Factoring means breaking a number or an algebraic expression into the parts that multiply together to make it. This guide focuses on factoring common quadratic and simple polynomial expressions, a key skill for solving equations.
Step by step
- Pull out the greatest common factor firstLook for a number or variable that divides every term. For example, in 6x squared plus 9x, both terms share 3x, giving 3x times (2x plus 3).
- Count the termsCheck how many terms remain. Two terms may be a difference of squares, and three terms is often a factorable trinomial.
- Check for a difference of squaresIf you have two perfect squares subtracted, such as x squared minus 9, it factors into (x plus 3)(x minus 3).
- Factor a simple trinomialFor x squared plus bx plus c, find two numbers that multiply to c and add to b. For x squared plus 5x plus 6, use 2 and 3 to get (x plus 2)(x plus 3).
- Check your work by multiplying backMultiply the factors out again. If you get the original expression, the factoring is correct.
Handy tips
- Always check for a greatest common factor before trying other methods.
- For trinomials, list factor pairs of the last term and test which pair adds to the middle number.
- Not every expression factors neatly, so some may need the quadratic formula instead.
FAQ
What does it mean to factor an expression?
It means rewriting it as a product of simpler expressions that multiply to give the original, like turning x squared plus 5x plus 6 into (x plus 2)(x plus 3).
How do I factor when the leading coefficient is not 1?
Use the method sometimes called grouping or the AC method: multiply the first and last coefficients, find two numbers that fit, split the middle term, and factor by grouping.
What if the expression will not factor?
Some quadratics have no rational factors. In that case, use the quadratic formula to find the roots or leave the expression as it is.