C HAPTER 10 – P OLYNOMIALS AND F ACTORING 10.1 – Adding and Subtracting Polynomials

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Today we will be learning how to: Add and subtract polynomials Use polynomials to model real life situations

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Polynomial – an expression which is the sum of terms in the form ax k k is a nonnegative integer Standard form – terms are placed in descending order largest degree to smallest degree

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Degree – exponent of the variable Degree of a polynomial – largest degree of its terms Leading coefficient - coefficient of the first term Standard form

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Example 1 Identify the coefficients of 4 – x + 2 x 3

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Monomial – polynomial with one term Binomial – polynomial with 2 terms Trinomial - polynomial with 3 terms

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Example 2 PolynomialDegreeClassified by degree Classified by number of terms -5 ¼ x -9 x + 2 x 2 – 6 - x x x x 3 – x x – 8

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS To add or subtract polynomials, add and subtract the like terms Same variable, same exponent

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Example 3 Find the sum. Write the answer in standard form. (-8 x 3 + x – 9 x 2 + 2) + (8 x 2 – 2 x + 4) + (4 x 2 – 1 – 3 x 3 ) (6 x 2 – x + 3) + (-2 x + x 2 – 7)

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Example 4 Find the difference. Write the answer in standard form. (-6 x x – 3) – (2 x x 2 – 3 x + 1) (4 x 2 – 1) – (3 x – 2 x 2 ) (12 x – 8 x 2 + 6) – (-8 x 2 – 3 x + 4)

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS Example 5 The first floor of a home has the floor plan shown below. Find an expression in standard form for the area of the first floor.

10.1 – A DDING AND S UBTRACTING P OLYNOMIALS HOMEWORK Page 580 #26 – 62 even