What is the degree of the function f(x)= x(x+1)2 (2x-3)(x+2)2

Mathematics

1 answer:

Brums [2.3K]2 years ago

5 0

Answer:

Step-by-step explanation:

Given equation is $f(x)= x(x+1)^2 (2x-3)(x+2)^2$ .

Now we need to find about what is the degree of the give function.

We know that degree of polynomial function is the highest exponent of the variable (x).

So we can either expand the whole equation or count the degree of each factor then add those to get the degree of the given function.

Second choice will be easier.

Degree of $x$ = 1

Degree of $(x+1)^2$ = 2

Degree of $(2x-3)$ = 1

Degree of $(x+2)^2$ = 2

Hence degree of the given polynomial function = 1+2+1+2=6

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<em>The distance the length of a segment with endpoints Y(2, 8) and Z(-2, 5) is 5 units</em>

<h2>Explanation:</h2>

Endpoints of a Line segments are places where they end or stop. Line segments are named after their endpoints. In this case, those endpoints are Y and Z, so the line segment would be:

$\overline{YZ} \ or \ \overline{ZY}$

To find the length of this segment with endpoints Y(2, 8) and Z(-2, 5), let's use the Distance Formula:

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$Let's \ write: \\ \\ Y(x_{1},y_{1}) \rightarrow Y(2, 8) \\ \\ Z(x_{2},y_{2}) \rightarrow (-2, 5) \\ \\ \\ Substituting: \\ \\ d=\sqrt{(-2-2))^2+(5-8)}^2 \\ \\ d=\sqrt{(-4)^2+(-3)^2} \\ \\ d=\sqrt{16+9} \\ \\ d=\sqrt{25} \\ \\ \boxed{d=5}$

Finally, <em>the distance the length of a segment with endpoints Y(2, 8) and Z(-2, 5) is 5 units</em>

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Safara wants to rent a bicycle the graph shows the cost for renting a bicycle for different lengths of time. What is the slope o

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