If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
Answer: The mass of the object is 10 kg
Step-by-step explanation:
According to Newton's second law of motion, the force 
applied to an object with mass 
is directly proportional to its acceleration 
:
(1)
If we isolate :
(2) This means the acceleration of the object varies inversely with its mass
Now, we are given the following data to calculate a constant force using (1):
(3)
(4)
(5)
If we apply this same force calulated in (4) in another object with an acceleration of 
, its mass 
will be:
(6)
(7)
Finding :
This is the mass of the object
