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1) Use the listed graph characteristics to describe the degree and leading coefficient of the function f. 1.) f is increasing on the interval (-∞,3) and f is decreasing on the interval (3,∞). 2.) f(x)<0 on the intervals (-∞,2) and (4,∞); f(x)>0 on the interval (2,4). a) The degree is even and the leading coefficient is negative b) The degree is odd and the leading coefficient is negative c) The degree is even and the leading coefficient is positive. d) The degree is odd and the leading coefficient is positive. 2) Fully factor the polynomial: x4 − 7x2 − 18 a) (x + 3) 2(x 2 − 2) b) (x 2 + 9)(x 2 − 2) c) (x − 3) 2 (x 2 + 2) d) (x − 3)(x + 3)(x2 + 2) 3) Evaluate f(-6), when f(x)= -x6 + 5x4 +8x3 + 2x-7 a) f(-6)=233 b) f(-6)=-247 c) f(-6)=-38,443 d) f(-6)=-41,923 4) Add or subtract to simplify (6b3 + 6 - b4 ) - (8b3 - 6b4 + 2) a) 4b4 - 2b3 + 7 b) 5b4 - 2b3 + 4 c) b4 - 2b3 + 7 d) 5b4 - 2b3 + 7 5) Find the product of (x-3)(x2 + 2x+ 7) a) x3 -x2 +x-21 b) x3 -3x2 +7x-21 c) x3 +5x+13x-21 d) x2 +2x-3 6) If f(x) = x3+8x+24, then find f(-2) using synthetic division. a) 12 b) 8 c) 0 d) -6 7) Describe and correct the error in the graphing of the function f(x)=(x+2)4 -6. See the graph.  a) The graph is shifted down 6 units but it should be shifted up 6 units.  b) The graph  is shifted right 2 units but it should be shifted left 2 units. c) The graph has no vertical stretch but it should have a vertical stretch by 2. d) The graph is not reflected across the x-axis but it should be reflected across the x-axis. 8) The answer to this question will unlock Lock#6. What is the name of the lead female character in the Harry Potter series? a) Hermione b) Ronald c) Harry d) Bellatrix

Lock #6: Polynomials

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