skill.
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Regarding the first equation, you need to find two factors of the number 54 that sum up to -15.
If you keep the multiplication table in your head, you will answer immediately: the factors are -6 and -9.
Then, getting it, you will be able to write the factored form of this quadratic function:
= (w-6)*(w-9).
Regarding your second function, the things are different for you.
For me, they are different, too.
If I can not make factoring mentally in my mind in 5 seconds, I apply the quadratic formula and find the roots.
Let say, the roots are and .
Then the decomposition is with some number "a" as a factor.
Having this instruction, try to complete the job for the second quadratic function on your own.
You may ask: why 5 seconds ?
Because I need to care about my mind and do not spend it for nothing.
As a conclusion, my advise to you is to look in these lessons on solving quadratic equations:
- Introduction into Quadratic Equations
- PROOF of quadratic formula by completing the square
- Solving quadratic equations without quadratic formula
- Who is who in quadratic equations
- Using quadratic equations to solve word problems
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Quadratic equations".