This study guide covers polynomials, including classifying polynomials by degree and terms, adding and subtracting polynomials, multiplying polynomials, dividing polynomials using long division and synthetic division, factoring quadratics, solving quadratics, and graphing quadratics by finding the vertex, axis of symmetry, and x-intercepts. Key concepts are polynomials having only positive integer exponents, the degree being the highest exponent, and the leading coefficient being the coefficient of the term with the highest exponent.