This week in math 10 I learned how to factor trinomials. A trinomial is an expression with three terms, an example being . 

 

Example 1: 

 

For the first example we will be solving . To begin we will start by making an area model. Now we will place a x above the top left corner and an x to the left of the top left corner, this is because . Now we need to figure out what –9 when they are added together and are +8 when multiplied together. –8+-1 =-9, . So, because of this we will write –8 or –1 on either the top of the top right box or to the left of the bottom left box, (they are interchangeable). We can now start to fill in the area model , -1 x = -1, , . Now looking back at the numbers outside the square we can make our new expression, (x-8)(x-1). 

 

Example 2: 

 

For this example, we will begin by drawing a box around the expression and placing the GCF on the left side of the box. In this case the GCF is 3, now we must find the numbers that multiply with 3 in order to equal the original expression. . Now that we have figured this out, we will rewrite our expression as . Next, we will make an area model placing the two x’s on the top left and to the left of the top left square. Because –8+3 = -5 and we will place –8 above the top right square and the 3 will be placed to the left of the bottom left square. Now we will fill it in, will go inside the top left square, -8x will be in the top right square, 3x will be in the bottom left square, and –24 in the bottom right corner. Now the final product of factoring this trinomial should be, .