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Activity 34

Activity 34. Review (Sections 3.6+3.7+4.1+4.2+4.3). 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. No x – intercepts. y – intercepts is (0,8). y = x 4. y = 2x 4. y = 2x 4 + 8.

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Activity 34

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  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 = xn. Indicate all x- and y-intercepts on each graph.

  3. No x – intercepts y – intercepts is (0,8) y = x4 y = 2x4 y = 2x4 + 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 3x3

  6. Problem 31: Factor the polynomial P(x) = −x3 + x2 + 12x and use the factored form to find the zeros. Then sketch the graph. Zeros

  7. Problem 3: • Let P(x) = x4 − x3 + 4x + 2 and Q(x) = x2 + 3. • Divide P(x) by Q(x). • Express P(x) in the form P(x) = D(x) · Q(x) + R(x). x2 – x – 3 x4 − x3 + 4x + 2 x2 + 3 –x4 – 3x2 x4 + 3x2 − x3 – 3x2 + 4x + 2 + x3 + 3x – x3 – 3x – 3x2 + 7x + 2 – 3x2 – 9 +3x2 + 9 7x + 11

  8. Problem 9: Find the quotient and remainder using long division for the expression x + 2 x2 – 2x+2 x3 + 6x + 3 –x3 + 2x2 – 2x x3 – 2x2 + 2x 2x2 + 4x + 3 – 2x2 + 4x – 4 2x2 – 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) = 5x4 + 30x3 − 40x2 + 36x + 14 and c = −7.

  11. Problem 43: Use the Factor Theorem to show that x − 1 is a factor of P(x) = x3 − 3x2 + 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 x2 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. possible rational zeros: So we need only factor possible rational zeros: possible rational zeros:

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

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