let the function p be defined by p(x) = x^3 + 10x^2 - 23x - 132 where (x + 11) is a factor. to rewrite the function as the produ
1 answer:
In long division a polynomial is divided by another polynomial with a lower degree
- The two factors are; <u>(x² - x - 12) and (x + 11)</u>
Reason:
The given function is presented as follows;
x³ + 10·x² - 23·x - 132
A factor of the function is (x + 11)
By long division, we have;
Quotient; <u>x² - x - 12</u>
(x³ + 10·x² - 23·x - 132) ÷ (x + 11)
x³ + 11·x²
-x² - 23·x - 132
-x² - 11·x
-12·x - 132
-12·x - 132
0
Therefor, we have the two factors, are (x² - x - 12) and (x + 11)
Where;
(x² - x - 12) = (x - 4)·(x + 3)
Therefore, we have;
(x² - x - 12) × (x + 11) = x³ + 10·x² - 23·x - 132
Learn more about long division here;
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Answer:
1) See below for table.
2) Domain:
Range:
Yes, this is a function.
Step-by-step explanation:
We know that the electrician charges a base fee of $70 plus $45 for each hour of work.
We also know that the minimum the electrician charges is $160.
Let's write an equation. Let x denote the number of hours worked and y denote the total price. There's also a base fee of $70. So, we can write the following equation:
Part 1)
Let's create our table for 1, 2, 3, and 4 hours. To do so, we simply need to substitute each value for x in our equation.
1 Hour:
We have:
Multiply and add:
However, notice that the minimum the electrician charges is $160. Therefore, for one hour of work, the electrician will <em>still </em>charge $160. So:
2 Hours:
Substitute 2 for x:
So:
3 Hours:
Substitute 3 for x:
So:
4 Hours:
Substitute 4 for x:
So:
Therefore, for 1, 2, 3, and 4 hours of work, the prices will be $160, $160, $205, and $250, respectively.
We can create the following table (please scroll down to see the table. Also, y is measured in dollars).
Part 2)
The domain of a relation are the input values.
In this context, our input values are the amount of hours worked, and we calculated for 1, 2, 3, and 4 hours of work.
Therefore, our domain in this context is:
The range of a relation are the output values.
In this context, the output values are the price for x hours of work.
Therefore, our range in this context is:
This relation <em>does</em> represent a function. Remember that a function <em>cannot </em>have repeating input values. In other words, no one input can be equal to two or more different outputs. However, one <em>output</em> <em>can</em> be mapped to two or more different inputs.
For our table, none of the inputs are repeating. So, our relation <em>is</em> a function.
And we're done!
