Problem 6 · 2014 Math Kangaroo
Easy
Algebra & Patterns
factorization
For which of the following expressions is \(b+1\) not a factor?
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Answer: E — \(b^2+1\)
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Hint 1 of 2
For each option, try to pull a factor of (b+1) out.
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Hint 2 of 2
Four of them factor cleanly; one stubbornly will not.
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Approach: factor each candidate and look for (b+1)
- 2b + 2 = 2(b+1); b² − 1 = (b−1)(b+1); b² + b = b(b+1); −1 − b = −(b+1) — all have b+1 as a factor.
- Only b² + 1 leaves a remainder when divided by b+1 (it equals (b+1)(b−1) + 2).
- So b+1 is NOT a factor of b² + 1.
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