Section 3.4 Homework

1 List all possible rational zeros given by the Rational Zeros Theorem (but don’t check to see which actually are zeros). (Enter your answers as a comma-separated list.) 

$Q\left(x\right) = x^4–3x^3–8x+8$

x =  ________

2.  List all possible rational zeros given by the Rational Zeros Theorem (but don’t check to see which actually are zeros). (Enter your answers as a comma-separated list.) 

$$\begin{gathered} R\left(x\right) = 2x^5+4^3+4x^2–6 \\ x= \end{gathered}$$

3.  A polynomial function P and its graph are given. 

$P\left(x\right) = 7x^3–x^2–7x+1$

(a) List all possible rational zeros of P given by the Rational Zeros Theorem. (Enter your answers as a comma-separated list.) 

(b) From the graph, determine which of the possible rational zeros actually turn out to be zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

4. A polynomial function P and its graph are given. 

$P\left(x\right)=2x^4–9x^3+9x^2+x–3$

(a) List all possible rational zeros of P given by the Rational Zeros Theorem. (Enter your answers as a comma-separated list.) 

(b) From the graph, determine which of the possible rational zeros actually turn out to be zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

5. All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$P\left(x\right) = x^3+4x^2–19x+14$

x =

Write the polynomial in factored form. 

P(x) =

6. All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$P\left(x\right) = x^3+3x^2–4$

x =

Write the polynomial in factored form. 

P(x) =

7.  All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$$\begin{gathered} P\left(x\right) = x^3+12x^2+9x–22 \\ x= \end{gathered}$$

Write the polynomial in factored form. 

P(x) =

8.   All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$$\begin{gathered} P\left(x\right) = x^4+12x^3+31x^2–12x–32 \\ x= \end{gathered}$$

Write the polynomial in factored form. 

P(x) =

9. Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$$\begin{gathered} P\left(x\right) = 4x^4–45x^2+81 \\ x= \end{gathered}$$

Write the polynomial in factored form.

P(x) =

10 .  Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$$\begin{gathered} P\left(x\right) = 6x^4–7x^3–13x^2+4x+4 \\ x= \end{gathered}$$

Write the polynomial in factored form. 

P(x) =

11. Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$$\begin{gathered} P\left(x\right) = 2x^3+7x^2+4x–4 \\ x= \end{gathered}$$

Write the polynomial in factored form. 

P(x) =

12.  Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$$\begin{gathered} P\left(x\right) = 15x^3–32x^2+3x+2 \\ x= \end{gathered}$$

Write the polynomial in factored form. 

P(x) =

13.  Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$$\begin{gathered} P\left(x\right) = 2x^4–7x^3+3x^2+8x–4 \\ x= \end{gathered}$$

Write the polynomial in factored form. 

P(x) =

14.  Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

$$\begin{gathered} P\left(x\right) = 6x^4–x^3–7x^2+x+1 \\ x= \end{gathered}$$

Write the polynomial in factored form. 

P(x) =

15.  Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) 

Write the polynomial in factored form. 

P(x) =