Advanced MathHardSum of the constants in a factorisation
Advanced Math practice question
The polynomial 6x² + 7x − 20 is equivalent to (2x + a)(3x + b) for all x, where a and b are integers. What is the value of a + b?
Answer: 1
(2x + a)(3x + b) = 6x² + (2b + 3a)x + ab. Need ab = −20 and 2b + 3a = 7: a = 5, b = −4 works (2(−4) + 3(5) = 7). So a + b = 1.
Common wrong answers
- If you answered 9
- 9 is 5 + 4, ignoring the sign of b.
- If you answered -1
- −1 comes from a = −5, b = 4, which gives 2(4) + 3(−5) = −7.
- If you answered -20
- −20 is ab, not a + b.
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