SOLUTION: 5x^4 - 45x^3 + 25x^2 What is the complete factorization?

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Question 480903: 5x^4 - 45x^3 + 25x^2
What is the complete factorization?
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

...factor out -common factor for all three terms


..now try to factor
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to 5 and add to -9? Lets find out by listing all of the possible factors of 5


Factors:

1,5,

-1,-5,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 5.

1*5=5

(-1)*(-5)=5

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9

||
First Number|Second Number|Sum
1|5|1+5=6
-1|-5|-1+(-5)=-6
None of these factors add to -9. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.


as you can see, cannot be factored; so, your solution is:

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