polynomial assignment college

Name _________________

POLYNOMIALS ASSIGNMENT

1. Find a function ( )P x defined by a polynomial of degree 3 with real coefficients that

satisfies the given conditions.

Zeros of 3, 2, and 5. Let (1) 96.x x x P= − = − = =

In problems #2 and #3, one zero is given. Determine the remaining zeros. Rewrite the polynomial

in factored form.

2. 3 2

( ) 5 17 13 1P x x x x x= − + − = is a zero

3. 4 3 2

( ) 2 7 11 28 12P x x x x x= − + − + 2x i= is a zero

4. For the given polynomial determine the following.

3 2

( ) 6 7 4P x x x x= − + +

i) Determine the number of possible positive real zeros.

ii) Determine the number of possible negative real zeros.

iv) Determine the zeros of the polynomial in exact form. That is, no decimal

approximations.

v) Graph the function below. Please label your graph with ordered pairs.

Local minimum _________

Local maximum _________

Intervals increasing _______

Intervals decreasing _______

5. For the given polynomial determine the following.

3 2

( ) 2 5 20 9P x x x x= + − −

i) Determine the number of possible positive real zeros.

ii) Determine the number of possible negative real zeros.

iv) Determine the zeros of the polynomial in exact form. That is, no decimal

approximations.

v) Graph the function below. Please label your graph with ordered pairs.

Local minimum _________

Local maximum _________

Intervals increasing _______

Intervals decreasing _______

6. Use the graph below to answer the following.

Sign of n

a ______________

Degree of ( )P x __________

Zeros of ( )P x _____________

Factors of ( )P x _____________

Given that (1) 12P = and the zeros of ( )P x , write ( )P x in expanded form.

7 Use the graph below to answer the following.

Sign of n

a ______________

Degree of ( )P x __________

Zeros of ( )P x _____________

Factors of ( )P x _____________

Given that (0) 48P = − and the zeros of ( )P x , write ( )P x in expanded form.

W/2020