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Work Shown:
x^2+10x+21 factors to (x+3)(x+7) since
7+3 = 10 and 7*3 = 21
Or you can use the FOIL rule to see that (x+3)(x+7) expands to x^2+10x+21
When we divide x^2+10x+21 over x+7, we get,
[tex]\frac{x^2+10x+21}{x+7} = \frac{(x+3)(x+7)}{x+7} = x+3[/tex]
a pair of (x+7) terms cancel out when we divide
The quotient is x+3
The remainder is 0
See the diagram below for the long division table