4.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials.
Section 5.4 Adding and Subtracting Polynomials. 5.4 Lecture Guide: Adding and Subtracting...
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Transcript of Section 5.4 Adding and Subtracting Polynomials. 5.4 Lecture Guide: Adding and Subtracting...
5.4 Lecture Guide: Adding and Subtracting Polynomials Objective 1: Use the terminology associated with polynomials.
Monomials
Polynomials
Verbally
A monomial is a real number, a variable, or a product of real numbers and variables with _______________ number exponents.
A polynomial is a monomial or a sum of a finite number of _______________.
Algebraic Examples
– 5, , x, A, 5x, 7xy
and are monomials.
and are polynomials.
is a polynomial.
2r
2 27 9 3x xy y
5 7xy
Binomial
Trinomial
Verbally
A binomial is a polynomial containing _______________ terms.
A trinomial is a polynomial containing _______________ terms.
Algebraic Examples
3 4x
22 5 7x x
Degree of a Monomial
The degree of a monomial is the sum of the _______________ for all the variables in this term. A nonzero constant is understood to have degree _______________ with exponent , but no degree is assigned to the monomial 0.
0(4 4x 0)
1. Determine whether each expression is a monomial. If the expression is a monomial, give its coefficient and the degree of each monomial.
43x
Monomial? Yes / NoCoefficient: ______Degree: ______
Monomial? Yes / NoCoefficient: ______Degree: ______
Monomial? Yes / NoCoefficient: ______Degree: ______
Monomial? Yes / NoCoefficient: ______Degree: ______
(a) (b) (c) (d)43x xyz
2. Determine whether each expression is a polynomial. Classify each polynomial according to the number of terms it contains.
(a) (b) (c) (d)4 7x 92x 2
9x312 4x x
Polynomial? Yes / No
Polynomial? Yes / No
Polynomial? Yes / No
Polynomial? Yes / No
Classification:____________
Classification:____________
Classification:____________
Classification:____________
Standard Form of a PolynomialA polynomial is in standard form if (1) the variables in each term are written in ____________ order and (2) the terms are arranged in ____________ powers of the first variable.
Degree of a PolynomialThe degree of a polynomial is the same as the degree of the term with the ____________ degree. To find this highest degree, examine each term individually---do not sum the degrees of the terms.
3. Write each polynomial in standard form, and give the degree of each polynomial.
(a) 29 3 8x x
Standard form:
Degree:
3. Write each polynomial in standard form, and give the degree of each polynomial.
(b) 2 59y zx
Standard form:
Degree:
3. Write each polynomial in standard form, and give the degree of each polynomial.
(c) 5 2 34 9 3 1v v v v
Standard form:
Degree:
Objective 2: Add and subtract polynomials.
When adding or subtracting polynomials, remember to use the __________________ property to remove any grouping symbols and then add like terms.
Remember that like terms have exactly the same ________ factors.
11.
Determine the sum or difference and write the result in standard form.
2 22 3 4 5 3 4 5 1x x x x
12.
Determine the sum or difference and write the result in standard form.
2 2 23 7 3 4 2 2 1x x x x x
13.
Determine the sum or difference and write the result in standard form.
2 2 2 22 6 1 5 4 7 2x xy y x xy y
14. The profit in dollars made by selling x units is given by the polynomial
2( ) 25 46.P x x x
(a) Evaluate 0P
Evaluate and interpret each expression.
Interpret 0P
(b) Evaluate
Interpret
2P
2P
14. The profit in dollars made by selling x units is given by the polynomial
2( ) 25 46.P x x x Evaluate and interpret each expression.
(c) Evaluate 13P
13PInterpret
14. The profit in dollars made by selling x units is given by the polynomial
2( ) 25 46.P x x x Evaluate and interpret each expression.