Page 351 - Algebra 1

A polynomial is a monomial or the sum or difference of monomials.
Polynomials
A polynomial with one term is a monomial.
6x
A polynomial with two terms is a binomial.
6x + 10
A polynomial with three terms is a trinomial.
x2 +6x+10
Example
2
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The degree of a polynomial is the degree of the greatest-degree term in the polynomial.
The leading coefficient for a polynomial is the coefficient of the term with the greatest degree.
The standard form of a polynomial is a form of a polynomial where terms are ordered from greatest to least degree.
Writing a Polynomial in Standard Form
Write each polynomial in standard form. Then find the leading coefficient.
a. 2n2+n3
SOLUTION
2n2 : degree 2
n3 : degree 3
n3 + 2n2 is in standard form. The leading coefficient is 1.
b. 8xy2 - 9 + 5x3y3z SOLUTION
8xy2 Add the exponents of the variables: 1 + 2 = 3. 5x3y3z Add the exponents of the variables: 3 + 3 + 1 = 7. -9 A constant has a degree of 0.
5x3y3z + 8xy2 - 9
Arrange the terms in descending order.
730
5x3y3z + 8xy2 - 9 is in standard form. The leading coefficient is 5.
c. 9x2y - 3x2y2 - 5xy
SOLUTION
9x2y Add the exponents of the variables: 2 + 1 = 3. -3x2y2 Add the exponents of the variables: 2 + 2 = 4. 5xy Add the exponents of the variables: 1 + 1 = 2. -3x2y2 - 9x2y - 5xy
Arrange the terms in descending order.
432
-3x2y2 + 9x2y - 5xy is in standard form. The leading coefficient is -3.
336 Saxon Algebra 1