 | by Kenneth Chase | 24 comments

## The Zero-Product Property

– WELCOME TO A LESSON
ON THE ZERO PRODUCT PROPERTY. THE GOAL OF THIS VIDEO 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 AT LEAST ONE
OF THE NUMBERS MUST BE ZERO.” SO IF A x B=0 THEN EITHER
A MUST=0 OR B MUST=0 OR BOTH A AND B ARE=TO 0. AND WE CAN USE THIS IDEA TO HELP US SOLVE POLYNOMIAL
EQUATIONS IN FACTORED FORM. IF WE WANT TO SOLVE
THE EQUATION X x THE QUANTITY X -3=0, BECAUSE THIS PRODUCT IS=TO 0 EITHER THE FIRST FACTOR OF X
MUST=0 OR THE SECOND FACTOR
OF X -3 MUST=0. SO WE 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 WOULD
DIVIDE BOTH SIDES 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 WOULD START
BY SUBTRACTING 3 ON BOTH SIDES 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 IN THIS EQUATION
WE HAVE 3 FACTORS THAT HAVE A PRODUCT OF ZERO. SO IN THIS CASE WE’LL HAVE
3 SOLUTIONS EITHER X=0
FROM 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 HAVE
OUR PRODUCT=TO 0 WE CAN TAKE ADVANTAGE
OF THE ZERO PRODUCT PROPERTY TO SOLVE
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. #### Alanna Marie

May 5, 2013, 9:51 pm Reply

Thanks so much! This really helped! #### Nagaraj Tirumani

Mar 3, 2014, 5:55 pm Reply

good #### Nagaraj Tirumani

Mar 3, 2014, 6:09 pm Reply

There is one fallacy by multiplier zero:
5 x 0 = 0  and  5 x 0 =  5   Both are correct because one factor represents an entity or attribute while the other factor is only a multiplier.
There is a difference between an entity ( or attribute) and multiplier.
Universally 5 x 0 = 0 because in computer logic gate AND does not differentiate between entity (or attribute) and multiplier of entity.

Kindly  respond. #### Nagaraj Tirumani

Mar 3, 2014, 6:11 pm Reply

I hope my comments helps everyone to rethink once again logically. #### Diana Gaspar

Mar 3, 2014, 5:51 am Reply

I understand you more than my teacher xD thank you very much this helped me a lot . #### Tijs de Vries

Jul 7, 2014, 4:14 am Reply

thank you so much this really helped!!!! #### David Gerhold

Mar 3, 2015, 11:35 pm Reply

Helped a lot thank you. #### Alec Bertok

Mar 3, 2015, 8:31 pm Reply

great video it I am final starting to understand this problem #### opticrainbow

Apr 4, 2015, 6:53 am Reply

awesome video, thank you 🙂 #### Kansas

Apr 4, 2015, 2:43 pm Reply

Thanks for this video! It helped me understand this a lot! And it helped me pass a recent test #### Kael Abelon

Nov 11, 2015, 7:04 pm Reply

This helped none… sorry man. I need help on this problem.3x^2 + 10x – 32 #### wasup

Dec 12, 2015, 1:48 am Reply

thank you this really did help me a lot #### Ronnie Saini

Jan 1, 2016, 6:20 am Reply

Awesome. Works Everytime. #### the random brony

Feb 2, 2016, 2:44 am Reply

my God. this helped me So Much! I missed the lesson and didn't know what the hell everyone was talking about. Thank you SO MUCH! Feb 2, 2016, 6:17 am Reply

Thanks man! My teacher just started teaching a few months ago and really doesn't have the art of explaining mastered yet. #### CheeseMan

Mar 3, 2016, 1:32 am Reply

Thanks, This makes a TON more sense..
Its kinda funny that a video made in 2011 still helps people every week 😀 #### Samantha Sargent

Apr 4, 2016, 12:07 am Reply

thank you sir!! #### ThatoneBuescherfan37

Apr 4, 2016, 11:35 pm Reply

thank you #### ジョセフ・レイ

Jun 6, 2016, 10:46 am Reply

thank you so much, you saved my grade? #### Amin RanjbR

Dec 12, 2016, 7:58 pm Reply #### Yoyo Mathew

Apr 4, 2017, 1:51 am Reply

#betterthanmyteacher #### Luis Torres

Jun 6, 2018, 5:57 pm Reply

Awesome #### Sequoia

Jul 7, 2018, 7:53 am Reply

What program do you use for writing? #### Kim Dracula

Feb 2, 2019, 6:13 am Reply

I love your videos… they are helping me get through my math class!