Advanced MathHardCoefficient in a product of binomials
Advanced Math practice question
If (2x + a)(x − 5) = 2x² − 7x − 15 for all values of x, what is the value of a?
Answer: 3
Expand: 2x² − 10x + ax − 5a = 2x² + (a − 10)x − 5a. Matching: a − 10 = −7 gives a = 3, and −5a = −15 confirms it.
Common wrong answers
- If you answered 7
- 7 reads the x-coefficient as a itself.
- If you answered 15
- 15 reads the constant as a; the constant is −5a.
- If you answered -3
- −3 comes from a − 10 = −7 solved as a = −3 (sign slip); −5a must be −15, so a = 3.
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