POLYNOMIALS AND POLYNOMIAL FUNCTIONS By: Rut Arteaga

USING PROPERTIES OF EXPONENTS Before: You evaluated powers Now: You will simplify expressions invoving powers. After: So you can compare the volumes of the two stars, as your going to learn in a few. Example; Evaluate numerical expressions ( -5 X 42)2 = (-5)2x (42)2 = 25 x 42x2 = 25 x 44 = 6400

Add, Subtract, and Multiply Polynomials Before: You evaluated and graphed polynomials functions. Now: You will add, subtract, and multiply polynomials. After: So you can model collegiate sports participation.

Use direct substitution to evaluate f (x) = 2x4 – 5x3 – 4x + 8 when x = 3. f (x) = 2x4 – 5x3 – 4x + 8 when x = 3. (x) = 2x4 – 5x3 – 4x + 8 Write original function. f (3) = 2(3)4 – 5(3)3 – 4(3) + 8 Substitute 3 for x. = 162 – 135 – 12 + 8 Evaluate powers and multiply. = 23 Simplify

not a polynomial function p (x) = 9x4 – 5x – 2 + 4 A polynomial function: h (x) = 6x2 + π – 3x polynomial function; h(x) = 6x2 – 3x + π ; degree 2, type: quadratic, leading coefficient: 6

Examples g(x) = x3 – 5x2 + 6x + 1; x = 4 = 9 f (x) = x4 + 2x3 + 3x2 – 7; x = –2 = 5

Adding polynomials vertically and horizontally Adding 2x3 – 5x2 + 3x – 9 and x3 + 6x2 + 11 in a vertical format. 2x3 – 5x2 + 3x – 9 + x3 + 6x2 + 11 3x3 + x2 + 3x + 2

Add 3y3 – 2y2 – 7y and –4y2 + 2y – 5 in a horizontal format. (3y3 – 2y2 – 7y) + (–4y2 + 2y – 5)‏ = 3y3 – 2y2 – 4y2 – 7y + 2y – 5 = 3y3 – 6y2 – 5y – 5