Answer:
(5w - 3)(2w - 5)
Explanation:
As this polynomial is of the form ax² + bx + c, where a = 10, b = -31, and c = 15 (and x = w), in this case, as a is a number other than 1, the first step is to multiply a and c, replacing c with that product and removing the coefficient from the w² term, giving us:
w² - 31w + 150 (as 10 × 50 is 150)
Now, we are looking for two numbers that when they're multiplied together you get c, which is 150, and those same two numbers when added together gives us b, -31.
After looking through all of the possible factors of 150, we see that -25 and -6 fulfill both of these requirements (as -25 × -6 = 150 and -25 + -6 = -31)
Now, as we have our two numbers we can set up our factors:
(w - 6)(w - 25)
However, as we had to get rid of the 10 in front of the w², we now have to bring it back in front of both w's, giving us:
(10w - 6)(10w - 25)
Now we look and see if we can simplify.
We can see that 10 and -6 can both be simplified by 2, giving us:
(5w - 3)(10w - 25)
We can also see that 10 and -25 can be simplified by 5, giving us:
(5w - 3)(2w - 5)