Factor & Solve Higher Degree Polynomials

Front

Define a polynomial.

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is a higher degree polynomial?

Back

A higher degree polynomial is a polynomial of degree three or more.

Front

What is the Factor Theorem?

Back

The Factor Theorem states that if a polynomial f(x) has a factor (x - c), then f(c) = 0.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

How do you factor a sum of cubes?

Back

A sum of cubes can be factored using the formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Front

How do you factor a difference of cubes?

Back

A difference of cubes can be factored using the formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

What is the process to factor a polynomial completely?

Back

1. Look for a common factor. 2. Factor using special formulas (difference of squares, sum/difference of cubes). 3. Use synthetic division or long division if necessary. 4. Factor any remaining polynomial.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).