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.
Basic Concepts: Prime factorization, Multiplying binomial by binomial, Common factors of polynomials
Related Concepts: Factor by taking out the greatest common factor, Factor by grouping, Factoring difference of squares: x2−y2x^2 - y^2, Factoring trinomials

Lessons

  • Introduction
    a)

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

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

    b)
    How to Factor Polynomials?

  • 1.
    Factor the following
    a)
    x2+7x+10{x^2 +7x +10}

    b)
    x2−4x+4{x^2-4x+4}

    c)
    x2+7x−30{x^2+7x-30}

    d)
    x2−4x−21 {x^2-4x-21}

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

    b)
    −4x2−28x+120{-4x^2 - 28x + 120}

    c)
    x2−12xy+36y2 {x^2-12xy+36y^2}

    d)
    −x3y2−3x2y3+4xy4{-x^3y^2-3x^2y^3+4xy^4}

    e)
    14x3−x2−8x{1\over4}{x^3-x^2-8x}

  • 3.
    Factor with unusual exponents
    a)
    x6n−3x3n+2{x^{6n}-3x^{3n}+2}

    b)
    x2n−7xnxm+10x2m{x^{2n}-7x^nx^m+10x^{2m}}

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

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13.
Factoring polynomial Expressions
13.1
Common factors of polynomials
13.2
Factoring polynomials by grouping
13.3
Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
13.4
Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
13.5
Factoring polynomials: x2+bx+cx^2 + bx + c
13.6
Applications of polynomials: x2+bx+cx^2 + bx + c
13.7
Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
13.8
Factoring polynomials: ax2+bx+cax^2 + bx + c
13.9
Factoring perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2
13.10
Find the difference of squares: (a - b)(a + b) = a2−b2a^2 - b^2
13.11
Evaluating polynomials
13.12
Using algebra tiles to factor polynomials
13.13
Solving polynomial equations
13.14
Word problems of polynomials
Basic Algebra
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