Exponent
Polynomials
Examples:
- Exponent is a shorthand notation for repeated factors.The base of an exponential expression is the repeated factor. The exponent is the number of times that the base is used as a factor.
- Product rule for exponents: To multiply two exponential expressions with a common base, keep the base and add the exponents.
- Power rule for exponents: To raise a power to a power, keep the base and multiply the exponents.
- Power of a product rule: To raise a product to a power, raise each factor to the power.
- Power of a quotient rule: To raise a quotient to a power, we raise both the numerator and the denominator to the power.
- Quotient rule for exponents: To divide one exponential expression by another with a common base, keep the base and subtract exponents.
- Zero exponent: Any base raised to the 0 power is 1, as long as the base is 0.
Polynomials
- A polynomial in x is a finite sum of terms of the form ax^n, where a is a real number and the exponent n is a whole number.
- A monomial is a polynomial with exactly one term.
- A binomial is a polynomial with exactly two terms.
- A trinomial is a polynomial with exactly three terms.
- The degree of a term is the sum of the exponents on the variables contained in the term.
- The degree of a polynomial is the greatest degree of any term of the polynomial.
- To add polynomials, combine all the like terms.
- To subtracting polynomials, change the signs of the terms of the polynomial being subtracted and then add.
- Polynomials can be added vertically if we line up like terms underneath one another.
Examples: