Factoring a Quadratic Equation

Question

How do you factor 3x² – 8x – 3?

Answer

STEP 1:    You are given a quadratic expression of the form ax² + bx + c, where a, b, c are constants. The first step is to multiply the coefficient of the square term by the constant term. That is 3(–3) = –9.

STEP 2:    Now, find two numbers such that, their product equals to –9 and their sum equals –8, which is the coefficient of the linear term. The numbers are –9 and 1. Thus, we can split the middle term –8x as –9x + x.


STEP 3:    The next step is replacing the middle term –8x with –9x + x in the original expression.

                    3x² – 8x – 3 = 3x² – 9x + x – 3

STEP 4:    Now, there are four terms in the obtained expression and the next move from your side should be to factor the first two terms and the last two terms of the expression.

                    3x² – 9x + x – 3 = 3x (x – 3) + 1(x – 3)

STEP 5:    The common factor of the expression is (x – 3). The final step is to factor the expression again.

                    3x (x – 3) + 1(x – 3) = (3x + 1)(x – 3)

The factorized form of the expression

                    3x² – 8x – 3 is (3x + 1)(x – 3).