Factoring polynomials: x^2 + bx + c

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

    • - How does it work?
    • - How to use it?
  2. How to Factor Polynomials?
  1. Factor the following
    1. x2+7x+10{x^2 +7x +10}
    2. x2−4x+4{x^2-4x+4}
    3. x2+7x−30{x^2+7x-30}
    4. x2−4x−21 {x^2-4x-21}
  2. Factor with common factoring first
    1. 4x2+20x+24{4x^2+20x+24}
    2. −4x2−28x+120{-4x^2 - 28x + 120}
    3. x2−12xy+36y2 {x^2-12xy+36y^2}
    4. −x3y2−3x2y3+4xy4{-x^3y^2-3x^2y^3+4xy^4}
    5. 14x3−x2−8x{1\over4}{x^3-x^2-8x}
  3. Factor with unusual exponents
    1. x6n−3x3n+2{x^{6n}-3x^{3n}+2}
    2. x2n−7xnxm+10x2m{x^{2n}-7x^nx^m+10x^{2m}}
    3. (x−2y)2−8a(x−2y)+15a2{(x-2y)^2-8a(x-2y)+15a^2}
Topic Notes
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.