Could someone help to explain to me how factoring is used to solve quadratic equations? Also could you give me some example to try? Thank You.
These sites should help you.
http://www.purplemath.com/modules/solvquad.htm
http://www.intmath.com/Quadratic-equations/1_Solving-quadratic-equations-factoring.php
Thank you they were very helpful.
You're welcome.
Of course! Factoring is a powerful algebraic technique used to solve quadratic equations. The process involves expressing the quadratic equation in the form of a product of two binomials. This allows us to find the values of the unknown variable that make the equation true. Here's how you can use factoring to solve quadratic equations:
Step 1: Write down the quadratic equation in the standard form, which is ax^2 + bx + c = 0, where a, b, and c are constants.
Step 2: Attempt to factor the quadratic expression on the left side of the equation. Look for two binomials that, when multiplied together, give you the original quadratic expression.
Step 3: Set each binomial equal to zero and solve for the variable. This will give you the possible values of the variable that make the equation true.
Let's go through an example to make it clearer:
Example 1: Solve the quadratic equation 2x^2 + 5x + 3 = 0
Step 1: The equation is already in standard form.
Step 2: We need to find two binomials that multiply to 2x^2 + 5x + 3. In this case, since the coefficient of x^2 is 2, we look for two binomials in the form (px + q)(rx + s), where p and r are the factors of 2 (which are 2 and 1), and q and s are the factors of 3 (which are 3 and 1).
Step 3: Now, we expand the binomials (2x + 3)(x + 1) to see if it matches the original quadratic expression. If it does, it means we've successfully factored the equation.
Expanding (2x + 3)(x + 1) gives us: 2x^2 + 5x + 3
Since the expanded form matches the original quadratic expression, we can set each binomial equal to zero:
2x + 3 = 0 and x + 1 = 0
Now, solve for x:
2x = -3 => x = -3/2
x = -1
Therefore, the solutions to the quadratic equation 2x^2 + 5x + 3 = 0 are x = -3/2 and x = -1.
I hope this explanation helps you understand how factoring is used to solve quadratic equations!