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3x^2-17x+10

not sure how a factor of 30 goes into -17

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Michael J. | Effective High School STEM Tutor & CUNY Math Peer LeaderEffective High School STEM Tutor & CUNY ...
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Another alternative is to use the quadratic formula:
 
x=(-b±sqrt(b²-4ac))/(2a)
 
where a=3, b=-17, c=10
 
This will give you the roots.  Then write the roots in a product of binomial form that is equal to zero.  The two binomials will be your factors.
 
For example:  If you have roots x=8 and x=-5,  you can say that (x-8)(x+5)=0.  This means that (x-8) and (x+5) are your factors.
Shailin S. | Experienced Math Tutor at an affordable rateExperienced Math Tutor at an affordable ...
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Factor of 30 will go and make 17 if you choose 15 and 2. So you can use = 3x^2 - 2x - 15x + 10 = x(3x - 2) -5(3x-2) = (3x-2)(x-5)

Kevin S. |
5.0 5.0 (4 lesson ratings) (4)
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Look at the factors of 3 (3 and 1) and of 10 (1 and 10, 2 and 5).

Can you combine them so that some combination equals 17?

Let's check:

(3x - 1)(x - 10) ==> 3x2 - x - 10x + 10 = 3x2 - 11x + 10  (No)

(3x - 2)(x - 5) ==> 3x2 - 2x - 15x + 10 = 3x2 - 17x + 10 (yes)