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:
see explanation
Step-by-step explanation:
Euler's formula for polyhedra is
V- E + F = 2
where V is number of vertices, E number of edges and F number of faces
Answer:
k=9
Step-by-step explanation:
4/3 = 8/6 = 12/9
Step-by-step explanation:
wow, how complicated can one phrase this ...
the point being :
1 ft = 12 in and vice versa (1 in = 1/12 ft)
so, any measurements given in feet but needed in inches need to be multiplied by 12.
and any measurements given in inches but needed in feet need to be divided by 12.
so,
3.5 ft = 3.5×12 = 7/2 × 12 = 7×6 = 42 in
27 in = 27/12 = 9/4 = 2 1/4 or 2.25 ft
Number one should be the right answer.
