Factoring Trinomials and Factoring by Grouping

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"

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

Factor 5x² -13x - 6

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

  5x² -15x + 2x + 6

• Write the binomial factors.

  (5x + 2)(x - 3)

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

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

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

  a⋅c = 5⋅-6 = -30

  b = -13

• x⁴(x² - 5x - 24)
• (x - 8)(x + 3)
• x⁴(x - 8)(x + 3)
• (x³ - 8)(x³ +3)

Factor Completely: 14p²-24p-8

• (5p+3)(p-4)

• (3p-2)(p+10)

• 2(7p-2)(p+2)

• 2(7p+2)(p-2)

Mathematical Equivalence

ON

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 should go in the final step?

• (4x + 1) ( x + 2)

• 
• (4x - 1) ( x - 2)

• (4x + 1) ( x -2)