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:
Numerical expression 1
Numerical expression 2
Numerical expression 3
Step-by-step explanation:
Numerical expression 1
Numerical expression 2
Numerical expression 3
Answer:
b
Step-by-step explanation:
the anwser to this question is b i think
To avoid distortion of extreme
values, a good indicator would be the
B. median.
7x + 14 + 3x + 15 = 14x + 14 + 2
10x + 14 = 14x + 16
14 - 16 = 14x - 10x
-2 = 4x
X = - 2/4
X = - 1/2 OR X = - 0.5
