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Adding and Subtracting Polynomials Module VII, Lesson 1 Algebra Online [email protected] What is a polynomial? A polynomial is one term or the sum or difference of two or more terms. Examples of polynomials are: 5xy 2 3x 3x 9 2 12a 14 We classify polynomials by degrees or by number of terms. Classifying by Degree Degree of a term is the exponent of the term. x4 + 2x2 – 4 The degreeThe degree The degree The degree a polynomial is the degree of thisofterm is of 2x2 isof2 any 4. with the constant for the term highest ispower. In 0. this case it is 4. Classifying by Degrees Polynomials with degrees of 0 – 3 have special names. They are: 0 degree – constant 1st degree – linear 2nd degree – quadratic 3rd degree - cubic Classifying By Number of Terms Polynomials can also be named by the number of terms that make it up. One term (6xy) Monomial Two terms (4x – 9) Binomial Three terms (5d2 + 5d – 10) Trinomial Three or more terms is considered a polynomial Classify each polynomial by it’s degree and number of terms. 1. 2x2 1. Quadratic monomial 2. 4b3 – 3b + 8 2. Cubic trinomial 3. -2t4 4. 5 + 5t 3. 4th degree binomial 4. 0 degree constant Simplifying Polynomials Recall from earlier lessons that to add or subtract terms they must have exactly the same variable. 5x2 + 12x2 = 17x2 2w3 – 4w + 3w3 = 5w3 – 4w -3r3 + 5r3 – 8r3 = -6r3 14x – 9 = 14x - 9 Just add or subtract the coefficients of terms with the same variable Adding Polynomials (5x2 – 3x + 7) + (2x2 + 5x - 7) To add these polynomials we just add the like terms. The easiest way to do this is like we always have added. Line them up on top of each other and add. 5 x 2 3x 7 2 x 2 5 x 7 7x2 + 2x Subtracting Polynomials (2x3 + 4x2 – 6) – (3x3 + 2x – 2) Recall that subtracting is the same as adding the opposite. So change everything in the second polynomial to its opposite and add. 2x 4x 0x 6 3 2 3x3 0 x 2 2 x 2 -x3 + 4x2 – 2x - 4 Try some on your own. 1. (3y2 + 5y – 6) + (7y2 – 9) 1. 10y2 + 5y – 15 2. (9y – 7x + 15a) + (-3y + 8x – 8a) 2. 6y + x + 7a 3. (7a – 10b) – (3a + 4b) 3. 4a – 14b 4. (5x2 – 4) – (3x2 + 8x + 4) 4. 2x2 – 8x - 8 Wrap-Up Polynomials can be classified by degree (constant, linear, quadratic or cubic) or number of terms (monomial, binomial and trinomial). Terms can only be added or subtracted if they have the exact same variable.