Factor Trinomials by Grouping

To factor 3x² + 14x + 8, find the 2 clue numbers first. Then, use the clue numbers to find the 2 numbers we will use for "bx".

• the 2 numbers that multiply to 24 and add to 14 are 6 and 4.

• the 2 numbers that multiply to 24 and add to 14 are 24 don't exist.

• the 2 numbers that multiply to 24 and add to 14 are 2 and 12.

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:

• 30; -13; 5x² - 10x - 3x + 6

• 30; -13; 5x² - 2x - 15x + 6

• 30; -13; 5x² - 3x - 10x + 6

• 30; -13; 5x² + 2x + 15x + 6

Factor 5x² -13x - 6

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

  5x² -15x + 2x + 6

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

  a⋅c = 5⋅-6 = -30

  b = -13

• 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 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 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

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

• Write the 2 binomial factors.

  (7x + 2) (x + 2)

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

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

To factor the trinomial 6x² + 11x +3, start by multiplying "a" times "c" and identifying "b". Use ax² + bx + c to find these values.

• true

• false

To factor 2x² +11x + 5, 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.

• 10; 11; 2x² + 5x +2x + 5

• 22; 5; 2x² + 9x +2x + 5

• 10; 11; 2x² + 10x +x + 5

• 10; 11; 2x² + x +10x + 5

Factor: 2x² + 11x + 12

• (x + 4)(2x + 3)

• (x + 4)(x + 6)

• (x + 6)(2x + 4)

• (x + 3)(2x + 3)