HS.A.2.g

Perform and explain operations such as addition, subtraction, multiplication, division, and factoring on polynomials.

Example Problems

Multiply:

(-x)(5x^9)

Multiply:

(4x^9)(5x)

Multiply:

(x^4)(x^5)

Khan Academy Resources

Intro to factors & divisibility Solving quadratics by completing the square Solving quadratics by factoring review Factoring polynomials by taking a common factor Warmup: Multiplying binomials Factoring quadratics in any form Quadratic formula proof review Completing the square review Factoring quadratics: Difference of squares Factoring quadratics: Perfect squares Multiplying binomials by polynomials review Adding and subtracting polynomials review Binomial special products review Factoring by grouping Factoring quadratics: leading coefficient = 1 Factoring simple quadratics review Factoring quadratics: leading coefficient ≠ 1 Multiplying monomials by polynomials review Solving quadratics by factoring Multiply difference of squares Quadratics by factoring (intro)Add polynomials (intro)Multiply binomials by polynomials Completing the square (intermediate)Completing the square Difference of squares Factoring quadratics intro Difference of squares intro Quadratics by factoring Multiply binomials intro Factor polynomials using structure Factor quadratics by grouping Multiply binomials by polynomials: area model Polynomial special products: perfect square Divide quadratics by linear expressions (no remainders)Divide quadratics by linear expressions (with remainders)Multiply monomials by polynomials Quadratic word problems (standard form)Solve equations by completing the square Divide polynomials by x (no remainders)Polynomial special products: difference of squares Polynomial identities Identify quadratic patterns Factor polynomials: common factor Multiply monomials Add & subtract polynomials Multiply binomials: area model Completing the square (intro)Divide polynomials by linear expressions Multiply monomials by polynomials (basic): area model Factor higher degree polynomials Multiply perfect squares of binomials Perfect squares intro Factorization with substitution Multiply monomials by polynomials: area model Factor using polynomial division Subtract polynomials (intro)Multiply binomials Factoring quadratics with a common factor Perfect squares Divide polynomials by x (with remainders)GCF factoring introduction Strategy in solving quadratics Factoring quadratics as (x+a)(x+b) (example 2)Subtracting polynomials Multiplying monomials by polynomials Multiplying binomials Special products of the form (ax+b)(ax-b)Squaring binomials of the form (ax+b)² Divide polynomials by x (with remainders)Multiplying binomials by polynomials Factoring perfect squares Factoring using the difference of squares pattern Quadratic equations word problem: triangle dimensions Worked example: completing the square (leading coefficient ≠ 1)More examples of factoring quadratics as (x+a)(x+b)Intro to grouping Completing the square Proof of the quadratic formula Intro to long division of polynomials Adding polynomials Taking common factor from trinomial Factoring quadratics by grouping Factoring quadratics: common factor + grouping Factoring quadratics: negative common factor + grouping Factoring perfect squares: negative common factor Factoring using the perfect square pattern Solving quadratics by factoring Quadratic equations word problem: box dimensions Worked example: Completing the square (intro)Solving quadratics by completing the square: no solution Factoring perfect squares: missing values Multiply monomials by polynomials: Area model Polynomial special products: difference of squares Factoring using polynomial division Perfect square factorization intro Dividing quadratics by linear expressions with remainders: missing x-term Factoring quadratics as (x+a)(x+b)Factoring higher-degree polynomials: Common factor Polynomial identities introduction Squaring binomials of the form (x+a)² Solve by completing the square: Non-integer solutions Identifying perfect square form Factoring using polynomial division: missing term Polynomial division introduction Solve by completing the square: Integer solutions Taking common factor: area model Least common multiple of polynomials Multiplying binomials: area model Factoring difference of squares: shared factors Factoring perfect squares: shared factors Difference of squares intro Strategy in solving quadratic equations Strategy in factoring quadratics (part 1 of 2)Special products of the form (x+a)(x-a)Factoring difference of squares: analyzing factorization Factoring difference of squares: leading coefficient ≠ 1 Strategy in factoring quadratics (part 2 of 2)Identifying quadratic patterns Dividing polynomials by linear expressions Solving quadratics by factoring: leading coefficient ≠ 1 Area model for multiplying polynomials with negative terms Factoring quadratics with a common factor Analyzing polynomial identities Taking common factor from binomial Polynomial subtraction Multiplying monomials by polynomials: area model Multiplying binomials intro Factoring higher degree polynomials Factoring completely with a common factor Introduction to factoring higher degree polynomials Polynomial special products: perfect square Multiplying monomials Factorization with substitution Dividing quadratics by linear expressions (no remainders)Multiplying binomials by polynomials: area model Dividing polynomials by linear expressions: missing term Dividing quadratics by linear expressions with remainders Intro to factors & divisibility Worked example: Rewriting & solving equations by completing the square Worked example: Rewriting expressions by completing the square Dividing polynomials by x (no remainders)

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