Find zeros of a polynomial function

1. Use the Rational Zero Theorem to list all possible rational zeros of the function.
2. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial.
3. Repeat step two using the quotient found with synthetic division.
4. Find the zeros of the quadratic function.

1. Step 1: Determine the graph’s end behavior.
2. Step 2: Find the x-intercepts or zeros of the function.
3. Step 3: Find the y-intercept of the function.
4. Step 4: Determine if there is any symmetry.
5. Step 5: Find the number of maximum turning points.
6. Step 6: Find extra points, if needed.
7. Step 7: Draw the graph.

Identify the x-intercepts of the graph to find the factors of the polynomial. Examine the behavior of the graph at the x-intercepts to determine the multiplicity of each factor. Find the polynomial of least degree containing all of the factors found in the previous step.

A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising). A polynomial of degree n will have at most n−1 turning points. Find the maximum possible number of turning points of each polynomial function.

The easiest way to find the turning point is when the quadratic is in turning point form (y = a(x – h)2 + k), where (h, k) is the turning point. To get a quadratic into turning point form you need to complete the square.

A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising). A polynomial of degree n will have at most n – 1 turning points.

The degree of a function determines the most number of solutions that function could have and the most number often times a function will cross the x-axis. As a result, sometimes the degree can be 0, which means the equation does not have any solutions or any instances of the graph crossing the x-axis.

It is a theorem that links factors and zeros of the polynomial. According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a)=0. Also, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0.