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:
brainly.com/question/145452
#SPJ1
(-7) * 8 = -56
answer
A. -56
hope it helps
The total mass of the living things on the farm is 588 kg.
<h2><u>Mass calculation</u></h2>
Since on a farm there was a cow, 2 sheep and 3 chickens, to determine what is the total mass of the 1 cow, the 2 sheep, the 3 chickens, and the 1 farmer on the farm, the following calculation must be performed :
- (6.2 x 10) + (4 x 10 x 10) + (2 x 6 x 10) + (3 x 2 x 1) = X
- 62 + 400 + 120 + 6 = X
- 588 = X
Therefore, the total mass of the living things on the farm is 588 kg.
Learn more about mass calculation in brainly.com/question/14695611
Step-by-step explanation:
[tex] - 24 \div 4 = \\ \frac{ - 24}{4} \\ = \frac{ - 12}{2} \\ = /frac{-6}{1}
