Addition Subtraction of Polynomials Chapter 7 1 What

Addition / Subtraction of Polynomials Chapter 7. 1

What are Polynomials? A polynomial is an expression in which the terms are monomials. n Monomial: number, variable or a product of a number and variable. e. g. 6, a, 6 a, 13 xy 2 n Binomial: polynomial with two terms. e. g. 3 x+4 n Trinomial: polynomial with 3 terms. x 2+4 x-1 n A Polynomial that has four or more terms is referred to as a “Polynomial. ” n

Polynomials - Degrees & Order n The degree of a polynomial is the monomial with the highest exponent. The degree of 4 x 3+5 x 2+3 x+4 is 3 The degree of 7 x 4+x 3+11 x+4 is 4 Polynomials are written in descending order, the highest degree is first, the second highest degree next …

Adding Polynomials Recall: it is only possible to add like terms. n Add (4 x 3+5 x 2+9 x+4) + (3 x 5+x 2+3 x-13) n n 4 x 3+ 5 x 2 +9 x + 4 +3 x 5+ x 2+ 3 x -13 3 x 5+4 x 3+6 x 2+12 x -9

n Add (14 x 3 -11 x 2+9 x+11) +(-4 x 3+18 x 2 -21 x-17) 14 x 3 -11 x 2 n + -4 x 3 +18 x 2 n 10 x 3 +7 x 2 n + 9 x +11 -21 x -17 -12 x -6

Subtracting Polynomials Subtract (8 x 3+25 x 2+19 x+7) - (4 x 3+9 x-4) n The negative sign is distributed and the polynomials are added. n (8 x 3+25 x 2+19 x+7)+ (-4 x 3 -9 x+4) n 8 x 3+25 x 2+19 x+7 n + -4 x 3 -9 x+4 n 4 x 3+25 x 2+10 x+11 n

Subtract (8 x 3+2 x 2 y+x+7)– (x 3+5 x 2+9 xy+7) n The negative sign is distributed and the polynomials are added. n (8 x 3+2 x 2 y+x+7)+(-x 3 -5 x 2 -9 xy -7) n 8 x 3+2 x 2 y +x+7 n + -x 3 -5 x 2 -9 xy -7 n 7 x 3+2 x 2 y-5 x 2 -9 xy +x+0 n

Now You Try n 1. (x 3 -5 x 2+9 x+7) + (4 x 3+7 x 2+3 x-4) n 2. (8 x 3+19 x+7) - (4 x 3+10 x -4) n 3. (5 x 3 -2 x 2+19 x+7) + (13 x 3 -15 x 2+x-27) n 4. (25 x 2+19 x+7) - (-14 x 2+19 x-4)

Answers n n 1. 5 x 3+2 x 2+12 x+3 2. 4 x 3+9 x+11 n 3. 18 x 3 -17 x 2+20 x-20 n 4. 39 x 2+11