SOLUTION: Factor each trinomial. 10w^2-19w-15 I can not get this.

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Question 190084: Factor each trinomial. 10w^2-19w-15 I can not get this.
Found 3 solutions by Earlsdon, solver91311, feliz1965:
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Factor:

The factors of 10 are:
1*10 =10
2*5 = 10
The factors of -15 are:
-1*15 = -15
1*-15 = -15
-3*5 = -15
3*(-5) = -15
Let's try:
Multiply using FOIL.
Combine like-terms.

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


You can go through the process of finding all of the possible factors of -15 and 10, blah blah blah, but there is a much simpler and quicker method. Use the idea that if is a root of the equation formed when you set the polynomial equal to zero, then must be a factor of the polynomial. Since this is a quadratic trinomial, you can set it equal to zero and use the quadratic formula to find the roots -- then the factors become obvious.

Step 1: Set the trinomial equal to zero.



Step 2: Solve with the quadratic formula:



So



Or



Verifying that



is left as an exercise for the student.

By the way, if you end up with a pair irrational roots, then the trinomial is not factorable over the rational numbers.

John


Answer by feliz1965(151)   (Show Source): You can put this solution on YOUR website!
Start by multiplying 10 x -15.
So, 10 x -15 = -150.
Ask yourself, what two numbers when multiplied together will yield -150 BUT when added will yield -19? Do you see -19 in your trinomial?
How about -25 times 6?
Yes, that will work!
10w^2 - 25w + 6w - 15
We now make two groups.
10w^2 - 25w is the first group.
6w - 15 is the second group.
Factor each group individually.
10w^2 - 25w becomes 5w(2w - 5)
6w - 15 becomes 3(2w - 5)
Do you see the quantity 2w - 5?
We only need one of them.
Final answer: (5w + 3)(2w - 5)

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