Official Guide Explanation:
Problem Solving #41




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Solution and Metadata

Question: 41
Page: 158
Difficulty: 5 (Moderate)
Category 1: Algebra > Solving Quadratic Equations > other
Category 2: Algebra > Solving Equations by Factoring >

Explanation: Whenever you see something like a biominal, turn it into something you can work with. In this case, x2 + 3x + k = 10 can be better viewed as x2 + 3x + (k - 10) = 0. Since one of the solutions is 4, one of the factors must be (x - 4). Putting all of this together, we know that (x - 4)(x + q) = x2 + 3x + (k - 10). Because -4 and q must sum to 3, q must be 7. If x + q is one of the factors, -q is the other solution, so the correct answer is -7, choice (A).

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