Lesson 3 Building Strong Roots Solidify Understanding

Ready

Divide using long division. (These problems have no remainders. If you get one, try again.)

1.

2.

If , what is the value of ?

3.

4.

If , what is the value of ?

5.

6.

If , what is the value of

7.

8.

If , what is the value of ?

Set

Predict the number of roots for each of the given polynomial equations.

9.

10.

11.

12.

13.

14.

The graphs of the polynomials from the previous problems are shown. Check your predictions. Then, use the graph to help you write the polynomial in factored form.

15.

a parabola opening up with the points (-5,0) and (2,0) graphed on a coordinate plane x–5–5–5555y–10–10–10–5–5–5000

16.

a positive cubic function with the points (-3,0), (-1,0), and (3,0) graphed on a coordinate plane x–5–5–5555y–15–15–15–10–10–10–5–5–5555000

17.

a linear function with a negative slope and the points (-2,0) and (0,-5) graphed on a coordinate plane x–5–5–5555y–5–5–5555000

18.

a positive quartic function with the points (-2,0), (0,0), (1,0), and (2,0) graphed on a coordinate plane x–5–5–5555y–5–5–5555000

19.

a negative quadratic function with the points (-9,0), (3,0), and (6,-9) graphed on a coordinate plane x555y–10–10–10–5–5–5000

20.

a positive function with the points (-2,0), (-1,0), (0,0), (1,0), and (2,0) graphed on a coordinate plane x–5–5–5555y–5–5–5555000

21.

The graphs of problems 19 and 20 don’t seem to follow the Fundamental Theorem of Algebra, but there is something similar about each of the graphs. Explain what is happening at the point in problem 19 and at the point in problem 20.

Go

Find the roots of each quadratic function.

22.

23.

24.

25.

26.

27.