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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For this case we have that by definition, the GCF (Greatest Common Factor) is the largest integer that divides the numbers.
We have the following expressions:
We find the factors of 9 and 6:
Thus, the largest number that divides 9 and 6 is 3
It is also observed that "b" is the common variable of both expressions
Therefore, the GCF of the expressions is:
Answer:
Answer:
1. brandon can read 30 words per minute
Step-by-step explanation:
When you want to write a polynomial, you should write the term with the highest degree first.
Here, it should go like this: d^3 + d^2 - d + 3
This means that the term which should be written first is the cubic term.
Answer: The rate of change decreased.
Step-by-step explanation:
