Show the expression 𝑥^2−𝑥−6 in factored form and explain what the solution would mean for the equation. Show your work.
𝑥^2−𝑥−6 = (𝑥−3)(𝑥+2)
The solution (𝑥−3)(𝑥+2) means that the equation 𝑥^2−𝑥−6 can be factored into two linear factors, (𝑥−3) and (𝑥+2). This means that the equation has two solutions, 𝑥=3 and 𝑥=-2.
to find the solution to the equation
𝑥^2−𝑥−6 = 0
you factor the expression to get
(𝑥−3)(𝑥+2) = 0
The zero property of multiplication says that of the product of two numbers is zero, then one or the other of the numbers must be zero. So, that means
x-3 = 0
or x+2 = 0
giving the two solutions above.