Advanced MathHardFactoring a difference of squares with a binomial
Advanced Math practice question
The expression 16 − (x − 3)² can be written as (a − x)(x + b), where a and b are positive constants. What is the value of a + b?
Answer: 8
16 − (x − 3)² = [4 − (x − 3)][4 + (x − 3)] = (7 − x)(x + 1). So a = 7, b = 1, and a + b = 8.
Common wrong answers
- If you answered 6
- 6 comes from (4 − x)(x + 2), forgetting to combine the 4 with the −3 inside the square.
- If you answered 7
- 7 is a alone.
- If you answered -8
- −8 has the wrong signs.
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