What multiplies to make 12 and adds up to 16

To solve Q.15, remember to multiply the first numerical coefficient, in this case 3 to -12, to find the numbers to multiply and get that product. The middle term represents the sum the same two numbers must add to.

For example:

3r^2 - 16r - 7 = 5
3r^2 - 16r - 12 = 0

What 2 numbers multiply to give you -36, and add to give you -16, are -18 and +2, since -18 • 2 = -36, and -18 + 2 = -16.

3r^2 - 18r + 2r - 12 = 0
Factor
3r(r - 6) + 2(r - 6) = 0
(3r + 2)(r - 6) = 0
r = 6

3r + 2 = 0
3r = -2
r = -2/3.

Your 2 solutions for r are -2/3 and 6.

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