Advanced MathMediumSum of coefficients after expanding
Advanced Math practice question
When the expression (3x − 2)(x + 4) is written in the form ax² + bx + c, where a, b, and c are constants, what is the value of a + b + c?
Answer: 5
Expand: 3x² + 12x − 2x − 8 = 3x² + 10x − 8, so a + b + c = 3 + 10 − 8 = 5. (Shortcut: a + b + c is the expression's value at x = 1: (1)(5) = 5.)
Common wrong answers
- If you answered 7
- 7 sums 3 + 12 − 8, using the cross term 12x before combining it with −2x.
- If you answered 21
- 21 adds 3, 10, and 8 without the minus sign on c.
- If you answered -5
- −5 comes from b = −10 (wrong signs on the cross terms).
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