Download Unit 7 Review – Polynomial Functions

Unit 5 Review – Polynomial Functions
Analysis BC
1.) Write TRUE or FALSE next to each statement. JUSTIFY your answers.
__________ a.) Every polynomial equation has at least one real root.
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__________ b.) The zeros of a certain quartic polynomial are  , 0, and 1  i
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__________ c.) No polynomial function can have an odd number of imaginary roots.
__________ d.) Suppose P(x) is a polynomial with real coefficients. If a+bi, b≠0, is a zero
of the function, then the function must have an even number of zeros.
2.) The graph of f(x) = (x – 2)2 is tangent to the x-axis at ___________.
3.) Write a polynomial function of third degree with exactly one positive real zero and exactly
one negative real zero.
4.) Find all the zeros of h(x) = 4x3 + 23x2 + 34x – 10 (hint: -3 + i is a zero)
5.) A third degree polynomial function f has zeros -2, ½, 3 and a negative leading coefficient.
Write an equation for f then sketch a graph.
6.) Graph a fifth degree polynomial function with exactly 3 distinct real roots.
7.) Given f(x) = x4 – 3x2 – 10:
a.) Write f(x) as the product of factors that are irreducible over the rationals.
b.) Write f(x) as the product of factors that are irreducible over the reals.
c.) Factor completely.
d.) What are the zeros of f?
e.) What are the x-intercepts of f?
8.) Find all zeros of f(x) = 2x3 – 5x2 + 12x – 5. Sketch a graph.
9.) Find all zeros of g(x) = x3 – 5x2 – 25x + 125. Sketch a graph.
10.) Write a quadratic function with zeros 2 and 5 passing through the point (3,7). Graph the
function.
11.) Challenge: A cylinder is inscribed in a cone of height 10 cm and radius 5 cm. Write the
volume of the cylinder as a function of its height. Find the domain for the volume function.
Ans Key: 1.) false, false, true, false 2.) x = 2 3.) ans will vary 4.) x = -3 + i, -3-i, ¼
5.) ans will vary 6.) ans will vary 7.) a) (x2 – 5)(x2 + 2) b) (x - √5)(x + √5)(x2 + 2)
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c) (x - √5)(x + √5)(x - i√2)(x + i√2) d) x = ±√5, ±i√2 e) (√5, 0)(-√5,0) 8.) x  ,1  2i
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 10  h 
x  35 11.) V (h)   
9.) x = 5(mult 2), -5 10.) f ( x)  x 2 
  h , domain: o<h<10
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 2 
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