What is the new and improved factoring Ac method ?

Expert Answers

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Consider the polynomial expression `ax^2 + bx + c.`

When the constant c is positive, the polynomial can be factored if there are 2 factors of ac that add to be the absolute value of b.

When the constant c is negative, the polynomial can be factored if there are 2 factors of ac that have a difference of the absolute value of b.

Example 1:

`6a^2 + 7a + 2`

Are there 2 factors of 2(6) or 12, whose sum is 7 (middle number)?  This is 3 and 4.  Rewrite by problem and factor by grouping.

`6a^2+3a + 4a + 2`

`3a(a+1) + 2(a+1)`

`(3a+2)(a+1)`

Exampe 2:

`2x^2+7x-15`

Are there 2 factors of 2(15) or 30 whose difference is 7 middle number)?  The 2 numbers are 3 and 10

`2x^2 + 10x - 3x - 15`

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

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

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