PFGSA Polynomials Functions and Graphs Summary Assignment Name: Please complete this assignment in its entirety, justifying your answers as you go. Using a method other than the requested method will not earn full credit. 1. Complete the following for the graph of p(x) to the left. a. Describe the end behavior: to the left and to the right b. What does the end behavior tell you about the degree and leading coefficient of the equation? Fill in each blank with one of the following words: even, odd, positive, or negative. The degree must be _ and the leading coefficient must be c. Assuming there are no nonreal zeros, write the equation for the FUNction in factored form. Don't forget to solve for a! Show your algebraic steps. 2. Divide using box division. (6x3+ 5x] - 11x + 3) : 3. Divide using long division. (8x + 3x2 - 5x - 7) : (3x + 1) Use the quotient to write the dividend (x2 - 1). Use the quotient to write the dividend in P(x) = D(x) Q(x) + R(x) form. in P(x) = D(x) Q(x) + R(x) form. Quotient: Quotient: P(x) = D(x) Q(x) + R(x) form: P(x) = D(x) Q(x) + R(x) form: 148Divide using synthetic division. Use your results to write a sentence to describe your conclusions based on the factor theorem and the remainder theorem. Be specific and be sure to include a statement about both theorems in your sentence. 4. Given pix} = 2x3 332 9x + 10. 5. Given pix} = 2x\" 5x2 11 [2x53x29x+1D]:{x+2] {fo5x111}+(x2] Quotient: Quotient: Based on your results and the factor theorem, what can Based on your results and the factor theorem, what can you conclude about it = -2? you conclude about x = 2? According to the remainder theorem, of }= According to the remainder theorem, p }= because . beca use 6. Complete the following for the graph of pix} to the left. a. Complete the table by identifying each zero and its Multiplicity multiplicity. b. What does the end behavior tell you about the degree and leading coefficient ofthe equation? Fill in each blank with one of the following words: even, add, positive, or negative. The degree must be , and the leading coefficient must be c. Assuming there are no non real zeros, write the equation for the FUthion in factored form. Don't forget to solve for a! Show youralgebraic steps. 1:19 7. Complete the following for the graph of p(x) to the left. a. Complete the table by identifying each zero and its multiplicity. Zeros Multiplicity 200 [0, 192) b. Assuming there are no nonreal zeros, write the equation for the FUNction in factored form. Don't forget to solve for a! Show your algebraic steps. 100 -3 2 2 Complete the following information for each polynomial. 8. y= -2x(x - a)?(x- b)(x -c)3 a. degree: b. end behavior: to the left and to the right c. Complete the table. zeros: multiplicity: d. Sketch a graph of the FUNction on the axes to the right. Don't worry about the relative heights of the extrema, but be sure to include the correct end behavior, x-intercepts, and behavior at each x-intercept. 9. y= (x-k) (x - m) (x- n)(x-p) a. degree: b. end behavior: to the left and to the right c. Complete the table. zeros: k m n p multiplicity: d. Sketch a graph of the FUNction on the axes to the right. Don't worry about the relative heights of the extrema, but be sure to include the correct end behavior, *-intercepts, and behavior at each x-intercept. 150