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:

Step-by-step explanation:
we are given two temperature
4 degrees and -10 degrees
since it says to figure out the changed
substract

remove parentheses and change its sign

simplify addition:

and we are done!
Answer:
hey! This was the only part of mathematics I ever enjoyed! So consider this both of our lucky days: Answer is : (2,7)
Step-by-step explanation:
basically plug in Y to the first equation as sox + 4(-x + 9) = 30
x - 4x + 36 = 30- 3x = - 6
x = 2
then plug that in to Y!
Y = -(2) + 9
so Y = 7
and our answer is : (2,7)
Lol u thought I was writing an answer hahahaha
As a decimal .375 as a percentage it would be 37.5