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
Answer:
Median: 10
Mean: 9
Range: 15
Step-by-step explanation:
Have a good day :)
Answer:
626.7 
Step-by-step explanation:
Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.
CIRCLE
A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7
RECTANGLE
A = l*w = 15*30 = 450
176.7 + 450 = 626.7
9514 1404 393
Answer:
(b) √65
Step-by-step explanation:
The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts.
|1 -8i| = √(1² +(-8)²) = √(1+64) = √65
Answer:
108
Step-by-step explanation:
237-129= 108
hope it helps
