2.1 Sums and Differences of Polynomials. Goals SWBAT simplify expressions for sums and differences of polynomials SWBAT solve first-degree equations

2.1 Sums and Differences 2.1 Sums and Differences of Polynomialsof Polynomials

GoalsGoals

SWBAT simplify expressions for sums SWBAT simplify expressions for sums and differences of polynomialsand differences of polynomials

SWBAT solve first-degree equations in SWBAT solve first-degree equations in one variableone variable

DefinitionsDefinitions

A A is a numeral, a is a numeral, a variable, or an indicated product of a variable, or an indicated product of a numeral and one or more variables. numeral and one or more variables.

Example: Example:

monomial

232 9,4,,2 yxabm


When looking at the monomialWhen looking at the monomial , the , the number denoted by number denoted by aa is called the is called the

of the variable.of the variable.

The symbol The symbol represents a represents a of of xx, where , where xx is called the is called the and and nn is called the is called the ..

nax

nx

coefficient

power

base

exponent


A monomial with no variable (i.e. 9 or -6) is A monomial with no variable (i.e. 9 or -6) is called a called a ..

The The of a monomial is the of a monomial is the exponent, exponent, nn. If the monomial contains more . If the monomial contains more than one variable, the degree of the monomial than one variable, the degree of the monomial is the is the of the exponents. of the exponents.

Example: What is the degree of Example: What is the degree of ? ? What is the coefficient?What is the coefficient?

constant

degree

428 ba

sum


A monomial or sum of monomials is called a A monomial or sum of monomials is called a . .

The monomials of the expression are called the The monomials of the expression are called the of the polynomial. The of the polynomial. The

coefficients on each term of the polynomial are coefficients on each term of the polynomial are called the coefficients of the polynomial.called the coefficients of the polynomial.

The The of a polynomial is the degree of a polynomial is the degree of the term with the highest degree. of the term with the highest degree.

polynomial

terms

degree

State the coefficients and the degree State the coefficients and the degree of each polynomial.of each polynomial.

1.1.

2.2.

22695 37 xxx

abbaba 933 225

5, -9, 6, -22

Degree: 7

3, -3, -9

Degree: 6

DefinitionsDefinitions Two monomials are said to be Two monomials are said to be

if they have the same variable(s) with if they have the same variable(s) with the same exponent(s) and their only difference is the same exponent(s) and their only difference is their coefficient. their coefficient.

A A is a polynomial with two is a polynomial with two terms. A terms. A is a polynomial with is a polynomial with three terms. three terms. Example:Example: Binomial: Binomial:

Trinomial: Trinomial:

When simplifying a polynomial expression, combine When simplifying a polynomial expression, combine the the terms by adding or subtracting their terms by adding or subtracting their coefficients. coefficients.

liketerms

binomial

trinomial

xx 47 3 1729 3 xx

like

Simplify. Simplify.

3.3.

4. 4.

3564 2 xxx

11310 22 nmmnnm

Given the two polynomials: Given the two polynomials: and and

this is the this is the of the polynomials of the polynomials

this is the this is the of the of the polynomials. polynomials.

xxA 34 2 122 xxB

1234 22 xxxxBA

1234 22 xxxxBA

sum

difference

To simplify these expressions you can To simplify these expressions you can add the like terms. If it is a subtraction add the like terms. If it is a subtraction problem, distribute the negative and then problem, distribute the negative and then combine the like terms. combine the like terms.

Questions 5-8Questions 5-8: Find the sum or : Find the sum or difference and write the answer in difference and write the answer in simplest form.simplest form.

Let Let 975 23 xxA

82 2 xxB

1223 xxC

5.5. AA + + BB

6.6. BB – – CC

7.7. CC – – AA

8.8. AA + + C C - - BB

Questions 9-10Questions 9-10: Simplify.: Simplify.

9.9.

10. 10.

dccdcc 105473 22

5284732 xxxx

2.2 Solving 2.2 Solving EquationsEquations

To solve an equation we canTo solve an equation we can the equation into an the equation into an

equivalent equation to get the solution.equivalent equation to get the solution.transform

Ways to Transform and Ways to Transform and Solve an EquationSolve an Equation::

1. Substituting for either side of the given 1. Substituting for either side of the given equation an expression equivalent to it.equation an expression equivalent to it.

2. Adding to or subtracting from each side 2. Adding to or subtracting from each side of the given equation.of the given equation.

3. Multiplying or dividing each side of the 3. Multiplying or dividing each side of the equation by the same nonzero number.equation by the same nonzero number.*This also includes multiplying by a *This also includes multiplying by a reciprocal*reciprocal*

Make sure when transforming equation to Make sure when transforming equation to only combine only combine terms! terms!like

Solve the equation. Solve the equation.

1.1. 625

m

Solve the equation.Solve the equation.

2. 2. vv 19214


3. 3. 665 xx

Your turn!

Solve #4-6


7. 7. yyy 12223125


8. 8. 6934

552

4

3 bb

Solve for the variable indicated.Solve for the variable indicated.

9. 9. Solve for Solve for nn. .

cdnc 32

15

Solve for the variable indicated.Solve for the variable indicated.

10.10. Solve for Solve for xx

kxhkx 74

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2.1 Sums and Differences of Polynomials. Goals SWBAT simplify expressions for sums and differences of polynomials SWBAT solve first-degree equations