Algebra I : Semester II : Polynomials

Sections:

Introduction  |   Section 1  |   Section 2  |   Section 3  |  Section 4  |  Section 5  |  Section 6

Section Two

Part 1  |  Part 2

Algebra 1: Section 2: Polynomials Polynomials If a baseball player can hit a ball with a velocity of 65 feet per second (ft/s), with the bat tip at a height of four feet, find the height of the ball at any second after hitting it by using the equation: h = -16t2 + 65t + 4. A table of the heights after different time intervals: # Seconds Height (ft) 0 4 1 53 2 70 3 55 4 8 4.1 1.54 4.2 -5.24   An example of a polynomial is -16t2 + 65t + 4. More specifically, it is a trinomial. Polynomials A polynomial is a monomial or a sum or difference of monomials. Remember that a monomial is a constant (a number), or the product of a coefficient and a variable, or variables with whole number exponents. Monomials: -3x, 4x, 5r2, 6xy, ½ x2y3 Polynomial: 5r2 + 6xy – ½x2y3 + 4x – 3 We have special names for some polynomials: Trinomial – the sum or difference of three monomials: 4x2 – 3x + 2 Binomial – the sum or difference of two monomials: 36 – 25y2  Note the prefixes. Mono means one, as in monorail. Bi means two, as in bicycle (2 wheels). Tri means three, as in tricycle. Poly means many, as in polygon (many sides Example 1:  Identifying a Polynomial Tell if each of the following is a polynomial. Look back at the definition if you are unsure. 5m + 2 Yes a-1 +  5a No. a-1 = 1/a. A quotient cannot be a monomial. -3.2x2 – 6x + 8.1 Yes The Degree of a Polynomial The degree of a polynomial is found by considering its exponents.  The degree of a monomial is the sum of the variable’s exponents. The degree of a polynomial is the greatest degree of a term in the polynomial. Example 3:  Finding the Degree Find the degree of each of the polynomials. Polynomial Terms Degree of Each Term Degree of the Polynomial 4mn2 4mn2 3 (The exponents of m and n are 1 and 2.) 3 4x3y2 – 6xy + 8x – 2 4x3y2, -6xy, 8x, -2 5, 2, 1, 0 5   To Write a Polynomial in Descending Order Write the term with the greatest power of one variable in the first position. Each subsequent term should have a smaller power of this variable. If there is a constant, it should be written last. Example 4:  Writing a Polynomial in Descending Order Write each of the following polynomials in descending order. 5 + 2x4 – 4x3 + x – 9x2 2x4 – 4x3 – 9x2 + x + 5 5x2y2 – 3 + y4 + 3x3 Since we have two variables, choose one to begin with. Let’s use x. 3x3 + 5x2y2 + y4 – 3   Matching Game Practice Match each polynomial with the correct type and degree. Write each of the following polynomials in descending order. 8x2 – 6 + x 8x2 + x – 6 5x + 2x3 + 3 – 2x2 2x3 – 2x2 + 5x + 3 2xy2 -10 + 3x2y + 4x3 4x3 + 3x2y + 2xy2 – 10 -2x4y + 2xy4 + 3 -2x4y + 2xy4 + 3 Now go on to the next part

© 2006 Aventa Learning. All rights reserved.