Factor by Grouping and Binomial Factoring

A rectangle has an area of 2x² – 19x +45 ft². What are the dimensions of the rectangle?  

• (2x - 9)(x - 5)

• (2x + 9)(x + 5)

• (2x - 5)(x - 9)

• (2x - 5)(x + 9)

Factor 4b⁵+4b³+16b²

• 4b³(b⁴+b²+4b)

• 4b³(b⁴+4b+5)

• 4(b⁵+b³+4b²)

• 4b²(b³+b+4)

Factor by grouping:
3x³-x²+6x-2

• (x²+2)(3x+1)

•  (x²+2)(3x-1)

• (3x³+6x)(x²-2)

• none of the aboe

What are the factors of
25x² - 81?

• (5x - 9)(5x + 9)

• (5x - 9)(5x - 9)

• (5x + 9)(5x + 9)

• Cannot be factored

Mathematical Equivalence

ON

Mathematical Equivalence

ON

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

• 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)

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 are the factors of 7x² + 16x + 4?

• 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)

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

  a⋅c = 7⋅4 = 28

  b = 16

• Write the 2 binomial factors.

  (7x + 2) (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