I know how to factor, but I am not sure of the rule if products of 12 don't equal 35.
Stacey Warren - Expert brainly.com
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So you factored out the x, left the 12 by itself, but then how did you get that?
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Okay, I see what you did there. I think, anyway. You pulled out x(18x-35) + 12. Well, actually, I still don't get how you got (2x-3)(9x-4)
Since it's not a monic quadratic, you're trying to find two numbers that multiply to be 216 rather than 35, and add to be -35. [[216 comes from 18*12]]
-27 and -8 work, so split 35x into -27x and -8x
18x² - 35x + 12
= 18x² - 27x - 8x + 12
= 9x(2x - 3) - 4(2x - 3)
= (9x - 4) (2x-3)
So you can multiple the coefficient of a by c, then find something in there that equals 35?
Just pick some representation of 18 as the product of two factors:
18 & 1
9 & 2
6 & 3
Since the middle term is negative and the first and last terms are positive you know you have something in the form
(ax - c)(bx - d)
And you know that a and b must be 2 numbers on that list.
So you have
c*d = 12
ad + bc = 35
And you have 3 different sets you can test for a/b to solve for the c and d using the system above.
To factorize the polynomial ax² + bx + c, you need to find 2 numbers (let them be m and n) that satisfy these two conditions:
1) m*n = a*c
2) m + n = b
Then you split bx into mx and nx and factorize by grouping in pairs