Question

Sketch a graph of polynomial p(x) which has a known factor of (x - 6).

Answer 1

To sketch a graph of a polynomial with a known factor of (x - 6), identify the root at x = 6, choose a scale for the axes, and draw the curve passing through the x-intercept at x = 6, with the direction of the curve determined by the assumed sign of the leading coefficient.

Step-by-step explanation:

To sketch a graph of a polynomial p(x) with a known factor of (x - 6), follow these steps:

1. On the graph, mark the x-intercept at x = 6, as the factor (x - 6) indicates that the polynomial will have a root at x = 6.
2. Choose a reasonable scale for the x-axis and y-axis, ensuring that x = 6 is clearly labeled.
3. The exact shape of the polynomial curve will depend on the other factors and the leading coefficient. If no other information is given, you can assume a simple case where p(x) just touches the x-axis at x = 6 and moves away, which would look like the graph of a quadratic that has a double root at x = 6.
4. Draw the curve so that it passes through the x-intercept at x = 6. If this is the only intercept, then we assume the curve approaches infinity as x goes to plus or minus infinity.
5. Indicate the direction of the ends of the polynomial; if the leading coefficient is positive, the ends will go up, and if it is negative, they will go down.

Since no other factors or the degree of the polynomial is given, we sketch the graph based on the known factor and make general assumptions about the behavior of the polynomial.