The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
Learn more about prime numbers here:
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Use this formula: C=2πr. Divide 14/2 to get the radius. Substitute the radius into the formula.
The answer is 14pi units.
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Step-by-step explanation:
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No! a liter is as much as a big bottle of soda! he should use 3 milileters. please vote me brainliest if i helped :) ❤️
Answer: 67.353
Step-by-step explanation:
60.000
+07.000
+00.300 Writing the numbers like this helps me keep track of them!
+00.050 It lets me see what place each number is in relative to the others
+00.003
67.353
