Question

How do you convert a quadratic equation from standard form into factored form?

Answer 1

To convert a quadratic equation from standard form to factored form, set the equation to zero and find two binomials that multiply to the given quadratic, or use the quadratic formula to find the roots.

Step-by-step explanation:

To convert a quadratic equation from standard form into factored form, you begin with the equation in the form ax^2 + bx + c = 0. Firstly, ensure that one side of the equation is equal to zero. The standard form can be factored if the quadratic is factorable, which involves finding two binomials that multiply to give the original quadratic. This process sometimes requires factoring out a greatest common factor first, if applicable, and then applying techniques such as the FOIL method (First, Outside, Inside, Last) to find factors that produce the given coefficients.

If the quadratic equation cannot be easily factored, you can use other methods such as completing the square or applying the quadratic formula to find the roots of the equation. Once you have the solutions, or roots, these can be placed into binomial factors in the form of (x - r1)(x - r2) = 0, where r1 and r2 are the solutions of the quadratic equation.

For the example equation t^2 + 10t - 200 = 0, one would look for two numbers that multiply to -200 and add up to 10 to factor it. If such numbers cannot be found, using the quadratic formula may be necessary. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), substituting a, b, and c with the coefficients from the quadratic equation.

Answer 2

Step-by-step explanation:

I’m assuming that you’re asking about quadratic equations, but suffice it to say that the method may even work for polynomials of higher degrees.

Let’s take an example. You have x^2+6x+8.

First, multiply the term in x^2 with the constant; in this case we get 8x^2.Next, break the value in x into two numbers, such that when you add them, the value becomes that of the middle term and when you multiply them, the value becomes that which you have just calculated.

Step 1:

x^2 * 8= 8x^2

Step 2:

(break the middle term)

x^2+4x+2x+8 (notice how 4x when added to 2x gives 6x but when multiplied, gives 8x^2)

Step 3:

(separate the common terms)

x(x+4)+2(x+4)

(x+2)(x+4)