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Math Help?? Factoring Step By Step

posted in Various
03/12/2014
  • Factoring
    Factoring
  • Ax^2 + Bx + C

    A, B, and C are numbers

    If A is 1, it may be invisible.

    1. Simplify problem

    Example: 4x^3 + 8x^2 + 16x

    4x (x^2 + 2x + 4)

    2. Determine how many terms there are.

    Ax^2 is a term
    Bx is a term
    C is a term

    2, 3, or 4 terms?

    --->

  • If your problem has 2 terms

    Ax^2 + B

    Ex: 4x^2 - 9

    If B is not negative, then the problem cannot be solved. 'Unfactorable'

    If A and B are perfect squares;
    1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
    the problem is factorable

    Square root both numbers and put them into 2 sets of parentheses ->

  • 2 term example: 4x^2 - 9

    (2x + 3) (2x - 3)

    Answers must have 1 positive sign and 1 negative sign.

    2x * 2x = 4x^2
    -3 * 2x = -6x
    3 * 2x = 6x
    3 * -3 = -9

    The 2 middle terms cancel each other out.

  • If you have 3 terms, determine if A = 1 or 2.

    If A = 1

    1. take all factors of C

    Ex: x^2 + 6x - 16

    Factors of C (-16)
    1 + -16
    -1 + 16
    2 + -8
    -2 + 8
    4 + -4

    *notice I added in 2 for each because C is negative.

    2. Add up all possibilities. Which one adds up to B?

    Answer = -2 + 8 = +6

    --->

  • -2 and 8

    3. Write 2 sets of parentheses;

    ( ) ( )

    4. Put in 2 x's

    (x ) (x )

    5. Add in -2 and +8.

    (x - 2) (x + 8)

    And that's your answer.

  • If A = 2.

    Ex: 2x^2 + 9x + 4

    1. Multiply A and C together
    Ex: 2 * 4 = 8

    2. Write down all factors of the product.

    If A * C = 8, then factors are:

    1 + 8
    2 + 4

    3. Add up factors, which one adds up to match B? B = 9.
    1 + 8 = 9.

    4. Replace B with x (1x) and 8x

    2x^2 + x + 8x + 4

    --->

  • now you have 4 terms.

    If you have 4 terms;

    Ex: 2x^2 + x + 8x + 4

    1. Put parentheses around the first 2 terms and parentheses around the second 2 terms.

    (2x^2 + x) (8x + 4)

    2. Simplify each.

    x (2x + 1) 4 (2x + 1)

    The parentheses will match.

    --->

  • 3. Take the outside terms and put them into a set of parentheses. Take a copy of the matching parentheses and use that as your second set of parentheses.

    (x + 4) (2x + 1)

    And that's your answer.

    If any factoring problem turns out not to work, then that is when the quadratic formula comes in handy

  • πŸ˜„πŸ˜ƒπŸ˜€πŸ˜Šβ˜ΊοΈπŸ˜‰πŸ˜„πŸ˜ƒπŸ˜€πŸ˜Šβ˜ΊοΈπŸ˜‰πŸ˜„ Thanks for reading. πŸ‘πŸ‘πŸ‘πŸ‘πŸ‘πŸ‘

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