## 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 pmThanks so much! This really helped!

## Nagaraj Tirumani

Mar 3, 2014, 5:55 pmgood

## Nagaraj Tirumani

Mar 3, 2014, 6:09 pmThere 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 pmI hope my comments helps everyone to rethink once again logically.

## Diana Gaspar

Mar 3, 2014, 5:51 amI understand you more than my teacher xD thank you very much this helped me a lot .

## Tijs de Vries

Jul 7, 2014, 4:14 amthank you so much this really helped!!!!

## David Gerhold

Mar 3, 2015, 11:35 pmHelped a lot thank you.

## Alec Bertok

Mar 3, 2015, 8:31 pmgreat video it I am final starting to understand this problem

## opticrainbow

Apr 4, 2015, 6:53 amawesome video, thank you 🙂

## Kansas

Apr 4, 2015, 2:43 pmThanks 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 pmThis helped none… sorry man. I need help on this problem.3x^2 + 10x – 32

## wasup

Dec 12, 2015, 1:48 amthank you this really did help me a lot

## Ronnie Saini

Jan 1, 2016, 6:20 amAwesome. Works Everytime.

## the random brony

Feb 2, 2016, 2:44 ammy 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!

## ELPAdog

Feb 2, 2016, 6:17 amThanks 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 amThanks, 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 amthank you sir!!

## ThatoneBuescherfan37

Apr 4, 2016, 11:35 pmthank you

## ジョセフ・レイ

Jun 6, 2016, 10:46 amthank you so much, you saved my grade?

## Amin RanjbR

Dec 12, 2016, 7:58 pmThanks , it was helpful.

## Yoyo Mathew

Apr 4, 2017, 1:51 am#betterthanmyteacher

## Luis Torres

Jun 6, 2018, 5:57 pmAwesome

## Sequoia

Jul 7, 2018, 7:53 amWhat program do you use for writing?

## Kim Dracula

Feb 2, 2019, 6:13 amI love your videos… they are helping me get through my math class!