Trinomials Requiring Decomposition

Example #1:
      6x2 + 19x + 10
Find numbers that:
multiply to 60 and add to 19:
They are 15 and 4 ... use them to split the middle term:
= 6x2 + 15x + 4x + 10
Now find common factors for each group of two:
= 3x(2x + 5) +2(2x + 5) The common bracket is the common factor:
= (2x + 5) (3x + 2)
Another example:
      8x2 - 2xy - 3y2
Find numbers that:
multiply to -24 and add to -2:
They are +4 and -6 ... use them to split the middle term:
= 8x2 + 4xy - 6xy - 3y2
Now find common factors for each group of two:
= 4x(2x + y) -3y(2x + y)
The common bracket is the common factor:
= (2x + y) (4x - 3y)

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