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The Ultimate Guide to Zero Product Property And Calculator with example, Zero product property definition.
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Zero Product Property definition, zero product property calculator, zero product property example and formula
Zero product property
Hello Algebra one students.
Welcome back. In this lesson we're going to look at another way to solve a quadratic equation.
Today's method is going to be by using Factoring and the Zero Product Property.
So I hope in this article zero product property I will succeed in solving many problems. And I will share Best zero product property calculators For Factoring Zero Product property.
In the last lesson we looked at how to solve quadratics that did not have an x term.
They only had x squared's and constants.
zero product property calculator
Today we're going to explore how to solve a quadratic if it does have an x term.
Like in this one,
the 8x. We cannot just isolate the x because we have two different x terms.
It makes it impossible to get x by itself.
So instead we are going to use something called the Zero Product Property.
What is the zero product property
What the Zero Product Property says is that if you have two factors that when multiplied equal zero, then either an equals zero,
b was equal to zero or maybe it was both.
We can use the Zero Product Propertywith numbers or with polynomial factors.
zero product property khan academy.
How to use the zero product property
Let's look at an example of how you use it with polynomial factors. In this example I have two factors:
 x plus 2
 x minus 3
and when multiplied, they equal 0.zero product property formula how to use the zero product property
That means that either the first factor x plus 2 was equal to 0 or the second factor x minus 3 was equal to 0. If I solve each one individually,
on this one I would have to subtract 2 from both sides and on this one I would have to add 3 to both sides.
My solutions will be x equals negative 2 and x equals 3. Therefore, the solutions are negative 2 and 3.zero product property definition
Remember from last lesson that most quadratics do have two solutions.
That is why I ended up with two solutions.
Zero product property calculator
It is better to have a calculator without all these definitions.
And use the zero product property calculator
But today I am sharing with you the Best Zero Product Property Calculators through which you can make Zero Product Factory for free. And it will be a very good choice for you.
So let's get started,,
1. factoringpolynomials.com ›
It's completely free, and I've been using it for a while, I like it very much and it works smoothly. I hope you like it too.
2. mathpapa.com ›
It's completely free and better for factoring zero product property calculator.
3. wyzant.com ›
It's completely free and bes tit works smoothly for zero product property calculator with steps
So you know amazing to useuse the zero product property calculator and solve zero factor property calculator.
Zero product property definition:
Zero Product Property states that when the product of two expressions is equal to zero, the expression of both is equal to zero. In the case of variables, when $ ab = 0, then either $ a = 0 $ or $ b = 0.
Example of definition:
Other example:
For more definitions you can visit
1 MathsIsFun
2 Wikipedia
3 medium.com ›
Zero product property quadratic equations
Because of the Zero Product Property wecan factor quadratics with an x term and use those factors to solve.
Here are the three steps in order to use this method.
Zero product property.
1. First, make sure that the equation isequal to zero, otherwise you can't use the Zero Product Property if it's not equal to zero.
Also read
2. The second step is to factor the quadratic into two factors. And finally set each of those factors equal to zero and solve for x.
zero product property example
In this equation,
x squared plus 8x plus 12 equals zero, notice that I have a squared and an x term.
I'm going to have to factor. So make sure first that the equation is equal to zero. It is.
That's good.
zero product property calculator. We can start factoring. When I factor this quadratic, I get x plus 6 and x plus 2. Using the Zero Product Property that means either the first factor,
x plus 6 was equal to zero or the second factor x plus 2 was equal to zero.
I solved each equation.
So I subtracted 6 from the first equation and got x equals negative 6 and I subtracted 2 on the second factor and got x equals negative 2.
Remember most quadratics have two solutions so my solutions are x equals negative 6 and x equals negative 2.
Let's look at one last example.
Zero product property.
zero product property example
Always start off by making sure thatyour equation says equals zero so you can use the Zero Product Property.
Unfortunately this one does not.
It says equals ten. So in order to get that side to be a zero, I'm going to have to subtract 10 because 10 minus 10 is zero.
So I will subtract 10 from both sides and get x squared minus 3x minus 10equals zero.
Now I can move on to factoring.
This quadratic will factor to x minus 5, x plus 2.
If I set each factor equal to 0,
x minus 5 equals 0, I'd have to add 5 to both sides of that equation and x will equal 5.
In the other one, x plus 2 equals 0. I would subtract 2 from both sides and x equals negative 2. Therefore this quadratic has solutions 5 and negative 2. So just to recap,
after this lesson you should know what the Zero Product Property means and how to use the Zero Product Property to solve a quadratic by using its factor.
zero product property quadratic equations
If any of these are confusing, please review this lesson again. zero product property calculator no it
Zero product property examples
In this article we are going to explore the zero power property of exponents.
The zero power property of exponents states that anything this weekend to the zero power is the number one.
It's that simple.
Let's dive right into our first example. In example 1 we have two x to the fourth power times the quantity x to the third power y to the fifth power z to the seventeenth powerball raised to the power of zero.
Zero product property.
The first step here is to apply the zero power property.
That makes what is in the entire set of parenthesis equal to the number one.
We then multiplythat by what was outside the parenthesis, two x to the fourth power and get an answering 2 x to the fourth power.
zero product property example
I love this property of exponents because of its pure simple nature. In example 2 it appears at first glance thatthere is a lot going on.
Let's first read the problem. The quantity four x to the third power y to the zero power z to the fifth power times 9 xy to the zero power z to the negative three power all raised to the one half power.
So much going on.
Let's break it up into more manageable pieces. First lets group like terms together and apply the product property of exponents.
Zero product property.
Identify the constant terms. That's four and 9. Next, identify common bases. I see x, y and z.
Next add the exponents of the common bases. For x that three plus one.
For y that 0 plus 0 and for z that's 5 and negative three. When we combine allof those we get 4 times 9 to be equal to thirty six. And x raised to the three plus one poweris x to the fourth power.
zero product property formula
That leaves y to the o power and z to the five minus threewith is 2.
Now we apply the power property, which distributesthe ½ power to everything in parenthesis.
Now we have 36 to the one half power x tothe four times ½ power y to the zero times one half power and z to the two times ½ power. Simplifying again 36 to the one half poweris like taking the square root, and the square root of 36 is 6.
X to the four times is2. Y to the zero power raised to the one half power is the same thing as saying y to thezero power,
which is one and z to the second power times the one half power leaves us withz to the first power.
Zero product property
That brings us to a minal answer of 6 x squared z to the firstpower.
Zero product property example 2
Example three: We have the quantity six xto the 0 power y to the fifth power over the quantity 2 y to the third power. zero product property formula
zero product property example
First simplify what you can easily. Starting with the fraction6 / 2.
That simplifies to 3 Next x to the zero power simplifies to the number one,
and nowlet's apply the quotient property and subtract common base y's exponents to the top of the fraction.
That's 53. Since there is nothing left on the bottom of the fraction, zero product property formula
we can put it over the number one, or we can choose not to write the denominator at all.It's personal preference.
zero product property calculator
Finishing out our simplifying we end up with 3 y square din the numerator all over 1,
which more simply stated is three y squared. Example four:
Give this one a try on your own.
Start off with the quantity two x to the third power y to the zero power times the quantity 12y to the third power x to the twelfth power.
Pause the video and give it try.
Step one.
Zero product property
First multiply the constant terms.
2 and 12. Next, add the exponents of your common bases.
That's x to the three plus 12 power.
Finally add the exponents of the y's. That's y to the zero plus three.
Your final answer is twenty four x to the fifteenth power y to the third power.
zero product property example.
Zero product property formula
 WELCOME TO A LESSON ON THE ZERO PRODUCT PROPERTY. THE GOAL OF THIS article
IS TO USE THE ZERO PRODUCT PROPERTY TO SOLVE POLYNOMIAL EQUATIONS IN FACTORING FORM.
SO THE ZERO PRODUCT PROPERTY IS ONE OF THE MAIN REASONS WHY WE LEARN HOW TO FACTOR QUADRATIC EQUATIONS AND POLYNOMIAL EQUATIONS. THE ZERO PRODUCT PROPERTY STATES,
"IF TWO NUMBERS,
A AND B ARE MULTIPLIED TOGETHER "AND THE RESULTING PRODUCT IS ZERO,
THEN a minimum of one among THE NUMBERS MUST BE ZERO." SO IF A x B = 0 THEN EITHER a requirement = 0 OR B MUST = 0 OR BOTH A AND B ARE = TO 0.
AND WE CAN USE this concept to assist US SOLVE POLYNOMIAL EQUATIONS IN FACTORED FORM. IF we would like to unravel THE EQUATION X x the number X 3 = 0, BECAUSE THIS PRODUCT IS = TO 0 EITHER the primary FACTOR OF X MUST = 0 OR THE SECOND FACTOR OF X 3 MUST = 0.
SO we all know ONE SOLUTION IS X = 0. AND THE SECOND SOLUTION WE HAVE TO SOLVE THIS EQUATION FOR X SO WE'D ADD 3 TO BOTH SIDES OF THE EQUATION. SO  3 + 3 IS = TO 0.
SO OUR SECOND SOLUTION IS X = +3. AGAIN, WE HAVE TWO SOLUTIONS. X = 0 OR X = 3. OF COURSE, IF WE WANTED TO WE COULD CHECK THIS. TO CHECK X = 0 WE WOULD SUBSTITUTE 0 FOR X, WE WOULD HAVE 0 x THE QUANTITY 0  3. WELL,
THAT WOULD BE 0 x 3 WHICH = 0. THAT CHECKS. AND WHEN X IS = TO 3 WE'D SUBSTITUTE 3 FOR X, WE WOULD HAVE 3 x 3  3.
WELL, 3  3 IS = TO 0.
SO HERE WE WOULD HAVE 3 x 0,
WHICH ALSO = 0 AND THEREFORE CHECKS.
LET'S TAKE A LOOK AT SOME MORE EXAMPLES. IN THIS EQUATION WE HAVE 4 X x THE QUANTITY X + 5 = 0. AGAIN, BECAUSE THIS PRODUCT IS = TO 0 EITHER THE FIRST FACTOR OF 4 X MUST = 0 OR THE SECOND FACTOR OF X + 5 MUST = 0.
AND NOW WE NEED TO SOLVE EACH OF THESE EQUATIONS FOR X TO DETERMINE OUR SOLUTIONS. SO HERE TO ISOLATE X we might DIVIDE each side BY 4. SO THIS WOULD BE 1 X OR JUST X = 0 DIVIDED BY 4 IS 0. TO SOLVE THIS EQUATION FOR X WE WOULD SUBTRACT 5 ON BOTH SIDES +5  5 IS = TO 0.
SO WE HAVE X = 5. AGAIN, WE HAVE 2 SOLUTIONS, X = 0 OR X = 5. HERE WE HAVE THE QUANTITY X  2 x THE QUANTITY X + 7 = 0.
AGAIN,
BECAUSE THIS PRODUCT IS = TO 0 EITHER X  2 MUST = 0 OR X + 7 MUST = 0. AND NOW WE'LL SOLVE THESE EQUATIONS FOR X.
SO HERE WE ADD 2 TO BOTH SIDES OF THE EQUATION,  2 + 2 IS 0. SO WE'RE LEFT WITH X = +2 OR SOLVING THIS EQUATION FOR X WE WOULD SUBTRACT 7 ON BOTH SIDES OF THE EQUATION WHICH WOULD GIVE US X = 7.
SO THESE ARE THE 2 SOLUTIONS TO OUR POLYNOMIAL EQUATION IN FACTORED FORM.
SO HOPEFULLY NOW YOU'RE BEGINNING TO SEE WHY IT'S BENEFICIAL TO HAVE A POLYNOMIAL EQUATION IN FACTORED FORM. LET'S TAKE A LOOK AT TWO MORE EXAMPLES.
HERE WE HAVE THE QUANTITY 2 X + 3 x THE QUANTITY 5 X  1 = 0. SO EITHER THE FIRST FACTOR OF 2 X + 3 MUST = 0 OR THE SECOND FACTOR OF 5 X  1 MUST = 0. AND NOW WE'LL SOLVE THESE EQUATIONS FOR X.
SO HERE we might START BY SUBTRACTING 3 ON each side OF THE EQUATION.
THIS WOULD GIVE US 2 X = 3 AND THE LAST STEP HERE IS TO DIVIDE BOTH SIDES OF THE EQUATION BY 2. THIS WOULD BE 1 X OR X = 3 HALVES OR SOLVING THIS EQUATION FOR X WE WOULD START BY ADDING 1 TO BOTH SIDES OF THE EQUATION,
THIS WOULD BE 0.
SO IF 5 X EQUALS 1 AND DIVIDE BOTH SIDES BY 5. SO OUR SECOND SOLUTION IS X = 1/5th. LET'S TAKE A LOOK AT ONE MORE EXAMPLE.
NOTICE during this EQUATION we've 3 FACTORS THAT HAVE A PRODUCT OF ZERO.
SO IN THIS CASE WE'LL HAVE 3 SOLUTIONS EITHER X = 0FROM THIS FIRST FACTOR OR X  1 = 0 FROM THE SECOND FACTOR OR 6 X + 11 IS = TO 0.
AND NOW WE'LL SOLVE THESE FOR X. WELL, THE FIRST EQUATION IS ALREADY SOLVED FOR X. WE HAVE X = 0. THE SECOND EQUATION,
WE'LL ADD 1 TO BOTH SIDES. THIS WILL GIVE US THE SOLUTION X = +1. AND THEN FOR THE THIRD EQUATION WE HAVE A 2 STEP EQUATION SO WE'LL SUBTRACT 11 ON BOTH SIDES AND THEN DIVIDE BOTH SIDES BY 6. SO OUR THIRD SOLUTION IS X = 11/6. SO AS LONG AS we've OUR PRODUCT = TO 0 we will cash in OF THE ZERO PRODUCT PROPERTY to unravel THE POLYNOMIAL EQUATION.
SO BECAUSE OF THE ZERO PRODUCT PROPERTY WE WILL SPEND SOME TIME LEARNING HOW TO FACTOR A VARIETY OF POLYNOMIALS SO THAT WE CAN SOLVE POLYNOMIAL EQUATIONS. I HOPE YOU FOUND THIS HELPFUL
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