Factoring by Groups

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

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"

Mathematical Equivalence

ON

Mathematical Equivalence

ON

Mathematical Equivalence

ON

Factor 5x² -13x - 6

• Write the binomial factors.

  (5x + 2)(x - 3)

• 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)

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.