Q:

How Do You Factor Trinomials of the Equation Ax2+bx+c?

A:

A trinomial in the form of ax^2 + bx + c is called a "quadratic." To factor a quadratic equation, factor out the greatest common factor, find a pair of factors that add to equal "b" and multiply to equal "c," and then group all the factors together.

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1. Factor out the greatest common factor

If the quadratic has a greatest common factor, then factor it out and write it to one side. This number does not disappear just because it is factored out. For example, if given the quadratic 3(x^2 - 15x + 18), the greatest common factor is 3. The quadratic now looks like x^2 - 5x + 6.

2. Choose a pair of factors

Find a pair of numbers that, when added, equal "b" and when multiplied equal "c." In the case of the quadratic 3(x^2 - 5x + 6), "c" is equal to 6 and has factors of 1, 2, 3 and 6. The factors 2 and 3 add to 5. However, "b" is equal to negative 5. The solution is to make both factors negative, because this multiplies out to 6 and adds to negative 5.

3. Group the factors

Group the factors into two binomials: (x - 2)(x - 3). Placing the binomials with the greatest common factor gives the complete answer for the quadratic: 3(x - 2)(x - 3).