Question 1063324
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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^2-15w+54}}} = (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 {{{w[1]}}} and {{{w[2]}}}.
Then the decomposition is {{{a*(w-w[1])*(w-w[2])}}}  with some number "a" as a factor.


Having this instruction, try to complete the job for the second quadratic function on your own.
</pre>

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:

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/proof-of-quadratic-by-completing-the-square.lesson>PROOF of quadratic formula by completing the square</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Solving-quadratic-equations-without-quadratic-formula.lesson>Solving quadratic equations without quadratic formula</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Who-is-who-in-quadratic-equations.lesson>Who is who in quadratic equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Using-quadratic-equations-to-solve-word-problems.lesson>Using quadratic equations to solve word problems</A>


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Quadratic equations</U>".