Zero Factor Property

Key Questions

  • How do I use the zero factor property when solving a quadratic equation?

    You use the zero factor property after you have factored the quadratic to find the solutions.

    It is best to look at an example: x^2+x-6=0

    This factors into:

    (x+3)(x-2)=0

    We find our solutions by setting each factor to zero and solve:

    x+3=0
    x=-3

    or

    x-2=0
    x=2

    Previous answer (I was thinking some more complicated before):

    You are not using the words precisely. You use the factor theorem with the factor property. The factor theorem states that if you find a k such that P(k)=0, then x-k is a factor of the polynomial. The factor property states that k must a factor of the constant term in P(x).

    Having said all that, you wouldn't normally use the factor theorem or factor property to solve a quadratic; they are many used to find factors of higher order polynomials. Once you reduce the higher order polynomial to a quadratic, you use regular factoring methods such as FPS or PFS: Factors, Product, and Sum.

    P(x)=ax^2+bx+c

    The problem with the factor theorem and factor property is that it's not as easy to use when a!=1.

    Amory W. · · Aug 18 2014
  • How does the zero factor property relate to factoring a polynomial?

    Answer:

    Well, if you a polynomial is factorable then its roots/zeroes can be easily found by setting it to zero and using the zero factor property. Please see explanation below.

    Explanation:

    The Zero Product Property:
    A product of factors is zero if and only if one or more of the factors is zero. Or:
    if a*b = 0, then either a = 0 or b = 0 or both.
    Example: Find the roots of the polynomial by factoring:
    P(x) = x^3-x^2-x+1, set to zero:
    x^3-x^2-x+1=0, factor by grouping:
    x^2(x-1)-1(x-1)=0
    (x^2-1)(x-1)=0, use difference of squares to factor further:
    (x+1)(x-1)(x-1)=0, use the zero factor property:
    x+1=0=>x=-1
    x-1=0=>x=1
    Notice that x = 1 has a multiplicity of 2.

    iceman · 2 · Sep 24 2015
  • How do I factor using the zero factor property?

    The zero factor property states that if ab=0, then either a=0 or b=0.

    Example: find the roots of x^2-x-6.

    x^2-x-6=0

    (x-3)(x+2)=0

    Now, the zero factor property can be applied, since two thing are being multiplied and equal zero.

    We know that either

    x-3=0color(white)(ssss) or color(white)(ssss)x+2=0

    Solve both to find that x=3 or x=-2.

    mason m · 1 · Jan 9 2016

Questions

Real Zeros of Polynomials