Factoring polynomials: x2+bx+cx^2 + bx + c

Factoring polynomials: x2+bx+cx^2 + bx + c

This form of polynomials can be often factorized into a product of two binomials. Sometimes, we need to find the common factor of the polynomial before factorizing. We will learn it all in this lesson.

Lessons

  • 1.
    a)

    "What is the cross-multiplying method of factoring? (a.k.a the Decomposition method)

    • - How does it work?
    • - How to use it?


  • 2.
    Factor the following
    a)
    x2+7x+10{x^2 +7x +10}

    b)
    x24x+4{x^2-4x+4}

    c)
    x2+7x30{x^2+7x-30}

    d)
    x24x21 {x^2-4x-21}


  • 3.
    Factor with common factoring first
    a)
    4x2+20x+24{4x^2+20x+24}

    b)
    4x228x+120{-4x^2 - 28x + 120}

    c)
    x212xy+36y2 {x^2-12xy+36y^2}

    d)
    x3y23x2y3+4xy4{-x^3y^2-3x^2y^3+4xy^4}

    e)
    14x3x28x{1\over4}{x^3-x^2-8x}


  • 4.
    Factor with unusual exponents
    a)
    x6n3x3n+2{x^{6n}-3x^{3n}+2}

    b)
    x2n7xnxm+10x2m{x^{2n}-7x^nx^m+10x^{2m}}

    c)
    (x2y)28a(x2y)+15a2{(x-2y)^2-8a(x-2y)+15a^2}