Classify, add, subtract, multiply, and divide polynomials.
Common CoreA-APR.A.1A-SSE.A.2
6 lessons21 short videos5 key concepts, out loud
11.1
Classifying Polynomials (Degree & Terms)
Name a polynomial by its size and shape
A-SSE.A.1
Key idea
To classify a polynomial, identify its degree by finding the highest exponent of its variable terms, and count its terms to name it as a monomial, binomial, or trinomial.
Learn how to identify the degree and number of terms in an algebraic expression to give any polynomial its precise mathematical name.
Key concept · Lesson 11.1
Degree first, then count the terms
Listen0:00 / 0:24
Transcript. Find the degree by looking for the highest exponent on a single term. Never add exponents across different terms. Then count the terms: one is a monomial, two a binomial, three a trinomial. Pair the two names, so five x cubed minus two x plus seven is a cubic trinomial.
11.2
Adding & Subtracting Polynomials
Combine like terms across polynomials
A-APR.A.1
Key idea
To add or subtract polynomials, combine terms with matching variables and exponents, making sure to distribute the negative sign to every term in the second polynomial when subtracting.
Learn how to add and subtract polynomials by grouping like terms and safely distributing negative signs.
Key concept · Lesson 11.2
Flip every sign, then combine
Listen0:00 / 0:20
Transcript. Subtraction is the trap. The minus in front belongs to every term in the second group, so flip each of their signs before you combine. Then add like terms by adding coefficients only. The exponents never change, so y squared plus y squared is two y squared.
11.3
Multiplying Polynomials (FOIL & Area Models)
Multiply binomials and larger products
A-APR.A.1
Key idea
To multiply polynomials, distribute every term in the first polynomial to every term in the second, using either a visual area model grid or the FOIL method to organize the individual products.
Learn how to multiply binomials and larger polynomials using visual area models and the FOIL method to keep track of every term.
Key concept · Lesson 11.3
Every term times every term
Listen0:00 / 0:19
Transcript. Multiply every term in the first bracket by every term in the second. With two binomials that gives four products, not two. The two middle products are the ones people drop, so add them together. Watch the signs whenever a term is negative.
11.4
Special Products (Difference of Squares, Perfect Squares)
Difference of squares and perfect-square shortcuts
A-APR.A.1A-SSE.A.2
Key idea
Use the difference of squares pattern, (a - b)(a + b) = a^2 - b^2, and the perfect square trinomial patterns, (a + b)^2 = a^2 + 2ab + b^2 and (a - b)^2 = a^2 - 2ab + b^2, to multiply binomials instantly without full expansion.
Learn how to recognize special binomial patterns and use algebraic shortcuts to multiply them instantly without full expansion.
Key concept · Lesson 11.4
Double the product for the middle
Listen0:00 / 0:23
Transcript. Squaring a binomial is not just squaring each piece. The area picture shows two matching five x cells, so they double to ten x in the middle. Multiply x plus five by x minus five instead, and those middle terms cancel. That is a difference of squares, x squared minus twenty-five.
11.5
Dividing Polynomials by a Monomial
Divide a polynomial term by term
A-APR.A.1
Key idea
To divide a polynomial by a monomial, split the expression into separate fractions for each term in the numerator, then divide the coefficients and subtract the exponents of matching variables.
Learn how to break a polynomial division problem into smaller, individual fractions to simplify each term using exponent rules.
Key concept · Lesson 11.5
Split it, then simplify each part
Listen0:00 / 0:21
Transcript. Give every term its own copy of the denominator, then simplify each little fraction on its own. Divide the coefficients and subtract the exponents. And when a term divides by itself, it becomes one. That one must stay in your answer, or the answer is incomplete.
11.6
Review & Assessment
Polynomial operations, mixed
Review, practice, quiz and test
Key idea
Review polynomial operations with targeted mixed practice, a practice test, and a chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
