Unit 4 Part 2 Practice

Unit 4 Part 2 Test Quizizz Review

Polynomial Inequalities

& Synthetic Division

Unit 4 Part 2 Test Topics

• 4.3: Using Synthetic Division to Factor & Evaluate Functions

• 4.4: Factoring Trinomials w/ # In Front of x²

• 4.5: Finding Zeros, Local Max, and Local Min in a Calculator

• 4.7: Finding All Roots Using Synthetic Division & Factoring

• 4.8: Conjugate Roots (Similar to 4.7 but with Square Roots & i's)

• 4.9: Solving Polynomial Inequalities

Unit 4 Part 2 Schedule

• Wednesday, January 27 - Quizizz Review

• Thursday, January 28 - In-Person Review on Paper

• Friday, January 29 - Part 2 Test (Calculator)

Polynomial Inequalties

• Sketch the graph of the polynomial (given on the Quizizz Review)

• For < and ≤ , select the intervals BELOW the x-axis

• For > and ≥ , select the invervals ABOVE the x-axis

• Remember: Less than symbols point Left

• Use ( ) for open circles < and >

• Use [ ] for closed circles ≤ and ≥

Multiple Select

Use the graph to select all intervals that would solve this inequality: (x+4)(x+1)(x-2) ≥ 0

• (-∞, -4]

• [-4, -1]

• [-1, 2]

• [2, ∞)

Multiple Select

Use the graph to select all intervals that would solve this inequality: (x+4)(x+1)(x-2) < 0

• (-∞, -4)

• (-4, -1)

• (-1, 2)

• (2, ∞)

Multiple Select

Use the graph to select all intervals that would solve this inequality: (x-4)³(x-2)² < 0

• (-∞, 2)

• (-∞, 2]

• (2, 4)

• [2, 4]

• (4, ∞)

Multiple Select

Use the graph to select all intervals that would solve this inequality: (x-4)³(x-2)² > 0

• (-∞, 2)

• (-∞, 2]

• [4, ∞)

• [2, 4]

• (4, ∞)

Multiple Select

Use the graph to select all intervals for f(x) < 0

• (-4, -1)

• (4, ∞)

• (-∞, -4)

• (-1, 2)

• (2, 4)

Multiple Select

Use the graph to select all intervals for f(x) ≤ 0

• (-∞ , -3]

• [-3, -2]

• [-2, 2]

• [2, 3]

• [3, ∞)

Multiple Select

Use the graph to select all intervals for f(x) > 0

• (-∞ , -3)

• (-3, 0)

• [0, ∞)

• [-3, 0]

• (0, ∞)

Multiple Select

Use the graph to select all intervals for f(x) ≥ 0

• (-∞ , -3]

• [-3, 2]

• [2, 5]

• [5, ∞)

• (-∞, ∞)

Synthetic Division

• If dividing by x - 5, the value 5 would go in the top-left box

• The number in the bottom right box is the remainder

• If the remainder is zero, then the # in the top left box is a zero

• f(-2), the y-value when x=-2, is equal to the remainder of synthetic division with -2 in the top-left box

Multiple Choice

Is x - 3 a factor of the polynomial shown in this synthetic division problem?

• Yes

• No

Multiple Choice

What is the answer to this synthetic division problem?

• 2x³ + 7x² - 6x + 1

• 2x⁴ + 7x³ - 6x² + 1x

• 2x² + 7x- 6

• 2x +7x - 6 + 1

Multiple Choice

Is x + 4 a factor of the polynomial shown in this synthetic division problem?

• Yes

• No