![]() Since the sum of 3 and -5 is -2 and the product of 3 and -5 is -15, you have found out that the factors of the trinomial x² -2x -15 are (x+3) and (x-5) ![]() Since the product of two negatives is always positive and the product of two positives is also always positive, your factors will include one positive number and one negative number.Īfter some trial-and-error, you will find that 3 and -5 work because: In cases like this example, you need two number that will multiply to a -15. Another way to say this is: find two numbers with a sum of -2 and a product of -15. Once you have identified the values of b and c (-2 and -15 respectively in this example), you can use trial-and-error to find two numbers that both add to the b term (-2) and multiply to the c term (-15). ![]() In this example, the values of b and c are: b=-2 & c=-15 Now, we can find the factors of x² -2x -15 as follows: In this case, you can conclude that the factors of x² + 6x + 8 are (x+2) and (x+4). Step Three: Use your numbers from step two to write out the factors Since the sum of 2 and 4 is 6 and the product of 2 and 4 is 8, you can found out that the factors of the trinomial x² + 6x + 8 are (x+2) and (x+4) However, if you chose the numbers 2 and 4: In this case, 5+1=6, but 5x1≠ 8, so these two numbers would not work. Another way to say this is: find two numbers with a sum of 6 and a product of 8.įor example, let’s say that you chose the numbers 5 and 1. Once you have identified the values of b and c (6 and 8 respectively in this example), you can use trial-and-error to find two numbers that both add to the b term (6) and multiply to the c term (8). Step Two: Find two numbers that both ADD to b and MULTIPLY to c. In this example, the values of b and c are: b=6 & c=8 Step One: Identify the values of b and c. ![]() When we solve quadratic equations by factoring, we are actually figuring out where the parabola crosses zero on the x-axis, as shown in Figure 02 below. Why are we concerned with quadratic equations being equal to zero? You may already know that, when graphed, quadratic equations can be represented on the coordinate plane as a parabola (a U-shaped curved). So, we can say that a quadratic equation is of the form:įigure 01 above illustrates this key difference between trinomial expressions and quadratic equations, which is namely that a quadratic equation is an equation and includes a fourth term (=0). In algebra, a quadratic equation is a trinomial of the form ax² + bx + c that is equal to zero. Note that, since it is an expression, a trinomial does not include an equal sign. In algebra, a trinomial expression is a polynomial with 3 terms of the form ax² + bx + c. While the focus of this guide is on teaching you how to factor quadratic equations and how to solve quadratic equations by factoring, it is important that you first understand how the difference between a trinomial expression and a quadratic equation. However, before we learn how to factor quadratic equations and how to solve quadratic equations by factoring, let’s quickly review some important vocabulary terms related to quadratics and quadratic equations. While we will review general factoring in this guide, we will be more focused on how to factor a quadratic equation. Note that this guide is a follow-up to our free step-by-step guide How to How to Factor Polynomials, which reviews how to factor polynomials with 2 terms, 3 terms, and 4 terms. How to Factor Quadratic Equations when a≠1? How to Factor Quadratic Equations when a=1 What are the Solutions of a Quadratic Equation? This free Step-by-Step Guide on How to Factor Quadratic Equations will cover the following topics: Learning how to factor a quadratic equation comes down to being able to recognize a quadratic equation, being able to factor it, and then finally being able to solve for x and check your answer for mistakes. Being able to solve quadratic equations by factoring is an incredibly important algebra skill that every student will need to learn in order to be successful in Algebra I, Algebra II, and beyond. The word quad is Latin for four or fourth, which is why a quadratic equation has four terms (ax², bx, c, and 0). In algebra, a quadratic equation is an equation of the form ax² + bx + c = 0 where a can not equal zero.
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