please show work: factor, 10y squared-31y+15

Question

mathmale · Answer

$$10y squared-31y+15\rightarrow 10y^2-31y+15$$

mathmale · Answer

I'll guide you through the solution of this factoring problem.  
1.  Multiply the first coefficient (10) by the last coeff. (15).
2.  List all the factors of the result, in groups of 2, that combine to -31.

mathmale · Answer

(10)*(15)=?

anonymous · Answer

150

anonymous · Answer

erm -5 * -3?

mathmale · Answer

Right.  You must now list pairs of factors of 150 that combine to give yuo -31.
All will need to be (-) because of that -31.

Does 

-150
 -   1

combine to give you -31?  No.
Try again:

Does 

-75
 - 2

 combine to give you -31?  No

Try again.

mathmale · Answer

Think of possible divisors of 150 that will leave no remainder.  

Can you divide 150 by -30 and get no remainder?
If so, do the two negative factors add up to -31?

If not, try again.  You can do it!

anonymous · Answer

erm can't think of one

mathmale · Answer

Divide 150 by -6 and see what you get.