Question

Factor & Finding Zeros x^{2} -x-6=0

Answer 1

Answer:

x = 3, -2

Step-by-step explanation:

To help us factor, we can split the middle term up into the sum of the terms -3x and 2x:

$x^2+(-3x)+2x-6=0$

From there, we can factor out an x from the first two term and a 2 from the last two to obtain the equation

$x(x-3)+2(x-3)=0$

Factoring out an (x - 3) from each term gives us the equation

$(x-3)(x+2)=0$

At this point, we can divide by either x - 3 or x + 2 to obtain the two equations

$x-3=0$ and $x+2=0$

Solving both for x gives us the solutions x = 3 and x = -2. We can verify these by substituting them back into the original equation:

$3^2-3-6=0\\9-3-6=0\\6-6=0\\0=0$

$(-2)^2-(-2)-6 = 0\\4+2-6=0\\6-6=0\\0=0$