"Manuel" here put the arrow in the wrong place. Should be under 15, not 4. PLUS, 4 is not prime, cuz 2 goes into it...
What is the question itself?
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
Of course!
Cube: side length * side length * side length
So if it's a 6x6x6 cube, it's 6*6*6 = 216
Rectangular Prism: side length * side height * base width
So if it's a 6x7x8 prism, it's 6*7*8 = 336
Cylinder: π * (radius squared) * height
So if the base's radius is 6 and the height is 7, it's π*6^2*7 = 252π
