Algebra
Use synthetic division to solve (x³ + 1) ÷ (x – 1). What is the quotient?
Answer: The quotient of (x³ + 1) ÷ (x – 1) using synthetic division is x² + x + 1
August 12, 2025
All
What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
Answer: The solution set for x is x≥3. Solving Linear Inequalities To solve the inequality 2(3x – 1) ≥ 4x – 6, first expand and simplify it to get 6x – 2 ≥ 4x – 6. Then, solve for x, which results in x ≥ 3. Understanding and solving linear inequalities is crucial in algebra […]
January 19, 2024
Algebra
What is the axis of symmetry of the function f(x) = -(x + 9)(x – 21)?
Answer: The axis of symmetry of the function f(x) = -(x + 9)(x – 21) is x = 6
January 19, 2024
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All
Over what interval is the graph of f(x) = -(x + 8)² – 1 decreasing?
Answer: The graph of f(x) = -(x + 8)² – 1 is always decreasing because it is a downward-opening parabola. Analyzing Quadratic Graphs The graph of a quadratic function y = a(x – h)² + k will open upwards if a is positive and downwards if a is negative. For the function f(x) = -(x […]
January 19, 2024
All
What is the first step when rewriting y = 6x² + 18x + 14 in the form y = a(x – h)² + k?
Answer: The first step when rewriting y = 6x² + 18x + 14 in the form y = a(x – h)² + k is to factor out the 6 from the x² and x terms
January 19, 2024
All
What is the first step when rewriting y = 3x² + 9x – 18 in the form y = a(x – h)² + k?
Answer: The first step is to factor out the coefficient of x² (3) from the first two terms, giving y = 3(x² + 3x) – 18. Understanding the Vertex Form Rewriting a quadratic equation in vertex form, y = a(x – h)² + k, involves completing the square. The first step is to factor the […]
January 19, 2024
All
Use synthetic division to solve (x³ + 1) ÷ (x – 1). What is the quotient?
Answer: The quotient is x² + x + 1. Mastering Synthetic Division Synthetic division is a simplified method of dividing a polynomial by a binomial of the form (x – c). For (x³ + 1) ÷ (x – 1), set up the synthetic division and you’ll find the quotient is x² + x + 1. […]
January 19, 2024
All
What number should be added to both sides of the equation to complete the square (x² – 6x = 5)?
Answer: 9 should be added to both sides to complete the square in the equation x² – 6x = 5
January 19, 2024
All
In which quadrant is the number 6 – 8i located on the complex plane?
Answer: 6 – 8i is located in the fourth quadrant
January 9, 2024
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