Lesson Plan

Solve a higher-degree polynomial equation by reducing it to linear and quadratic factors, choosing the route from its form: GCF extraction (with grouping or the cubes identities), quadratic-form substitution, or finding a root by evaluation

Solve a quadratic-form equation — in $x^2$, in $\sqrt{x}$, or in a repeated binomial — by substitution, and back-substitute to recover all real roots in the original variable

Apply the factor theorem — $P(a)=0$ if and only if $(x-a)$ is a factor — to find a root or identify a factor by evaluation, and the remainder theorem to find the remainder of $P(x) \div (x-a)$ without dividing

Check a solution set against the degree, and account algebraically for any shortfall

A 703. Apply the remainder theorem for polynomials, that P(a) is the remainder when P(x) is divided by (x – a) F 501. Evaluate polynomial functions, expressed in function notation, at integer values F 509. Find the range of polynomial functions A 601. Manipulate expressions and equations A 605. Solve quadratic equations AF 703. Analyze and draw conclusions based on properties of algebra and/or functions