# Factoring a Quadratic Equation

##### Question
How do you factor 3x2 – 8x – 3?

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).

### Comments for Factoring a Quadratic Equation

Average Rating Jan 01, 2016 Rating Factorisation NEW by: Anonymous Step five is not so clear.

 Jul 26, 2011 Rating Awesome by: Sam Man this is the best site ever a lot of help and excellent answers I love it :)

 Jul 18, 2011 Rating finally,a helping hand. by: Anonymous it really was helpful.thanks a lot.

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