3x^2-17x+10

Question

not sure how a factor of 30 goes into -17

Answer 1

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.

Answer 2

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)

Answer 3

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)