Unit 2 Test: Polynomials
Knowledge
Application
Knowledge
1. A)
B)
2. A)
b)
Thinking
Communication
Determine an equation to represent the graph shown below
Sketch the function y=(x-1)2(x+2)(4-x)3 In the space provided.
Divide the expression x4-3x2+4x-1 by (2x-1)
Divide the expression x4-3x3+4x-1 by (3x+1)
3. Determine the equation of the cubic function that satisfies the following
conditions
i) only has roots at x=3 and x=-2
ii) passes through the point (2,-3) and
iii) as x approaches negative infinity, y approaches infinity
4. Determine the equation of the cubic function that satisfies the following
conditions
i) only has roots at x=-3 and x=2
ii) passes through the point (2,-3) and
iii) as x approaches infinity, y approaches negative infinity
5. Determine values of a and b for the expression x3 +ax 2-bx+4 given that the
expression is evenly divisible by x-2, and has a remainder of 8 when divided
by (x+4)
6. Find the values of a and b if (ax3  bx 2  3x  4) has a remainder of 2 when
divided by (x  2) and a remainder of -1 when divided by (x 1) .
7. Solve the following equations
a) x 4  x 3  13x 2  x 12
b) x4=1331x
8. a)
Explain how the degree of a polynomial function is related to the


number of zeros of the function.
b)
Explain the relationship between the degree of a polynomial function

and the number of turning points of its graph.
9. If x  2 , x  1 , and x  3 are divisors of a quartic polynomial and the
remainder when divided by x  1 is 16, find the other root of the polynomial.