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Home » The LCM is found by taking the highest power of all prime factors: - Simpleprint

The LCM is found by taking the highest power of all prime factors: - Simpleprint

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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Now factor the remaining terms:
Letâs try factoring by grouping. Try factoring $ x^4 + 8x^2 + 16 $ a...
x^4 + 8x^2 + 16 = (x^2 + 4)^2
-16y^4 + 64 = -16(y^4 - 4) = -16(y^2 - 2)(y^2 + 2)
Letâs now expand and factor directly:
x^4 + 8x^2 + 16 - 16y^4 + 64 = x^4 + 8x^2 + 80 - 16y^4
Now factor $ x^4 + 8x^2 + 80 $:
Try factoring as $ (x^2 + a)^2 + b $, or test rational root theorem. L...
x^4 + 8x^2 + 80 = x^2(x^2 + 8) + 80
Not helpful. Try factoring as a quadratic in $ x^2 $:

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Solution: Let the integer be $ n $. We have $ n \equiv 0 \pmod{16} $ a...
$$ 16k \equiv 1 \pmod{5} \implies k \equiv 1 \pmod{5} $$
$$ n = 16(5m + 1) = 80m + 16 $$
The smallest positive $ n $ occurs when $ m = 0 $, giving $ n = 16 $....
Question: What is the sum of all the squares of the divisors of $ 12 $...
Solution: The divisors of $ 12 $ are $ 1, 2, 3, 4, 6, 12 $. Compute th...
1^2 + 2^2 + 3^2 + 4^2 + 6^2 + 12^2 = 1 + 4 + 9 + 16 + 36 + 144 = 210
Question: What is the largest integer that must divide the product of...
Solution: The product of $ k $ consecutive integers is divisible by $...
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