Factor (x+2)^2-(x+2)-42

Problem

(x+2)2−(x+2)−42

Solution

1. Substitute a variable to simplify the expression. Let u=x+2

2. Rewrite the expression in terms of u

u2−u−42

3. Identify two numbers that multiply to −42 and add to −1 These numbers are −7 and 6

4. Factor the quadratic expression in u

(u−7)*(u+6)

5. Substitute back x+2 for u

((x+2)−7)*((x+2)+6)

6. Simplify the terms inside the parentheses.

(x−5)*(x+8)

Final Answer

(x+2)2−(x+2)−42=(x−5)*(x+8)

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