Adding and subtracting polynomials

5x 3 + 2x 2 – x – 7 5x 3 + 2x 2 – x – 7 This is a polynomial in standard form: Leading Coefficient Degree Constant term **Can not be a polynomial if the exponent is negative or a variable**

4 – x + 2x 3 4 – x + 2x 3 Example 1 2x 3 – x + 4 Rewrite in standard form. Rewrite in standard form, identify the degree and the leading coefficient Degree = 3 Leading Coefficient = 2

3x 3 + 2x 2 – x Match the number of terms with the expression: BinomialMonomialTrinomial 4x 2 5x 3 + x

classify the polynomial degree and # of terms: a) -5 b) x 2 – 6 c) -x 3 + 2x + 1 Example 2 0 Degree, Monomial 2 nd Degree, Binomial 3 Degree, Trinomial

Adding & Subtracting Polynomials 3x3 + 2x2 – x – 7 + x3 – 10x x3 – 8x2 – x + 1 Adding & subtracting can be done both vertically and horizontally. Adding & subtracting can be done both vertically and horizontally. = 2x 2 + 3x – 3x 2 – x +4 (2x 2 + 3x) – (3x 2 + x – 4) Example 3 Example 4 = -x 2 + 2x + 4

4x3 + 2x2 – 4 + x3 – 3x2 + x 5x3 – x2 + x – 4 = – x 3 + x 3 – 2x 2 + 3x 2 + 3x – 12 (–2x 2 + 3x – x 3 ) + (3x 2 + x 3 – 12) Class Work 5) 6) = x 2 + 3x – 12

= – x 3 – x 3 – 2x 2 – 3x 2 + 3x + 12 (–2x 2 + 3x – x 3 ) – (3x 2 + x 3 – 12) Class Work 7) 8) = -2x 3 -5x 2 + 3x + 12 (2c 2 – 8) – (3c 2 – 4c + 1) = – c 2 + 4c – 9