Advanced MathVery hardConstants in a factored quadratic
Advanced Math practice question
If (2x − 3)(ax + b) = 6x² − x − 12 for all values of x, where a and b are constants, what is the value of a + b?
Answer: 7
The x² terms give 2a = 6, so a = 3. The constants give −3b = −12, so b = 4. (Check: 2b − 3a = 8 − 9 = −1.) So a + b = 7.
Common wrong answers
- If you answered 1
- 1 subtracts b from a.
- If you answered 12
- 12 is 3 × 4, the product.
- If you answered -1
- −1 is the middle coefficient, not a + b.
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