Algebra 2 Review

Quadratic Inequalities

100

Solve x² - 2x - 24 ≤ 0 by graphing. State the solution using inequality notation.

What is -4 ≤ x ≤ 6?

200

Solve -x² + 2x + 5 < 0 by graphing. State the solution using interval notation. Round your answer to the nearest tenth.

What is (-∞,-1.5) ∪ (3.5,∞)?

300

Solve -(x - 4)² + 8 > 0 by graphing. State the solution using inequality notation. Round your answer to the nearest hundredth.

What is 1.17 < x < 6.83?

400

Solve x² + 4x ≥ -2x + 9 by graphing. State the solution using interval notation. Round your answer to the nearest hundredth.

What is (-∞,-7.24) ∪ (1.24,∞)?

500

The function h(t) = -0.8t² + 7.6t + 0.5 represents the height in meters of an object being launched into the air of Mars, where t represents time in seconds. Solve the inequality -0.8t² + 7.6t + 0.5 ≥ 7.5 to determine the interval of time during which the object will be out of the rover's camera view. Round your answer to the nearest tenth.

What is between 1 second and 8.5 seconds?

Add/Subtract Polynomials

100

Find the sum of 5x² + 3x + 2 and -x² + x + 8.

What is 4x² + 4x + 10?

200

Find the difference of -3x² + 8x - 12 and -2x² + 4x + 6.

What is -x² + 4x - 18?

300

Find the sum of 4m² - 13 + 2m and 32 - 13m² + 9m. Write your answer in standard form.

What is -9m² + 11m + 19?

400

Subtract -12a²+3a-4b+2 from 6a+4a²-3-2b. Write your answer in standard form.

What is 16a²+3a+2b-5?

500

Subtract 12a² - 5ab - 7b² from -12a² + 3ab - 4b².

What is -24a² + 8ab + 3b²?

Dividing Polynomials

100

Simplify (27x³ + 12x)(3x)^-1.

What is 9x² + 4?

200

Simplify (12v⁴ + 32v² - 16v)(4v)^-1.

What is 3v³ + 8v - 4?

300

Divide 2x³ - 5x² - 8x + 15 by x - 3. Use any method.

What is 2x² + x - 5?

400

Divide 27x³ + 9x² - 3x - 9 by 3x - 2.

What is 9x² + 9x + 5 + 1/(3x-2)?

500

Divide -3x⁶+2x³-x+2 by x-1.

What is -3x⁵-3x⁴-3x³-x²-x-2?

Multiplying Polynomials

100

Multiply 2(-3x - 4)(3x - 5).

What is -18x² + 6x + 40?

200

Multiply (x + 4)³.

What is x³ + 12x² + 48x + 64?

300

Multiply (3x - 5)(-2x² - 4x + 8).

What is -6x³ - 2x² + 44x - 40?

400

Simplify (2x² - 3x + y)(3x² + 4x -2y).

What is 6x⁴ - x³ - x²y - 12x² + 10xy - 2y²?

500

Expand (3x - 5)⁶.

What is 729x⁶ - 7290x⁵ + 30375x⁴ - 67500x³ + 84375x² - 56250x + 15625?

Factoring Polynomials

100

Factor 16x² + 100y².

What is (4x+10y)(4x-10y)?

200

Factor 216x³ + 512y³.

What is (6x + 8y)(36x² - 48xy + 64y²)?

300

Factor 250x³ - 1458.

What is 2(5x - 9)(25x² + 45x + 81)?

400

Factor 6x² - 2x - 20.

What is 2(3x + 5)(x - 2)?

500

Use the Factor Theorem to determine if k - 8 is a factor of 8k³ - 66k² + 14k + 8. If it is, determine the remaining factors.

What is k - 8 not a factor of 8k³ - 66k² + 14k + 8?