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Problem 12 - Entrance Test
Expand (x + 1)(x + 2)(x + 3).
A. x^3 + 6x^2 + 11x + 6
B. x^3 + 6x^2 + 6x + 6
C. x^3 + 5x^2 + 6x + 6
D. x^3 + 6x^2 + 11x + 5
Check Answer
Show Solution
Correct: A
First, expand (x + 1)(x + 2): (x + 1)(x + 2) = x(x+2) + 1(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2. Now multiply this result by (x + 3): (x^2 + 3x + 2)(x + 3) = x(x^2 + 3x + 2) + 3(x^2 + 3x + 2) = x^3 + 3x^2 + 2x + 3x^2 + 9x + 6 = x^3 + (3x^2 + 3x^2) + (2x + 9x) + 6 = x^3 + 6x^2 + 11x + 6.