Question

Write the quadratic equation in factored form. Be sure to write the entire equation.

x 2 + x - 12 = 0

Answer 1

so this answer to this equation i got this:

x^2+x-12=0
x^2+4x-3x-12=0
x(x+4)-3(x+4)=0
(x-3)(x+4)=0

so (x-3)(x+4)=0 should be the answer

Hope this helped :)
Have a great day 

Answer 2

Answer:

$(x+4)(x-3)=0$

Step-by-step explanation:

A general expanded form of a quadratic equation could be write as follws:

$ax^{2} +bx+c=0$

On the other hand, factored form equation could be generally write as:

$(x+q)(x+p)$

Where the parameters q and p are called the roots of the function.

1. In the case $x^{2} +x-12=0$, and taking into account the above, a = 1, b = 1 and c = - 12; and we need to find q an p.

2. Form the two factors taking into account the operation signs.

$(x+ p)(x-q)=0$

Note that in the first factor the sign of p is '+' because of the multiplication between the sign 'a (+)' and 'b (+)', then $+ * + = +$.  

In the same way, for the second factor the sign of q is '-' becasuse of the multiplication between the sign of 'b (+)' and 'c (-)', then $+ * - = -$.

3. As a=1, if you want to write a factored form you only need to find two numbers (p and q) whose multiplication is equal to -12, and whose sum is equal to +1.

By trial and error method you could determine that p=4 and q =-3 due to:

$p*q=12\\(4)*(-3)=12\\p+q=1\\(4)+(-3)=1$

4. Locate the results of p and q in the two factors form:

$(x+ p)(x-q)=0\\(x+4)(x-3)=0$

This is the factored form of the quadratic equation $x^{2} +x-12=0$