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You can start by dividing the entire polynomial by two to reduce terms.

(2x2-16x-18)/2 = x2-8x-9

Now you have to find two roots whose sum is equal to -8 and whose product is equal to -9. The negative product means that they will have opposite signs. Since the factors of nine are 1,3, and 9, the answer should be obvious: +1 and -9

(x-9)(x+1) is your answer

If you look at any factorization problem in its most generic form the answer to

ax2+bx + c will have two roots (sometimes a double root, and provided it has a solution)

so that if you started from:

(x+r1)(x+r2) and multiply it out you would get

x2+ r1x + r2x + (r1*r2) = x2 + (r1+r2)x + (r1*r2)

where a =1

b = (r1+r2)

 c = (r1*r2)