Answer:
4
Step-by-step explanation:
Answer:
The table represents a linear function because the rate of change is constant or all the points lie on a straight line.
Step-by-step explanation:
From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).
The slope of the line is
m= y2-y1/x2-x1 = 10-5/4-2 = 5/2
The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.
From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.
Since the rate of change (slope) is same for all points, therefore the table represents a linear function.
If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a linear function.
Answer:
For a third degree polynomial, we need 3 linear factors.
Since
5
and
2
i
are roots (zeros), we know that
x
−
5
and
x
−
2
i
are factors.
If we want a polynomial with real coeficients, then the complex conjugate of
2
i
(which is
−
2
i
) must also be a root and
x
+
2
i
must be a factor.
One polynomial with real coefficients that meets the requirements is
(
x
−
5
)
(
x
−
2
i
)
(
x
+
2
i
)
=
(
x
−
5
)
(
x
2
+
4
)
=
x
3
−
5
x
2
+
4
x
−
20
Any constant multiple of this also meets the requirements.
For example
7
(
x
3
−
5
x
2
+
4
x
−
20
)
=
7
x
3
−
35
x
2
+
28
x
−
140