Multiplying Polynomials

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, $$5x^2 + 2x - 10$$ is a polynomial.

A monomial is a polynomial with only one term. For example, $$3x^2$$ is a monomial.

A binomial is a polynomial with exactly two terms. For example, $$x + 7$$ is a binomial.

A trinomial is a polynomial with exactly three terms. For example, $$5x^2 + 2x - 10$$ is a trinomial.

The degree of a polynomial is the highest power of the variable in the expression. For example, in $$-3x^4 + 6x$$ , the degree is 4.

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, for (x + 7)(x - 2), the result is $$x^2 + 5x - 14$$ .

To subtract polynomials, distribute the negative sign and combine like terms. For example, $$(2a^2 + 5a + 3) - (a^2 - 3a - 4) = a^2 + 8a + 7$$ .

To add polynomials, combine like terms. For example, $$(3x^3 + 3x^2 - 4x + 5) + (x^3 - 2x^2 + x - 4) = 4x^3 + 1x^2 - 3x + 1$$ .

Like terms are terms that have the same variable raised to the same power. For example, $$3x^2$$ and $$5x^2$$ are like terms.

The coefficient is the numerical factor in a term of a polynomial. For example, in $$4x^3$$ , the coefficient is 4.