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.
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90,000*0.12 =1,080
1,080*7=7,560
90,000+7,560=97,560
Answer: 12.56
Step-by-step explanation:
If I remember correctly, the equation for circumference is C=2r*pi (R representing radius). For this problem, if 2 is your radius 2R would equal 4. Take this number and multiply it by 3.14 (pi) to get your final answer.
The answer to the question
Answer:
x = 1
Step-by-step explanation:
x + 8 = 9
=> x = 9 - 8
=> x = 1
