SAT Equivalent expressions Practice Question 15 (Hard)

Math · Advanced MathHard

The expression $(ax + 3)(5x + b)$ , where $a$ and $b$ are constants, is equivalent to $10x^2 + kx + 21$ , where $k$ is a constant. What is the value of $k$ ?

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Answer: 29

Expand: $5ax^2 + (ab + 15)x + 3b$ . Matching the $x^2$ terms, $5a = 10$ , so $a = 2$ . Matching the constants, $3b = 21$ , so $b = 7$ . Then $k = ab + 15 = 14 + 15 = 29$ .

Answering 14 stops at $ab$ and forgets the $15x$ term from $3 \cdot 5x$ .

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