can someone explain how an quadratic equation with factoring and give an example,PLEASE!
Of course! I'd be happy to explain how to factor a quadratic equation and provide an example.
When factoring a quadratic equation, we are essentially finding two binomials that, when multiplied together, produce the original quadratic equation. The general form of a quadratic equation is:
ax^2 + bx + c = 0
To factor a quadratic equation, follow these steps:
Step 1: Ensure that the quadratic equation is in standard form, where the coefficient of x^2 (a) is not equal to zero.
Step 2: Determine two numbers, let's call them p and q, such that their sum equals the coefficient of x (b) and their product equals the constant term (c) in the quadratic equation.
Step 3: Rewrite the middle term (bx) as the sum of px and qx.
Step 4: Group the terms and factor them separately.
Step 5: Finally, apply the zero product property and set each factor equal to zero to solve for x.
To illustrate, let's solve the quadratic equation by factoring with an example:
Example: Factor the quadratic equation: x^2 + 5x + 6 = 0
Step 1: The equation is already in standard form, so we can proceed to the next step.
Step 2: Determine two numbers whose sum is 5 and product is 6. In this case, the numbers are 2 and 3.
Step 3: Rewrite the middle term:
x^2 + 2x + 3x + 6 = 0
Step 4: Group the terms and factor them separately:
(x^2 + 2x) + (3x + 6) = 0
x(x + 2) + 3(x + 2) = 0
Step 5: Now, apply the zero product property and set each factor equal to zero:
x + 2 = 0 or x + 3 = 0
Solving for x gives us:
x = -2 or x = -3
Therefore, the factored form of the quadratic equation x^2 + 5x + 6 = 0 is (x + 2)(x + 3) = 0.