Algebra (ADDING AND SUBTRACTING POLYNOMIALS)

Find a - 2b + 3c diminished by a - 2b - 3c + d.

2a - 4b + d

Reduce -8 + b2 by 5 + b2.

2b² - 3

In your notebook, set up the following subtraction in a vertical format and select the correct answer. Reduce 7y + 2y 2 - 7 by 3 - 4y.

2y2 + 11y - 10

Which of the following are terms in the sum of the given polynomials? 3x2,-2x2y, 2xy2, 4y2, xy2, -y2,2x2y

3x2

After arranging the terms in descending powers of a variable, select the opposite of the polynomial. 9 - 12n 2 + 4n 3 - 7n

4n3 - 12n2 - 7n + 9

In your notebook, set up the following addition using a vertical format and find the sum of the given polynomials. 2mn + 4n^2 and 5m^2 - 7mn

5m^2 - 5mn + 4n^2

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Order the polynomial -x 4 y 2 + 7x 3 y 3 - 3xy 5 + 2x 2 y 4 in descending powers of x.

-3xy5, -x4y2, 7x3y3, 2x2y4

In your notebook, set up the following subtraction in a vertical format and select the correct answer. Take -4 + 3a 2 from 7a - a 2.

-4a2 - 7a - 4

In your notebook, set up the following subtraction in a vertical format and select the correct answer. Find 2p 2 + 3p - 4 less - 2p 2 - 3p + 4.

0

In your notebook, set up the following addition using a vertical format and find the sum of the given polynomials. 7b + 3, -4b + 5, and -3b + 2

10

In your notebook, set up the following addition using a vertical format and find the sum of the given polynomials. 3x^2 + 2x - 5 and -4 + 7x^2

10x^2 + 2x - 9

Which operations is the following set closed under: {2, 4, 6, ...}?

Closed for addition and multiplication.

Review

Polynomials are made up of terms having variables with whole number exponents. Terms are separated by + or - signs. Add polynomials by combining their like terms. Writing polynomials in descending order helps to line up the like terms. You can subtract polynomials by adding the opposite of the terms being taken away.

term

a number or a variable, or an indicated product of a number and variable(s)

monomial

a one-term polynomial

set closure

a set, well defined collection of objects such as numbers, is considered closed under a specific operation if applying that operation to two members of the set will result in another member of the same set

polynomial

a term or a sum of terms whose variables have whole number exponents

trinomial

a three-term polynomial

binomial

a two-term polynomial

Identify the polynomial. a 2 + bcd 3

binomial

Identify the polynomial. a^2 - b + c - d^3

four-term polynomial

Which of the following sets are closed under addition? Select all that apply.

integers

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Order the terms p 2, p 4, p 3, and p in descending powers of p.

p4, p3, p2, p

like terms

terms that have the same variable(s), with each variable raised to the same exponent

Identify the polynomial. a 2 + b - cd 3

trinomial

Find x - y less than 0.

x-y