Higher Powers
Classify the polynomial by degree and number of terms. Simplify if needed.
f(x)=(2x-5)(x2-1)
Cubic, 4 terms
Find the zeros of the function: y=x2(x+12)(x-9)(x-7)
X=0, -12, 9, 7
Factor x3-27
(x-3)(x2+3x+9)
A polynomial P (x) is divided by a binomial x- a. The remainder is 0. What conclusion can you draw? Explain.
x-a is a factor of P(x)
Find the number of roots for -x14-x8-x-7=0
14 roots
What is the maximum number of turning points AND zeros of the polynomial: P(x) = x8-6x4+40x-2
7 turning points and 8 zeros
Your friend says that to write a function that has zeros 3 and -1, you should multiply the two factors (x + 3)(x - 1). What is wrong with this answer?
It should be (x -3)(x + 1)
Solve by graphing:
2x2+7x-4=0
x=-4 and x=1/2
Divide (2x2+7x+11) by (x+2)
2x+3 + 5/(x+2)
Give an example of a conjugate pair.
Answers vary; 3-4i and 3+4i
Determine the end behavior:
f(x) = -x3-x2+5
Left: increasing, Right: decreasing
Find a fourth degree polynomial function with zeros 1, -1, i, - i. write the function in factored form
f(x)=(x+1)(x-1)(x+i)(x-i)
What method of solving polynomial equations will not identify imaginary roots. Explain
Graphing. Imaginary numbers dont exist on the real plane.
What is the remainder of (x3+4x2+x-6)/(x+1)?
-4
Write a polynomial function in standard form with rational coefficients such that P(x)=0 has roots -9 and -15.
x2+24x+135
Determine the end behavior:
f(x) = -8x11-2x9+3x6+4
Left: increasing
Right: decreasing
Find the zeros of the function, state their multiplicities, and describe their behavior on the graph: y=x3-144x
x=0 (1) x=12 (1) x=-12 (1)
Solve by factoring: 2x3+2x2-4x=0
X= -2, 0, 1
Is (x+2) a factor of (x3+4x2+x-6)? How do you know?
Yes; Remainder Theorem or 0 is a remainder when performing polynomial division
Write a QUARTIC polynomial function in standard form with rational coefficients such that P(x)=0 has roots 3, -6 and -15i.
x4+3x3+207x2+675x+4050
Write a polynomial function that has 3 turning points and end behavior increasing to the left and right.
Answers vary
Explain how the graph of a polynomial function can help you factor the polynomial.
The binomial factors can be determined by examining the X intercepts of the graph.
Solve: x4-64=0. Show all work.
x= -Sqrt(8), sqrt(8), -2i*sqrt(2), 2i*sqrt(2)
Simplify (2x4+6x3+5x2-6)/(x+3)
2x3+5x-15 +39/(x+3)
Without using a calculator find all the roots of the equation x5+3x3-4x=0
x = 0, 1, -1, 2i, -2i