### Home > PC3 > Chapter 8 > Lesson 8.3.5 > Problem 8-156

8-156.

Let

*f*(*x*) =*x*^{2}(*x*–*a*)^{2}(*x*–*b*)(*x*–*c*)^{3}(*x*–*d*). Assume*a*<*b*< 0 <*c*<*d*. Homework Help ✎Sketch a possible graph for

*y*=*f*(*x*).Solve

*f*(*x*) ≤ 0.Solve

≤ 0.

Begin by sketching the axes. Mark locations on the *x*-axis for *a*, *b*, *c*, and *d*. Then sketch a polynomial curve with roots at *x* = 0, *b*, and *d*, a double root at *x* = *a*, and a triple root at *x* = *c*.

Where is your curve below or touching the *x*-axis?

When do *f*(*x*) and *x* have opposite signs?

For example, where is the curve above the *x*-axis on the left side of the *x*-axis?