How do I factor using the zero factor property $?$
Answer
622.5k+ views
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.
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.
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