SAT Equivalent expressions Practice Question 8 (Medium)

Math · Advanced MathMedium

The expression $(3x + 2)(2x - 5)$ is equivalent to $ax^2 + bx + c$ , where $a$ , $b$ , and $c$ are constants. What is the value of $a + b + c$ ?

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Answer: -15

Expand: $6x^2 - 15x + 4x - 10 = 6x^2 - 11x - 10$ . So $a + b + c = 6 - 11 - 10 = -15$ . (Shortcut: $a + b + c$ is the value of the expression at $x = 1$ , which is $(5)(-3) = -15$ .)

Writing the middle term as $+11x$ instead of $-11x$ gives the incorrect value 7.

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