factor the polynomial

(4x+5)(2x+3).

Take factors of 8: (1,8), (2,4) and factors of 15: (1,15), (3,5) and "cross" them:

(1,8)(1,15), (1,8)(15,1), (2,4)(1,15), (2,4)(15,1), (1,8)(3,5), (1,8)(5,3), (2,4)(3,5), (2,4)(5,3):

1*1 + 8*15=121, ..., 2*5 + 4*3=22.

The cross that gives the coefficient of the x term is the one you want: the green are the x terms in brackets and the red are the numbers in brackets: (2x+3)(4x+5) or (4x+5)(2x+3). Outer product+inner product=middle coefficient.

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