Factoring Trinomials by Grouping

When factoring trinomials by grouping, after you multiply the "a" and the "c" term and identify the "b" term, use these 2 values as clues to find:

• 2 numbers that subtract to "a" times "c" and add to "b"

• 2 numbers that divide to "a" times "c" and add to "b"

• 2 numbers that sum to "a" times "c" and subtract to "b"

• 2 numbers that multiply to "a" times "c" and add to "b"

Factor 5x² -13x - 6

• First, find 2 numbers that multiply to -30 and add to -13.

  a⋅c = 5⋅-6 = -30

  b = -13

• The 2 numbers are -15 and 2, so use these to break up -13x.

  5x² -15x + 2x + 6

• Make 2 groups and factor out the GCF from each group.

  5x( x - 3) + 2(x - 3)

• Write the binomial factors.

  (5x + 2)(x - 3)

What should go in the final step?

• (4x + 1) ( x + 2)

• 
• (4x - 1) ( x - 2)

• (4x + 1) ( x -2)

To factor a trinomial by grouping, start by...

• multiplying the "a" term times the "c" term and identifying the "b" term

• saying a quick prayer

• multiplying the "b" term times the "c" term and identifying the "a" term

• multiplying the "x" term times the "y" term and identifying the "m" term

To factor 5x² -13x + 6, write the middle term using the 2 numbers that multiply to ___ and add to ___, make sure to include the "x". Write it like this:

*Choose 2 that apply.

• 30; -13; 5x² - 10x - 3x + 6

• 30; -13; 5x² - 2x - 15x + 6

• 30; -13; 5x² - 3x - 10x + 6

• 30; -13; 5x² + 2x + 15x + 6

What 2 numbers should go in the blanks instead of the "bx" term?

• The 2 numbers that multiply to 8 and add to -7, which are 8 and -1.

• The 2 numbers that multiply to -8 and add to -7, which are -8 and -1.

• The 2 numbers that multiply to -8 and add to -7, which are -8 and 1.

What should go in the 3rd step?

• 4x(x +2) -1(x+2)

• 4x(x - 2) -1(x-2)

• 4x(x - 2) +1(x-2)

• x(4x - 2) -1(4x-2)

What are the factors of 7x² + 16x + 4?

• First find the 2 numbers that multiply to 28 and add to 16.

  a⋅c = 7⋅4 = 28

  b = 16

• The numbers are 14 and 2, so use these to break apart 16x.

  7x² + 14x + 2x + 4

• Make 2 groups and factor out the GCF from each group.

  7x(x + 2) + 2(x + 2)

• Write the 2 binomial factors.

  (7x + 2) (x + 2)

What formula do we use to identify the "a", "b", and "c" when factoring?

• ax² +bx + c

• ax² +cx + b

• bx² +ax + c

• cx² +bx + a