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.
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.
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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