1. ACTIVITY 34 Review (Sections 3.6+3.7+4.1+4.2+4.3)

2. Problems 3 and 5: Sketch the graph of the function by transforming an appropriate function of the form y = x n. Indicate all x- and y-intercepts on each graph.

3. y = 2x 4 y = x 4 y = 2x 4 + 8 No x – intercepts y – intercepts is (0,8)

4. Problems 11, 13, and 15: Match the polynomial function with the below graphs

5. Problems 21: Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. The leading term is 3x 3

6. Problem 31: Factor the polynomial P(x) = −x 3 + x 2 + 12x and use the factored form to find the zeros. Then sketch the graph. Zeros

7. Problem 3: Let P(x) = x 4 − x 3 + 4x + 2 and Q(x) = x 2 + 3. (a)Divide P(x) by Q(x). (b)Express P(x) in the form P(x) = D(x) · Q(x) + R(x). x 4 − x 3 + 4x + 2 x 2 + 3 x2x2 x 4 + 3x 2 –x 4 – 3x 2 − x 3 – 3x 2 + 4x + 2 – x – x 3 – 3x+ x 3 + 3x – 3x 2 + 7x + 2 – 3 – 3x 2 – 9+3x 2 + 9 7x + 11

8. Problem 9: Find the quotient and remainder using long division for the expression x 3 + 6x + 3x 2 – 2x+2 x x 3 – 2x 2 + 2x –x 3 + 2x 2 – 2x 2x 2 + 4x + 3 + 2 2x 2 – 4x + 4 – 2x 2 + 4x – 4 8x – 1

9. Problem 21: Find the quotient and remainder using synthetic division for the expression

10. Problem 35: Use synthetic division and the Remainder Theorem to evaluate P(c) if P(x) = 5x 4 + 30x 3 − 40x 2 + 36x + 14 and c = −7.

11. Problem 43: Use the Factor Theorem to show that x − 1 is a factor of P(x) = x 3 − 3x 2 + 3x − 1. Showing that x = 1 is a zero. Therefore, (x – 1) is a factor

12. Problem 53: Find a polynomial of degree 3 that has zeros 1, −2, and 3, and in which the coefficient of x 2 is 3.

13. Problem 3: List all possible rational zeros given by the Rational Zeros Theorem (but don’t check to see which actually are zeros). possible rational zeros:

14. Problems 13 and 23: Find all rational zeros of the polynomial. possible rational zeros:

15. Consequently, the zero’s are x = 2 and x = – 1

16. possible rational zeros:

17. So we need only factor possible rational zeros:

18. So we need only factor possible rational zeros: Consequently, the roots are x = -4, x = -2, x = -1, and x = 1