Factoring trinomials, was known as quadratic equations, are important sectors in learning mathematics. The quadratic equation is a polynomial equation of order two. The general form of a quadratic equation is in the picture below.
Attached figure 7.1
Where a is the coefficient for squared, b is for the linear coefficient, and c is for the constant. While x and y are the variables that affect the equation. When depicted in the graph, x will be the x – axis, and y will be the y – axis.
The intercept on the x-axis is when the value of y = 0 or when written: ax2 + bx + c = 0. The corresponding x value for the equation will usually be referred to as the roots of the quadratic equation.
3 Methods to Solve Factoring Trinomials
There are 3 methods to solve quadratic equations, namely factoring, completing the quadratic equation, and using formulas. And we are going to show you each of them but this article will concern about using this formula in the worksheet.
The first one is the factoring Trinomials method. The main thing is you need to find the factor of the equation. Here is an example of solving a quadratic equation using the factoring method. Solve the equation x2-3x+2=0!
x2-3x + 2 = 0
(x-2) (x-1) = 0
(x-2) = 0 so that x = 2
(x-1) = 0 so that x = 1
So, the solution to the equation x2-3x+2=0 is x = 2 and x = 1
The second one is by completing perfect squares. Perfect square means this equation have a special coefficient value. For the result you will get the same number, one is positive number and the other is negative number. Here is the example of this method: Solve the equation x2-8x+7=0!
x2-8x + 7 = 0
x2 -8x + 16-9 = 0
x2 -8x + 16 = 9
(x-4)2 = 9
(x-4) = 3 so that x = 7; and
(x-4) = (- 3) so that x = 1
So, the solution to the equation x2-8x+7=0 is x = 7 and x = 1
The last method is using a formula. Factoring trinomials can simply be calculated using the ABC formula quadratic equation. And with this formula, we will learn how to solve the quadratic equations using a worksheet. Attached figure 7.2
The values of b2-4ac are often referred to as the Determinant value. This value determines whether the parabolic equation has an intercept on the x – axis. If the determinant is less than zero (negative) then the roots of the equation are imaginary.
Solve Quadratic Equations Using Student Worksheet
To learn deeper about the calculation of the factoring trinomials formula, we can use the student worksheet. Exercise is the most important thing for every student in learning something. Here is some example of quadratic equations.
Let’s solve this equation 4×2 + 1 = 8x using the ABC formula. Express the solutions in their exact and decimal form (three digits after the decimal point). Test one of its exact solutions into the equation.
The quadratic equation 4×2 + 1 = 8x has the standard form 4×2 – 8x + 1 = 0. So that from this standard form we get a = 4, b = –8, and c = 1. Next, we determine the solutions of the quadratic equation by quadratic formula. Attached figure 7.3
Next, we test one of the solutions, namely x = 1 + √3 / 2 into the equation. Attached figure 7.4.
Then, it turned out that the solution fulfilled the quadratic equation. By using the worksheet, you can find the quadratic equation easily. Exercise in student worksheet will make you an expert. Not only factoring trinomials, but also other mathematical problems.