ADDING AND SUBTRACTING POLYNOMIALS

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.

2y^2 + 11y - 10

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

3x2

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.

4p2 + 6p - 8

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

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

6c - d

Reduce -8 + b^2 by 5 + b^2.

-13

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.

-4a^2 + 7a + 4

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

Find x - y subtracted from 0.

-x + y

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.

-x^4 y^2 + 7x^3 y^3 + 2x^2y^4 - 3xy^5

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

Remember:

Always write terms from highest power to lowest power.

Terms of a polynomial can be:

a constant such as 5, -23, 0.3 or 1/2 a variable such as x, t, or m. a product of constants and variables such as -7a, 1/2x, mn, and 4/9 pq2.

term

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

monomial

a one term polynomial ex: 5y

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 sum of terms whose variables have whole number exponents

trinomial

a three- term polynormial ex: 2x + 2y+ z

binomial

a two term polynomial ex: 5y+ 4x

Identify the polynomial. a 2 + bcd 3

binomial

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

closed for addition and multiplication

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 and polynomials

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.

p^4, P^3, P^2,P

polynomial addition

stack them vertically, aligning all like terms

like terms

terms that have the same variables, with each variable raised to the same exponent

Identify the polynomial. a^2 + b - cd^3

trinomial