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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Answer:
nnrm
Step-by-step explanation:
.725 , .572 , .275, .2
You look at the first decimal place to see which is the greatest. 7 is greater than 5 and 2 so it's first. Then 5 is greater than 2 so it is next. For the last two numbers since 2 is the same value you look at the next decimal place. Since 7 is greater than 0 it comes next!
2x + 10...the common number between these 2 terms is 2...so factor the 2 out
2(x + 5) <==
We are given with the function of r (x) that represents the revenue or the total sales of the company and e(x) which represents the expenses of the company. Profit, p(x), is expressed as the difference between the revenue and the sales. The answer to this problem is B.
