Question

Find the quotient when x2 + 10x + 21 is divided by x + 7

Answer 1

Answer:   x+3

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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,

$\frac{x^2+10x+21}{x+7} = \frac{(x+3)(x+7)}{x+7} = x+3$

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