Factoring x2 bx c

1
Factoring x2 bx c
2
Factor x² 7x 12

• You will come up with two binomials.
• What could you multiply together to get x²?
• x times x
• So I start the two binomials like this
• (x )(x )
• Now, what would I multiply together to get 12
  that will also add (because the 12 is positive)
  to get 7?
• 3 and 4

3

• So fill in the parentheses
• (x 4)(x 3)

4
Try x² - 3x 2

• Start with (x )(x )
• Now I need to find two numbers that multiply to
  get 2, but add to give 3.
• (-2, and 1)
• Put those in the parentheses
• (x 1)(x 2)

5
Try x² - 2x - 8

• You can start with (x )(x )
• This time I know the signs in the parentheses
  will be different because the last term is
  negative.
• So, I need two numbers that will multiply to give
  8, and add to give 2 (remember the signs are
  different!)
• -4 and 2
• So, (x 4)(x 2)

6
3x² 5x - 2

• This is a little harder. I would start with
  this (3x )(x )
• Now multiply a and c (3 and 2). You get
  negative six. You need two numbers that multiply
  to get negative six that combine (subtract
  because the signs must be different) to get 5.
  Try 6 and 1.
• You must place numbers so that the inner and
  outer products will be 6 and 1.
• (3x - 1)(x 2)

7
Another WayThe Box

• When factoring trinomials, you could use the box
  again.
• Put the first term in the top left of a 2 by 2
  box.
• Put the last term in the bottom right square.
• Multiply them (a and c) together. That is
  your magic number.
• In y1 in the calculator, enter your magic number
  () y1 /x
• In y2 /x x

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Another WayThe Box

• Go to the table. In the y2 column find the b
  number (the middle term).
• In the two remaining boxes, enter the numbers
  next to that b number (the numbers in the X
  column and the y1 column). Be sure to put an x
  after each number.
• Going across the top row find the GCF. Write it
  to the left of the box.
• Then find the GCF of the bottom row and write it
  to the left of the box.

9
Another WayThe Box

• Then find the GCF of the first column and write
  it above that row.
• Last find the GCF of the second column and write
  it above that row.
• You now have the binomial factors of this
  trinomial.

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Example 1

• Factor 6x² 13x 5

• Multiply them to get the magic number.
• Now enter in y1 -30/x
• In y2 enter -30/x x

11
Example 1

• Go to the table and look in the y2 column and
  look for 13.
• It is next to the 15 and 2
• So, write 15x and 2x in the remaining boxes.

12
Example 1

• Find the GCF of each row and write it next to the
  row.
• Find the GCF of each column and write it above
  the column.

So it is (2x 5)(3x 1)
13
Try these

• x2 8x 7
• x2 6x 5
• x2 x 6
• 5x2 2x 7
• 5x2 22x 8
• 2x2 13x - 24

• (x 1)(x 7)
• (x 1)(x 5)
• (x 3)(x 2)
• (5x - 7)(x 1)
• (5x - 2)(x - 4)
• (2x - 3)(x 8)