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To show physically a factorization of a quadratic I would use algebra tiles. First the upper left would be the number of squares I had put in a rectangular array.

The lower left would be the number (constant) I had in a rectangular array. The deminsions of the squares would be my variable and the deminsions of the small square would be my constants.

x^2+5x+6

x + 3

x x^2+3x

+

2 2x +6

(x+2)(x+3)

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