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How To Factor Trinomials How To Factor Trinomials Today in this session we are going to discuss about Factoring Trinomials. Trinomials are the very interesting and important part of the elementary algebra. Trinomial is a polynomial which has three terms. The three terms can be any variable. For instance 2x + 4y +9z and x^3 + 4x^2 + 5x are trinomials. Factoring a trinomial is similar to the finding factors of a given integer. It completely depends on ones skills of multiplication because factoring a number is just reverse process of multiplication. In this session we will learn how to find factors of the trinomials that have the following forms: 1.

x^2 + bx + c


ax^2 + bx +c

So first of all we should know the whole procedure to solve these problems. Know More About How do you Find the Circumference of a Circle

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1. The procedure of finding factors of trinomial of the form x^2 + bx + c. a. First of all make a set up for the product of two brackets ()*() where each bracket will have two terms. b. Now we need to find the factors that will placed at the first position. For this to get back the square of x we need to set x in first position of both the brackets say (x ¹ a) * (x ¹ b). c. Now the task is to get the factors that we will place in the last positions of the brackets. The factors for the last position must be two expressions such that their multiplication become equal to c that is a constant and their sum become equals to b that is a number and coefficient of the variable x. Now in this case: If the constant c is positive then our factors both have the same sign which will depend on the sign of b. If constant c is negative then our factors both have the opposite signs which also depend on the sign of b. For example x^2 – 5x + 6 = (x -2) (x -3) here the first place of both the brackets have x to satisfy the square of x in the equation and the next two factors are 2 and 3 where (2 + 3) = 5 and (2*3) = 6 so it satisfy the conditions as above mentioned. 3. The procedure to find the factors of trinomials of the form ax^2 + bx +c:

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a. Similarly in this we will set up a product of two brackets ()*() where each of the bracket will have two terms. b. Now we will use trial and error method to find the required factors. In this the factors of a will be placed in the first term and in the last term we will place factors of c. For example: 3y^2 – 5y + 2 = (3y - 2) ( y - 1). Here this is the right combination. The first term is satisfying the 3x^2 of the equation if we will multiply them.

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How To Factor Trinomials