Learning Resource Type

Classroom Resource

Factoring Perfect Squares

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this video from Khan Academy, students learn about factoring quadratics as a perfect square of a difference. This video can be used during a lesson on factoring quadratics. The video is 4 minutes and 54 seconds in length and can be assigned through Google Classroom

    Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

    MA19.A1.9

    Select an appropriate method to solve a quadratic equation in one variable.

    Unpacked Content

    UP:MA19.A1.9

    Vocabulary

    • Completing the square
    • Quadratic equations
    • Quadratic formula
    • Inspection
    • Imaginary numbers
    • Binomials
    • Trinomials

    Knowledge

    Students know:
    • Any real number has two square roots, that is, if a is the square root of a real number then so is -a.
    • The method for completing the square.
    • Notational methods for expressing complex numbers.
    • A quadratic equation in standard form (ax2+bx+c=0) has real roots when b2-4ac is greater than or equal to zero and complex roots when b2-4ac is less than zero.

    Skills

    Students are able to:
    • Accurately use properties of equality and other algebraic manipulations including taking square roots of both sides of an equation.
    • Accurately complete the square on a quadratic polynomial as a strategy for finding solutions to quadratic equations.
    • Factor quadratic polynomials as a strategy for finding solutions to quadratic equations.
    • Rewrite solutions to quadratic equations in useful forms including a ± bi and simplified radical expressions.
    • Make strategic choices about which procedures (inspection, completing the square, factoring, and quadratic formula) to use to reach a solution to a quadratic equation.

    Understanding

    Students understand that:
    • Solutions to a quadratic equation must make the original equation true and this should be verified.
    • When the quadratic equation is derived from a contextual situation, proposed solutions to the quadratic equation should be verified within the context given, as well as mathematically.
    • Different procedures for solving quadratic equations are necessary under different conditions.
    • If ab=0, then at least one of a or b must be zero (a=0 or b=0) and this is then used to produce the two solutions to the quadratic equation.
    • Whether the roots of a quadratic equation are real or complex is determined by the coefficients of the quadratic equation in standard form (ax2+bx+c=0).
    Link to Resource

    CR Resource Type

    Audio/Video

    Resource Provider

    Khan Academy
    Accessibility

    Accessibility

    Video resources: includes closed captioning or subtitles
    License

    License Type

    Custom
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