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il63 [147K]
3 years ago
12

Graph the function f(x)= 5x^5 + 4x^4 - 4x^3 - 7x^2 +6 by making a table of values.

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
6 0

Answer:

You can see the graph in the attached file.

Step-by-step explanation:

You need to propouse values of x, and substitue into the equation to get the corresponding value of y. In other words you need to evaluate the function for each value of x. With those values you can build the table.

For  example choose the value x = 0, then you can calculate the value of y:

f(x) = 5x^{5}  +4x^{4}  - 4x^{3}  -7x^{2} +6

f(0) = 5(0)^{5}  +4(0)^{4}  - 4(0)^{3}  -7(0)^{2} +6

f(0) = 6

Then when x = 0, y = 6

The coordinates for the graph (x, y) = (0, 6)

For the table choose different values, include: zero, negative and positive numbers.

x y

x = f(x)=

-20 -15330794

-15 -3582444

-10 -456694

-5 -12794

-1 2

0 6

1 4

5 17456

10 535306

15 3984306

20 16605206

Review the attached excel file, there you will see the table and how to do the calculations in the cell.

Once you have the values in the chart, select the data. Then from the bar choose insert and then select the xy scatter.

Also you can see the graph in the file.

Download xlsx
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3 years ago
The polynomial p(x)=3x^3-20x^2+37x-20 has a known factor of (x-4). Rewrite p(x) as a product of linear factors. p(x) =
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Answer:

p(x) = (3x^{2} - 8x + 5)(x - 4)

Step-by-step explanation:

p(x) has degree 3

(x - 4) has degree 1

So p(x) can be rewritten as a polynomial of degree 2 multiplying (x-4)

So

p(x) = (ax^{2} + bx + c)(x - 4)

To find a, b and c, we have to divide p(x) by x - 4.

So

Finding a:

Dividing the first term of p(x) by x - 4.

\frac{3x^{3}}{x - 4} = 3x^{2}

So a = 3.

Now multiplying 3x² by, x - 4, we have:

3x^{2}(x - 4) = 3x^{3} - 12x^{2}

Subtracting p(x) from this:

3x^{3} - 20x^{2} + 37x - 20 - (3x^{3} - 12x^{2}) = 3x^{3} - 20x^{2} + 37x - 20 - 3x^{3} + 12x^{2} = -8x^{2} + 37x - 20

Finding b:

Dividing the first term, after the subtraction, by x - 4.

\frac{-8x^{2}}{x - 4} = -8x

So b = -8.

Multiplying -8x by x - 4, we have:

-8x(x-4) = -8x^{2} + 32x

Then

-8x^{2} + 37x - 20 - (-8x^{2} + 32x) = -8x^{2} + 37x - 20 + 8x^{2} - 32x = 5x - 20

Finding c:

\frac{5x}{x - 4} = 5

So c = 5.

Just to verify if the remainder is 0.

5(x - 4) = 5x - 20

5x - 20 - (5x - 20) = 0

Ok

Then:

p(x) = (ax^{2} + bx + c)(x - 4)

p(x) = (3x^{2} - 8x + 5)(x - 4)

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Answer:

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