How do you solve quadratic equations by factorising?

Answer 1

Factoring a quadratic equation is the opposite of expanding an equation. FOILing (first, outer, inner, last) is the common technique used to do this.

Example of foiling: (x + 4) (x + 1) = x2 + 1x + 4x + 4, which simplifies to x2 + 5x + 4.

Because factoring is the opposite of foiling we are going to move backwards, but in a different way. The solution to a factoring problem is the beginning of a foiling problem.

Factoring Example:

x2 + 5x + 4 = 0

NOTE: your equation might not be equal to anything. It may appear as x2 + 5x + 4. In that case do the following steps as they appear but leave out the "= 0" from your answer because it's not there. Also do not do STEP 4 if it's not equal to zero.

STEP 1. x2 is equal to x multiplied by x, so separate the x's.

(x ) (x ) = 0

STEP 2. Look at the last number in the quadratic equation (4), take the multiples of that number (4) and see which set of multiples adds up the the middle number (5).

Multiples of 4: 2 and 2 (2 x 2 = 4), 4 and 1 (4 x 1 = 4).

2 + 2 = 4, 4 is not the middle # (5). 4 + 1 = 5!! Use 4 and 1.

(x 4) (x 1) = 0

STEP 3. Look at the sign (positive or negative) of the middle number you are trying to add up to. The signs of the 4 and 1 must fit too.

Middle number is a POSITIVE 5.

postive 4 + positive 1 = positive 5 <--- that's right!

but negative 4 + positive 1 = negative 3 <--- that's wrong!

negative 4 + negative 1 = negative 5 <--- that's wrong!

positive 4 + negative 1 = positive 3 <--- that's wrong!

(x + 4) (x + 1) << GRAND ANSWER!!! (unless equal to 0)

(x + 4) (x + 1) = 0

STEP 4. Sometimes the equation will not be set equal to anything. If that's the case, then (x + 4) (x + 1) is the correct answer. If it is set equal to zero then take each part of the new equation equal to zero and solve for x.

x+4 = 0 >> subtract 4 from both sides and you get x = -4

and

x + 1 = 0 >> subtract 1 from both sides and you get x = -1

x = -4 or x = -1 << GRAND ANSWER!!! :)