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:
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 The only way that x 2 - 14x - 32 can = 0 is if x = 16 or x = -2 Rearrange the terms to have zero on one side: Factor: Set each factor equal to zero and solve:
Zeros of a Polynomial Function The Zeros of a Polynomial Function are the solutions you get when the function is set equal to zero.
Graph of a Polynomial Function Here is the graph of our polynomial function: The zeros of 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 factors are: (x + 2) and (x - 1) The roots are: x = -2 and 1 The zeros are at: (-2, 0) and (1, 0)