Question

How do I factor using the zero factor property $?$

Answer 1

Hint: The zero factor property states that if $ab = 0$, then either $a = 0$ or $b = 0$. I mean if a product of two numbers is zero then one of those must be zero.

Complete step by step answer:
To show I factor using zero factor property, Let’s consider an example
Example: Find the root of ${x^2} - x - 6$.
${x^2} - x - 6 = 0$
$ \Rightarrow \left( {x - 3} \right)\left( {x + 2} \right) = 0$
Now, the zero factor property can be applied, since two things are being multiplied and equal zero.
We know that either
$x - 3 = 0$ or $x + 2 = 0$

Solve both to find that $x = 3$ or $x = - 2$.

Note:
As, we know that zero property status means that if $ab = 0$, then either $a = 0$ or $b = 0$.
The zero product property simply states the above statement. A product of factors is zero if and only if one or more of the factors is zero. This is particularly useful when solving quadratic equations .${x^2} + x - 20 = 0$.
We equate the equation to zero as essentially the zero is stating where the equation intersects with the x-axis. Also , it makes it really convenient for equations like $y = 8{x^2} - 16x - 8$ because when finding the root (or solution ) (or value of $x$ when $ = 0$), we can divide out the $8$.
We use the zero product property when we solve quadratic equations. You may have noticed that we always manipulate quadratic equations to $ax{}^2 + bx + c = 0$.
This is because factoring the equation gives us two expressions that multiply to zero. We can set each factor equal to zero and solve for x.