Question

X^2 + 2x - 3 = x(x + 2) - 3 Is this a factoring error?

Answer 1

There's a specific procedure for factoring quadratic expressions. The above is not a correct approach.

Answer 2

For a quadratic expression in the form ax^2 + bx + c, if it is factorable, the general method is as follows:

`1.` Find two numbers that multiply to get ac, yet add to get b.
`2.` Split the middle term bx, using those two numbers
`3.` Factor the first two terms and the last two terms by grouping
`4.` Factor out the remaining common term

Answer 3

Thanks Hero! Why does the approach in my question not work?

Answer 4

For x^2 + 2x - 3:

`1.` The two numbers are 3 and -1, since ac = (3)(-1) = -3 and b = 3 - 1 = 2
`2.` Splitting the middle term you get:
x^2 + 3x - 1x - 3
`3.` Factoring by grouping you get:
(x^2 + 3x) + (-1x - 3)
x(x + 3) - 1(x + 3)

`4.` x + 3 is the remaining common term, so that is factored out to get:
(x + 3)(x - 1)

Answer 5

So the algebraic steps alone look like this:

x^2 + 2x - 3 Original Problem
= x^2 + 3x - 1x - 3 Subtraction Property (2x = 3x - 1x)
= x(x + 3) - 1(x + 3) Factor by Grouping
= (x + 3)(x - 1) Distributive Property ab + ac = a(b + c)

Answer 6

Some students are able to factor in their heads and do it all in one step, going from the original quadratic to the final result:

x^2 + 2x - 3 = (x + 3)(x - 1)

It's a very intuitive method that requires use of mental math and mastery of multiplication and addition/subtraction.