3-2 Adding, Subtracting, Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, p(x) = 4x^3 + 3x^2 - 2x + 1 is a polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degree. For example, p(x) = 3x^4 + 2x^3 - x + 5 is in standard form.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x^2 + 2) - (x^2 + 4) = (3x^2 - x^2) + (2 - 4) = 2x^2 - 2.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in p(x) = 5x^3 + 2x^2 - 3, the leading coefficient is 5.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in p(x) = 4x^5 + 3x^2 - 1, the degree is 5.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two powers with the same base, you add the exponents. For example, x^a * x^b = x^(a+b).

Front

What is the power of a power property?

Back

The power of a power property states that when raising a power to another power, you multiply the exponents. For example, (x^a)^b = x^(a*b).

Front

What is the zero exponent rule?

Back

The zero exponent rule states that any non-zero base raised to the power of zero equals one. For example, x^0 = 1 (where x ≠ 0).