Learning Goal
Higher-degree polynomial equations
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
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
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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
What you'll learn
- 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
Slides
Step through the lesson, or watch it as a narrated video
Slides
In development
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