Factorization of Quadratic Expressions

Key Questions

  • How do you factor quadratic equations with a coefficient?

    Good question .

    basically what are asking me to factor is :

    ax^2 + bx +c

    here is an eg.

    4x^2 – 15x + 9.

    First you need to make column like this

    SUM = COEFFICIENT OF x =( -15)
    product = (COEFFICIENT of x^2 * COEFFICIENT of constant)= 36
    Now you have to find factors which have a sum of -15 and a product of 36

    THE FACTORS ARE (-12), (-3)

    So now what we do is split the middle term in the equation and factor it out

    4x^2 – 12x– 3x +9.
    4x(x – 3)–3 (x-3).

    (4x–3 )(x – 3).

    HENCE FACTORED

    f(4x^2 – 15x + 9.) = (4x–3 )(x – 3)

    Sidharth · 1 · Dec 21 2014
  • What are some examples of factoring quadratic expressions?

    Example 1

    x^2-x-6=(x+2)(x-3)

    Example 2

    2x^2-9x-5=(2x+1)(x-5)

    Example 3

    x^2-9=(x+3)(x-3)

    I hope that this was helpful.

    Wataru · 2 · Nov 13 2014
  • How do you check that you factored a quadratic correctly?

    Answer:

    If both the roots satisfy the quadratic equation, then you have factorised it correctly.

    Explanation:

    I will try explaining with an example.
    x^2+4x-12=0
    The roots are 2 and -6.
    Now simply put the values in the quadratic equation.

    First, I will try -6
    (-6)^2+4(-6)-12=0
    36-24-12=0
    cancel36-cancel36=0
    0=0
    which is true.

    Now, I will try 2
    2^2+4*2-12=0
    4+8-12=0
    cancel12-cancel12=0
    0=0
    which is also true.

    :. Our answer was correct.

    Hope you got it :)

    Jade · 3 · Mar 15 2018
  • How do you factor trinomials?

    Extension to factoring, when the trinomials do not factor into a square (it also works with squares).

    Sum-product-method
    Say you have an expression like x^2+15x+36
    Then you try to write 36 as the product of two numbers, and 15 as the sum (or difference) of the same two numbers. In this case (with both being positive) it's not so hard. You take the sum.

    You can write 36=1*36=2*18=3*12=4*9=6*6
    Sums of these are 37,20,15,13,12 respectively
    Differences are 35,16,9,5,0 respectively
    15=+3+12 will do. So the factoring becomes:
    (x+3)(x+12)
    Check your answer! =x^2+12x+3x+36

    It's a bit harder when one or two of the numbers are negative, let's take x^2-15x+36
    Same as the first, only now both factors are negative
    (x-3)(x-12)=x^2-12x-3x+36= the original

    Extra
    If the last number (36) is negative, you will have to work with the difference of the factors. Check the next one yourself:
    x^2+5x-36=(x+9)(x-4)=?

    And now try: x^2-5x-36=?

    MeneerNask · 1 · Jan 4 2015
  • What is factorization of quadratic expressions?

    Factorization of a quadratic expression is the opposite of expansion, and is the process of putting the brackets back into the expression rather than taking them out.

    To factorize a quadratic expression of the form ax^2+bx+c you must find two numbers that add together to give the first coefficient of x and multiply to give the second coefficient of x.

    An example of this would be the equation x^2 + 5x + 6, which factorizes to give the expression (x+6)(x-1)

    Now, one might expect the solution to include the numbers 2 and 3, as these two numbers both add together to give 5 and multiply to give 6. However, as the signs differ in the factorized equation, then the solution to the equation must be (x+6)(x-1), as +6 -1 gives 5, and 6 times 1 yields a solution of 6.

    The equation can be checked by multiplying the solutions back into the equation to give the original quadratic of x^2 + 5x + 6.

    Callum S. · 3 · Oct 28 2014

Questions

Polynomials and Factoring