Variables and Coefficients

Polynomials are algebraic expressions consisting of variables and coefficients linked by addition, subtraction, and multiplication

Terms and Exponents

Each term of a polynomial is the product of a coefficient and a variable raised to a non-negative integer exponent

Standard Form and Degree

Polynomials are typically presented in standard form with terms ordered from highest to lowest exponent, and the degree is the highest exponent of the variable

Substitution and Arithmetic

Evaluating a polynomial involves substituting a specific value for the variable and performing arithmetic to find the result

Addition and Subtraction

Polynomial addition and subtraction are carried out by combining like terms using the distributive property and carefully managing the signs of each term

Factoring Polynomials

Factoring polynomials is the process of decomposing them into products of simpler polynomials

Factoring and Reducing Common Factors

Simplifying polynomial fractions involves factoring the numerator and denominator and reducing common factors to their lowest terms

Examples of Simplifying Polynomial Fractions

Examples of simplifying polynomial fractions include canceling common factors and factoring the numerator and denominator

Polynomial Division Process

Polynomial division is analogous to long division with numbers, involving dividing the leading term of the dividend by the leading term of the divisor and repeating until the remainder's degree is less than the divisor's degree

The Factor Theorem

The Factor Theorem states that if a polynomial has a value of zero for a specific value of x, then x - p is a factor of the polynomial

Applying The Factor Theorem

The Factor Theorem can be applied by testing potential values of x until the polynomial equals zero, then dividing the polynomial by x - p and factoring the resulting quotient further if possible