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    • ▾Algebra 1
      • ▸Solving equations and inequalities
        • •Solving literal linear equations
        • •Solving and graphing multi-step inequalities in one-variable
        • •Solving and graphing compound linear inequalities
        • •Evaluating infinite series
      • ▸Working with units
        • •Rate conversion
        • •Word problems with multiple units
      • ▸Linear equations and graphs
        • •Intercepts from a graph
        • •Intercepts of a linear function from a table
        • •Solving for a variable given a linear equation in standard form
      • ▸Forms of linear equations
        • •Point-slope form
        • •Two point form
        • •Standard form for linear equations
        • •Intercepts from an equation
      • ▸Inequalities and systems of inequalities
        • •Graphing linear inequalities in two variables
        • •Graphing systems of linear inequalities in two variables
      • ▸Functions (algebra 1)
        • •Discrete vs continuous functions
        • •Evaluate a function from its graph
        • •Evaluating expressions with multiple variables
        • •Finding the domain and range of functions from graphs
        • •Interval notation
        • •Intro to multivariable functions
      • ▸Inverse functions (algebra 1)
        • •Determining if a discrete function is invertible
        • •Finding the inverse of discrete and linear functions
      • ▸Arithmetic series
        • •Intro to arithmetic sequences
        • •Find the explicit formula of an arithmetic series given terms
        • •Find the formula of an arithmetic sequence from two terms
        • •Univariate expressions representing consecutive terms
        • •Explicit to recursive formula for arithmetic series
      • ▸Geometric series
        • •Intro to geometric series
        • •Find the explicit formula of a geometric series given terms
        • •Explicit formula from two terms
        • •Expressions representing consecutive terms
      • ▸Absolute value, piecewise, and step functions
        • •Evaluating piecewise functions
        • •Graphs of piecewise functions
        • •Evaluating and graphing the floor function
        • •Solving floor and ceiling equations
        • •Absolute value function under transformations
        • •Solving absolute value equations and inequalities
      • ▸Exponents and radicals
        • •Product property for square roots
        • •Simplifying square root expressions
        • •Simplifying cube roots of integers
        • •Simplifying nested square roots
        • •Simplifying radicals of monomials
        • •Higher order roots
        • •Rationalization
      • ▸Exponential growth and decay
        • •Exponential vs. linear growth
        • •Graphing exponential functions under transformations
        • •Finding exponential functions from tables, graphs, and points
        • •Exponential growth and decay
      • ▸Polynomials
        • •Difference of squares
        • •Intro to polynomials
        • •Multiplying polynomials
        • •First and second differences of quadratics
        • •Proving polynomial identities
        • •Equating coefficients
      • ▾Factoring and solving quadratics
        • •Factoring monic quadratics using algebra tiles
        • •Factoring and solving monic quadratics
        • •Factoring non-monic quadratics by factoring out the GCD
        • •Factoring quadratics with difference of squares
        • •Identifying and factoring perfect square trinomials
        • •Choosing a factoring method (level 1)
        • •Factoring non-monic quadratics using algebra tiles
        • •Factoring non-monic quadratics
        • •Choosing a factoring method (level 2)
        • •Completing the square
        • •Quadratic formula
        • •Sign of the discriminant
        • •Golden ratio
        • •Po-Shen Loh method
      • ▸Quadratic equations
        • •Solving quadratics by u-substitution
        • •Solving equations in quadratic form using u-substitution
        • •Solving quadratic equations by taking square roots
        • •Intro to vertex form for quadratics
        • •Converting quadratics between standard form and vertex form
        • •Quadratic from the vertex and a point
        • •Finding the domain and range of quadratic functions from equations
        • •First and second differences
        • •Reducing to a linear equation
      • ▸Irrational numbers
        • •Sums and products of rational and irrational numbers
     › Algebra 1 › Factoring and solving quadratics

    Factoring non-monic quadratics

    First, students will learn how to factor non-monic trinomials using the box method.

    Watch these videos by Mario's Math Tutoring:

    • Box Method of Factoring Trinomials (In Under 2 Minutes)
    • Box Method of Factoring Trinomials

    Next, students will learn how to factor non-monic quadratics using the product and sum method, which is also sometimes called the decomposition method.

    Factoring the Form ax^2+bx+c: Ex. 2 by Michel van Biezen

    I don't like the FOIL method. It seems Michel van Biezen and Eddie Woo don't either.

    Conclude by giving your students these challenges:

    • A Bit of a Dicey Problem by NRICH
    • Making Sticks by NRICH
    • 2002 AMC 8, Problem 6
    • 2011 AMC 8, Problem 8
    • 2014 AMC 8, Problem 11
    • 2017 AMC 8, Problem 7

    Practice problems and additional lessons