I can add and subtract polynomial expressions, including those representing real-world situations.
I can add and subtract polynomial expressions, including those representing real-world situations.
Untitled Section
•A monomial is a number or a product of a number and variables with whole number exponents. A polynomial is a monomial or sum of monomials.
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Question 1
1.
The degree of a monomial is the sum of the exponents of the variables in the monomial.
The degree of a polynomial is the greatest degree of its monomial terms.
Polynomials are often written in standard form, in which the terms of the polynomial are ordered from greatest degree to least degree.
When written in standard form, the coefficient of the first term is called the leading coefficient.
Fill in the Degree and Leading Coefficient
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Question 2
2.
Write the polynomial
in standard form. Then identify the degree and leading coefficient.
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Question 3
3.
Write an example of a polynomial that has three terms, a leading coefficient of -4, and a degree of 5.
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Question 4
4.
Add Polynomials
To add two polynomials, add the like terms of the two polynomials. When working with polynomials in one variable, like terms are monomials that have the same variable and same exponent.
Subtract Polynomials
•Add the Opposite
•As you + or - polynomials match like terms in a vertical or horizontal manner.
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Question 5
5.
Perform the indicated operation. Write the result in standard form.
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Question 6
6.
Perform the indicated operation. Write the result in standard form.
1 point
1
Question 7
7.
A fitness supply company manufactures stretching rollers. The functions
and
give the number of online sales and retail sales, in thousands, during the xthmonth after being placed on the market, respectively. Estimate the total number of sales during the fourth month.
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Question 8
8.
According to data from 2010 to 2018, the monthly value of U.S. exports can be modeled by
where x is the number of months since the beginning of 2010 and E(x) is the value of exports in millions of dollars.
Similarly, the monthly value of U.S. imports can be modeled by the function
Estimate how much more the value of imports was at the end of January 2014 than the value of exports.
On Your Own
2 points
2
Question 9
9.
Perform the indicated operation. Write the result in standard form.
2 points
2
Question 10
10.
Perform the indicated operation. Write the result in standard form.
2 points
2
Question 11
11.
Perform the indicated operation. Write the result in standard form.
2 points
2
Question 12
12.
Perform the indicated operation. Write the result in standard form.
3 points
3
Question 13
13.
Water is being pumped into two tanks at variable rates. The volume of water in Tank A is modeled by
and the volume of water in Tank B is modeled by
where t is the time in minutes since the tanks started to be filled. The volume is measured in gallons.
Write an expression to model the total amount of water in tanks A and B after t minutes. How much water is in both tanks after 3 minutes?
4 points
4
Question 14
14.
Using the integers -9 to 9, at most one time each, fill in the boxes to make a true statement.
