We've narrowed the Last terms down to a few possibilities. Test which possibilities work with Outside and Inside multiplication. Write these pairs down somewhere to remember them. There are a few possibilities: -1 times 10, 1 times -10, -2 times 5, or 2 times -5.What are the factors of -10? What two numbers multiplied together equal -10?.In our example x2 + 3x - 10, the last term is -10.So to factor, we need to find two numbers that multiply to form the last term. If you go back and reread the FOIL method step, you'll see that multiplying the Last terms together gives you the final term in the polynomial (the one with no x). Use factoring to guess at the Last terms. We'll cover more complicated problems in the next section, including trinomials that begin with a term like 6x2 or -x2.Our example x2 + 3x - 10 just begins with x2, so we can write:.These are the factors of the term x2, since x times x = x2. For simple problems, where the first term of your trinomial is just x2, the terms in the First position will always be x and x. Don't write + or - between the blank terms yet, since we don't know which it will be.Ĥ.For now, just write (_ _)(_ _) in the space where you'll write the answer. Write a space for the answer in FOIL form. Because the highest exponent is 2 (x2, this type of expression is "quadratic."ģ.For example, rewrite 3x - 10 + x2 as x2 + 3x - 10. If the equation isn't written in this order, move the terms around so they are.If you start with an equation in the same form, you can factor it back into two binomials. When you multiply two binomials together in the FOIL method, you end up with a trinomial (an expression with three terms) in the form ax2+bx+c, where a, b, and c are ordinary numbers.
Multiply the Outside terms: (x+2)(x+4) = x2+4x + _.Multiply the First terms: (x+2)(x+4) = x2 + _.It's useful to know how this works before we get to factoring: You might have already learned the FOIL method, or "First, Outside, Inside, Last," to multiply expressions like (x+2)(x+4). Higher degree polynomials, with terms like x3 or x4, are not always solvable by the same methods, but you can often use simple factoring or substitution to turn them into problems that can be solved like any quadratic formula.ġ. There are several tricks to learn that apply to different types of quadratic trinomial, but you'll get better and faster at using them with practice.
Most likely, you'll start learning how to factor quadratic trinomials, meaning trinomials written in the form ax2 + bx + c. A trinomial is an algebraic expression made up of three terms.