Review - Operations with Polynomials

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, along with coefficients. For example, $$2x^2 + 3x + 5$$ is a polynomial.

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial $$4x^3 + 2x^2 - x + 7$$ , the degree is 3.

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

To add polynomials, combine like terms. For example, $$(2x^2 + 3x) + (4x^2 - 2x) = (2x^2 + 4x^2) + (3x - 2x) = 6x^2 + x$$ .

To subtract polynomials, distribute the negative sign and then combine like terms. For example, $$(5x^2 + 3) - (2x^2 + 4) = (5x^2 - 2x^2) + (3 - 4) = 3x^2 - 1$$ .

The product of two polynomials is found by using the distributive property (also known as the FOIL method for binomials). For example, $$(x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6$$ .

The area of a triangle is given by the formula $$A = \frac{1}{2}bh$$ , where b is the base and h is the height.

Using the area formula: $$A = \frac{1}{2}(2x + 4)(x + 8) = \frac{1}{2}(2x^2 + 16x + 4x + 32) = x^2 + 10x + 16$$ .

A monomial is a polynomial with only one term. For example, $$5x^3$$ is a monomial.

A binomial is a polynomial with exactly two terms. For example, $$3x + 4$$ is a binomial.