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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Answer:
The one that wieghs 10 grams
Step-by-step explanation:
There are 20 questions on the quiz.
Answer:
4. 1/25
5. 1/16
6. 2/9
7. 5/567
8. 1/40
9. 2/175
10. 1/30
11. 2/5
12. 9/8
13. 4/3
14. 1
Step-by-step explanation:
sorry I only know how to do 4-14. I hope this helps you.
The answer is moo-ltiplication
