Solving Polynomial Inequalities Graphically

Odd Multiplicities have which of the following effects on the x-axis?

• Cross the x-axis
• Turn on the x-axis

What are the zeros of the graph?

• -4, -1, 2, 1 multiplicity 2
• -4, -1, 1, 2
• 4, 1, -2, -1 multiplicity 2
• 4, 1, -1, -2

Based on the end behavior which option best describes the leading term?

• negative coefficient, even degree
• negative coefficient, odd degree
• negative degree, odd coefficient
• negative degree, even coefficient

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

• ±1, 8
• ±1, 2, 4, 8
• ±1, 2, 4
• 1, 2, 4, 8

To determine the number of possible negative real zeros using Descartes's rule of signs,
we need to evaluate f(-x).
If f(x) = -3x⁵+ 8x⁴ - 6x³ + 5x² - 7x - 1.
Then these are the signs of the terms for f(-x):

• -   +   -   +   -   -
• -   -   -   -   -   -
• +   +   +   +   +   +
• +   +   +   +   +   -

Use Descartes's rule of signs to determine the number of possible positive real zeros for
f(x) =3x⁴-7x³-4x²-5x-9.

• 0 possible positive real zeros
• 1 possible positive real zero
• 2 or 0 possible positive real zeros
• 3 or 1 possible positive real zeros

Assuming the scale is 1, determine where f(x) ≤ 0.

• (-oo, 2) U (2, 4)
• (-oo, 2] U [2, 4]
• (-oo, 4]
• Not given

Assuming the scale is 1, where is f(x) > 0?

• [-4, -1] U [2, +oo)
• (-4, -1) U (2, +oo)
• (-oo, -4] U [-1, 2]
• (-oo, -4) U (-1, 2)

Assuming the scale is 1, where is f(x) < 0?

• [-4, -1] U [2, +oo)
• (-4, -1) U (2, +oo)
• (-oo, -4] U [-1, 2]
• (-oo, -4) U (-1, 2)

Assuming the scale is 1, where is f(x) < 0?

• (-4, 2)
• [-4, 2]
• (-oo, -4) U (2, 4)
• (-oo, -4] U [2, 4]