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Addition / Subtraction of Polynomials

Addition / Subtraction of Polynomials. Chapter 7.1. What are Polynomials?. A polynomial is an expression in which the terms are monomials. Monomial : number, variable or a product of a number and variable. e.g. 6, a, 6a, 13xy 2 Binomial : polynomial with two terms. e.g. 3x+4

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Addition / Subtraction of Polynomials

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  1. Addition / Subtraction of Polynomials Chapter 7.1

  2. What are Polynomials? • A polynomial is an expression in which the terms are monomials. • Monomial: number, variable or a product of a number and variable. e.g. 6, a, 6a, 13xy2 • Binomial: polynomial with two terms. e.g. 3x+4 • Trinomial: polynomial with 3 terms. x2+4x-1 • A Polynomial that has four or more terms is referred to as a “Polynomial.”

  3. Polynomials - Degrees & Order • The degree of a polynomial is the monomial with the highest exponent. The degree of 4x3+5x2+3x+4 is 3 The degree of 7x4+x3+11x+4 is 4 Polynomials are written in descending order, the highest degree is first, the second highest degree next …

  4. Adding Polynomials • Recall: it is only possible to add like terms. • Add (4x3+5x2+9x+4) + (3x5+x2+3x-13) • 4x3+ 5x2 +9x + 4 +3x5+ x2+ 3x -13 3x5+4x3+6x2+12x -9

  5. Add (14x3-11x2+9x+11) +(-4x3+18x2-21x-17) • 14x3 -11x2 + 9x +11 • + -4x3 +18x2 -21x -17 • 10x3 +7x2 -12x -6

  6. Subtracting Polynomials • Subtract (8x3+25x2+19x+7) - (4x3+9x-4) • The negative sign is distributed and the polynomials are added. • (8x3+25x2+19x+7)+ (-4x3-9x+4) • 8x3+25x2+19x+7 • + -4x3 -9x+4 • 4x3+25x2+10x+11

  7. Subtract (8x3+2x2y+x+7)– (x3+5x2+9xy+7) • The negative sign is distributed and the polynomials are added. • (8x3+2x2y+x+7)+(-x3-5x2 -9xy -7) • 8x3+2x2y +x+7 • + -x3 -5x2 -9xy -7 • 7x3+2x2y-5x2 -9xy +x+0

  8. Now You Try • 1. (x3-5x2+9x+7) + (4x3+7x2+3x-4) • 2. (8x3+19x+7) - (4x3+10x -4) • 3. (5x3-2x2+19x+7) + (13x3-15x2+x-27) • 4. (25x2+19x+7) - (-14x2+19x-4)

  9. Answers • 1. 5x3+2x2+12x+3 • 2. 4x3+9x+11 • 3. 18x3-17x2+20x-20 • 4. 39x2+11

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