7-3 Polynomials and 7-4 Adding and Subtracting Polynomials Algebra 1 Glencoe McGraw-HillLinda Stamper

and any exponents on the variables are positive integers. A polynomial is an algebraic expression of one or more terms in which there are: no variables in a denominator, no variables under a radical sign (√), X X X When plus or minus signs separate an algebraic expression into parts, each part is a term.

Do you recall learning the names for triangles? triangle names classified by degree triangle names classified by length of sides

Classification by Degree Classification by Lengths acute right obtuse equilateral isosceles scalene Polynomials are classified by degrees and by terms.

Degree of a polynomial – the highest power (exponent) on any term. Constant – zero degree. Classification by Degree (means 4x 0 which equals 4(1) note: x 0 is understood) Linear – degree of one. Quadratic – degree of two. 4x 2 Cubic – degree of three. 4x 3 (means 4x 1 note: power of one is understood) 4 4x

Terms – expressions separated by addition. Example 3x + 5 Subtraction is just adding a negative, so indirectly, subtraction signs can separate terms. Example Monomial – one term (all items within are related by multiplication). Binomial – two terms. Trinomial – three terms. Polynomial – many terms (poly means many). Classification by Terms

Identifying Polynomials Polynomial# of Degree Classified by Degree Classified by Terms

Standard Form – the terms in order; the highest powers first in descending order. Standard Form 3x 3 + 2x 2 – 5x + 6 When terms need to be moved, first use the Commutative Property of Addition to reorganize terms that are subtracted. What is the degree name? What is the term name?

Write the polynomial in standard form. The problem. Change subtraction to addition. Circle the terms as you reorganize. The sign is in front of the term!

Write the polynomial in standard form. The problem. Circle the terms as you reorganize. The sign is in front of the term!

Example 1 Write the polynomial in standard form. Example 2 Write the polynomial in standard form.

Adding polynomials is combining like terms. Recall like terms have the same variable raised to the same power. Add the polynomials. Combine like terms – you may find it helpful to circle the terms as you combine them. The sign is in front of the term! Check if your answer is in standard form –the highest powers first in descending order. What is the degree name? What is the term name?

Example 3 Simplify the sum. Check if your answer is in standard form – the highest powers first in descending order. Example 4 Simplify the sum. Example 5 Write the perimeter of the rectangle as a polynomial. Simplify.

Example 3 Simplify the sum. Check if your answer is in standard form – the highest powers first in descending order. Example 4 Simplify the sum.

The perimeter is 8x – 4 units. Example 5 Write the perimeter of the rectangle as a polynomial. Simplify.

Subtract polynomials by adding the opposite of each term in the second polynomial. Then combine like terms. The problem. Combine like terms – you may find it helpful to circle terms as you combine them. Check if your answer is in standard form –the highest powers first in descending order. Write the opposite of each term in the second polynomial.

Example 6 Example 7 Simplify. Example 8 Example 9 Example 10 The measures of two sides of a triangle are given. If the perimeter is 10x + 5y, find the measure of the third side.

Example 6 Simplify the difference. Write the opposite of each term in the second polynomial. Example 7 Simplify the difference.

Example 8 Simplify the difference. Write the opposite of each term in the second polynomial. Example 9 Simplify the difference.

The measure of the third side is 2x + 2y units. The measures of two sides of a triangle are given. If the perimeter is 10x + 5y, find the measure of the third side. Example 10

7-A5 Pages # 11–28,47-49.