Multiplying and Factoring Trinomials

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

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

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 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)

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

(x + 3)(x + 7)

• x² + 10x + 21

• x² + 21

• x² + 4x + 21

• x² − 10x + 21

(2x - 1)(x + 2)

• 2x² + 3x - 2

• 2x² - 5x - 2

• 2x² + 3x + 2

• 2x² - 5x + 2

Factor

k²+7x+10

• (k+2)(k+5)

• (k-2)(k-5)

• (k+10)(k+4)

• (k+2)(k-5)