If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Algebra (all content)

### Course: Algebra (all content)>Unit 9

Lesson 2: Quadratic factored form

# Zero product property

The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.

## Want to join the conversation?

• how could you use the zero product property if the equation wasn't equal to 0?
• I assume you're dealing with a quadratic?

If yes, then you can force the equation equal to 0. Well, maybe not "force" but you can rearrange the equation such that you will have the quadratic in the form `Ax^2 + Bx^2 + C = 0`.

Example:
Solve for `5 = x^2 + 4x + 8`.
``5 = x^2 + 4x + 80 = x^2 + 4x + 3     { subtract 5 from both sides }0 = (x + 3)(x + 1)     { factorise }x = -3 or x = -1         {zero product property}``
• I still don't understand about which is the smaller x. In the practice after this video, it talks about the smaller x and the larger x. Which one is which? Is the smaller one the first one? I don't know if it's being literal or not.
• I'm pretty sure that he is being literal, saying that the smaller x has a value less than the larger x.
• how would you work out the equation...a^2-6a=-8? how would you find a?
• a^2-6a=-8
a^2-6a+8 = -8+8---------------add 8 to both sides
a^2-6a+8 = 0------------------- (-8) and 8 cancel out
(you might want to know "grouping", which is a way of factoring before you read the next steps.)
(a-2)(a-4) = 0-------------------factor using "grouping"
a-2=0, or a-4=0----------------solve for a
a=2, or a=4
• How do you write an equation in standard form if you’re only given a point and a vertex
• The standard form of quadratic functions is f(x) = a(x - h) ^ 2 + k. Since (h, k) is the vertex, you will just have to solve the equation for 'a' by changing f(x) and x into the coordinates of the point.
• Is it possible to have a zero-product equation with no solution? (such as when one or both values of x is a nonreal number)
• The solution x = 0 means that the value 0 satisfies
the equation, so there is a solution. "No solution"
means that there is no value, not even 0, which would satisfy the equation.
• I understood the concept of this no problem, and calculated all the values correctly, but....

For some reason the practice questions required we were asked to put the values in order, and on one question I put them in reverse order.

Is there is a mathematical reason for this order requirement? If so, I'll hold my hands up and say I should have concentrated more.

If it's because the web developer found it easier to test for a single specific value in each box, then I despair.
• I believe the reason is the later. Who ever designed the page found it easier to check the answers in order (easier programming). So, pay attention to the directions in the exercise set. They always tell you if they want the smallest result first.
• In the second example given in the video, how will you graph that example?
• So what would you do to solve if it was for example, 2x^2-11x-21=0 ??
• 0 times anything equals 0.....what if i did 90 X 0 + 1 = 1?