Curriculum placement
Algebra 1. This describes the skill, not a learner estimate.
Factoring quadratic expressions
Factor quadratic expressions using structure and products
Problem types
- Factor completely with a common factor or a nonmonic square
- Factoring patterns beyond trinomials
- Extract the greatest common factor
- Factor a monic quadratic
- Factor a nonmonic quadratic
- Select the equivalent factored and expanded forms
- Factor a monic trinomial with a large constant
- Choose the factored form of a quartic binomial with a common factor
Builds on
- Adding, subtracting, and multiplying polynomials
- Greatest common factor and least common multiple
- Structure of an expression · Useful idea
Seeing an expression as a product or sum of structured parts guides rewriting a quadratic as factors.
Leads to
- Solving quadratic equations
- Operations on rational expressions
- Proving a polynomial identity · Extend the idea
Factoring a difference of squares or a perfect-square trinomial uses identities such as a² − b² = (a + b)(a − b). Read from either side, the same identity also computes products and squares quickly.
Related skills
- Dividing polynomials · Shared foundations
Open the interactive map to explore lessons and skill connections.