Roots & Zeros of Polynomials I

Roots & Zeros of Polynomials I How the roots, solutions, zeros, x-intercepts and factors of a polynomial function are related.

Factoring Polynomials Terms are Factors of a Polynomial if they equal the polynomial when multiplied together: So, are Factors of

Factors as Products Since the factors of the polynomials are being multiplied together, for the entire polynomial to equal zero, at least one of the factors must equal zero.

Solving a Polynomial Equation Rearrange the terms to have zero on one side: Factor: Set each factor equal to zero and solve: The only way that x2- 14x- 32 can = 0 is if x = 16 or x = -2

Zeros of a Polynomial Function The Zeros of a Polynomial Function are the solutionsyou get when the function is set equal to zero.

Graph of a Polynomial Function Here is the graph of our polynomial function: The zerosof the polynomial are the values of x when the polynomial equals zero. In other words, the zeros are the x-values where y equals zero.

Graph of Polynomials • x-intercepts: The point or points where the graph of the function crosses the x-axis • At the x-intercept, the y-coordinate is equal to zero The x-intercepts are (0,0) and (4,0)

Factors, Roots, Zeros The factorsare: (x + 2) and (x - 1) The roots are: x = -2 and 1 The zerosare at: (-2, 0) and (1, 0)

Roots & Zeros of Polynomials I