Polynomials Polynomials are the sums of power functions with nonnegative integer exponents: Here is a nonnegative integer called the of the polynomial, and - 1, are n degree an, an a1, a0 …, constants, with leading coefficient 0. An example of a polynomial of degree = 3 is an n ≠ In this case = 2, = -1, = -5, and = -7. The shape of the graph of a polynomial depends on a3 a2 a1 a0 its degree; typical graphs are shown in Figure These graphs correspond to a positive coefficient for a negative leading coefficient turns the graph upside down. Notice that the quadratic xn; “turns around” once, the cubic around” twice, and the quartic (fourth degree) around” three “turns “turns times. An degree polynomial around” at most - times (where is a positive integer), nth n n “turns but there may be fewer turns.
Polynomials Polynomials are the sums of power functions with nonnegative integer exponents: Here n is a nonnegative integer called the degree of the polynomial, and an, an - 1, …, a1, a0 are constants, with leading coefficient an ≠ 0. An example of a polynomial of degree n = 3 is In this case a3 = 2, a2 = -1, a1 = -5, and a0 = -7. The shape of the graph of a polynomial depends on its degree; typical graphs are shown in Figure These graphs correspond to a positive coefficient for xn; a negative leading coefficient turns the graph upside down. Notice that the quadratic “turns around” once, the cubic “turns around” twice, and the quartic (fourth degree) “turns around” three times. An nth degree polynomial “turns around” at most n - times (where n is a positive integer), but there may be fewer turns.