Solving Polynomial Inequalities Graphically

The following are characteristics of the graph of a polynomial.

• Sharp corners

• Smooth curves

• Continuous

• Has jumps

The multiplicity of the factor (x+1) could be:

• 1

• 2

• 3

• 4

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

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)

Solve the inequality without a graph:
 (x - 3)² ≥ 1

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

Solve the inequality without a graph:
(x - 2)(x + 3)²(x² + 4) ≥ 0

• [2,∞)
• [-3] U [2,∞)
• (2,∞)
• Not Given

Solve the inequality without a graph:
x⁴ + 35x² > 36

• (-oo, -6) U (-6, -1) U (-1, 1) U (1, 6) U (6, +oo)
• (-oo, -1) U (1, +oo)
• (-oo, -6) U (6 +oo)
• Not given

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

Solve the inequality:
(x-2)(x+3)²(x²+4)≥0

• x= 3, x ∈ [2,∞]
• x=3, x ∈ [2,∞)
•  x ∈ (2,∞)
• x ≥ 3