M4: Adding & Subtracting Polynomials

Question 1

What are polynomial expressions, and how do you simplify them?

Answer 1

A polynomial can be a monomial or the sum of monomials. Polynomials are classified by the number of terms they contain. Polynomials are also classified by their degree. The degree of a polynomial is the greatest value among the sums of the exponents on the variables in each term.

Question 2

How do you start to add Polynomials?

Answer 2

You can add polynomials by combining like terms. Identify like terms,rearrange terms so that like terms are together, and combine like terms.

Add (5² + 7y + 2) + (4y² + y +8).
(5y²+ 7y + 2 ) + (4y² + y + 8 )
(5y² + 4y²) + (7y + y ) + ( 2 + 8 )
9y²+ 8y + 10

Question 3

What is (a-b+2c)-(a-b-2c)

Answer 3

Subtracting Polynomials is not much different than adding polynomials. Also the subtraction sign doesn’t exist.
(a-b+2c)-(a-b-2c)
(a-b+2c)+(-a+b+2c)

(a-b+2c)
(-a+b+2c)=
4c

Question 4

4.2 Adding Polynomials

y^2 - x^4) + (x^4-x^2

Answer 4

(y^2) + (-x^2) Eliminate Opposites
y^2 - x^2 Collect Like Terms (there are none)
pg.101

Question 5

When adding or subtracting polynomials, are exponents added or subtracted as well?

Answer 5

No, exponents are not affected. x^2 + x^3 does NOT equal x^5. They are two SEPARATE terms.

Question 6

What is (2a-b+5c)-(-2c+a-3b)

Answer 6

First, rearrange the terms to make is easier to add vertically.
(2a-b+5c)-(-2c+a-3b) =
(2a-b+5c)-(a-3b-2c)

Next, distribute the negative.
(2a-b+5c)-(a-3b-2c) =
(2a-b+5c)+(-a+3b+2c)

Finally, add vertically.
(2a-b+5c) +
(-a+3b+2c)

a+2b+7c

Question 7

What is a Polynomial?

Answer 7

A polynomial is an expression that with two algebraic terms. Especially ones that have powers of the same variable.

Question 8

What is a Monomial expression

Answer 8

A monomial is an expression that cannot have more than 1 term, and cannot have a variable in its denominator
Examples:
2 * 2 = 4 
2 * x = 2x
2 * 6 = 12
2 * y = 2y

Question 9

What is a binomial expression

Answer 9

A binomial is a polynomial expression that has two terms
Examples:
5+4x
7+3x
x^2+9
3^2+x

Question 10

What is a trinomial expression

Answer 10

A trinomial is a mathematical expression that has 3 terms
Examples:
x + y + z  
2a^2+5a+7
xy+x+2y^2
xyz+xyz+xyz

Question 11

Add these polynomials: (2x+y+z)+(-x+y-z)

Answer 11

Answer=x+2y
step 1: align vertically
2x+y+z
- x+y-z
step 2: add like terms
2x+y+z
- x+y-z
------------
Answer: x+2y

Question 12

Find the difference between the polynomials:

2x^2-2x^4)-(x^4-x^2

Answer 12

Step 1: inverse to add the opposite
( 2x^2-2x^4)+(-x^4+x^2)
step 2: add like terms 
( 2x^2-2x^4)
(-x^4+x^2)
----------------
3x^2+x^4
Answer: [3x^2+x^4]

Question 13

find the sum of the polynomials:

(x^2 + y + z) + (-x + y - z) + x - y

Answer 13

step 1: Add the outlying terms 
 (x^2 + y + z) + (-z) 
step 2: add the remaining terms
 (x^2 + y + z)
                 -z
-------------------
answer: x^2+y