Upcoming SlideShare
×

Like this presentation? Why not share!

# Punnett squares presentation teachership academy

## on May 22, 2013

• 1,629 views

How to use Punnett Squares to multiply and factor polynomials

How to use Punnett Squares to multiply and factor polynomials

### Views

Total Views
1,629
Views on SlideShare
1,629
Embed Views
0

Likes
0
8
0

No embeds

### Report content

• Comment goes here.
Are you sure you want to

## Punnett squares presentation teachership academyPresentation Transcript

• Multiplying PolynomialsMade EasyPunnett Squares are often used in Biology tohelp explain Genetics. We can use them inAlgebra to help explain multiplying polynomials.
• What are “Punnett Squares”?They are nothing more than large grids.You can use them to input any informationthat needs to be multiplied together.Let’s have somefun seeing howPunnettSquares canhelp us learnAlgebra.
• (x + 3) (x + 2)xx+2x22x3x6Answer: x2 + 2x + 3x + 6 = x2 + 5x + 6+3Let’s start with thefollowing problem.Multiply:Multiply row by column.
• (x + 2) (x2 + 2x + 3)x +2x2+2x+3x32x23x2x24x6Answer: x3 + 4x2 + 7x + 6Let’s try anotherproblem. Multiplyrow by column
• Now that we have seen howPunnett Squares can help uslearn to multiply polynomials,let’s get to work!
• Punnett SquaresPart 2Using them tofactor trinomialsWe can use Punnett Squares to factortrinomials very easily. Let’s take a tripdown Algebra Road to success!x22x3x6
• Now that we knowhow to use PunnettSquares to multiplypolynomials, let’s seeif we can use them tofactor trinomials.X2 + 5x + 6X262x3x???????How did that happen?
• The first step is tomake sure thetrinomial is indescending order.X2 + 5x + 6Seconddegree FirstdegreeConstantThis trinomialis already inthe properorder.
• X2 + 5x + 6The next step is to checkfor a common factor thatcan be factored out. Whatare the coefficents of eachterm?156Is there a numbercommon to all threethat can be dividedout? Not on thisparticular polynomial.
• X2 + 5x + 6We’re ready to begin!x26Now we’re readyto figure out themiddle terms.
• First we multiply thecoefficient of the x2term and the constanttogether.X2 + 5x + 61(6) = 6x26This sign tells usthe factors arethe same signThis signtells us bothfactors arepositiveNow we check thesigns, looking at thesecond sign first,then at the first sign.
• x2 + 5x + 6Now we need to determinethe factors of 6 because wewill add them together toequal the x term.x261 * 6 = 62 * 3 = 61 + 6 = 72 + 3 = 5There’s our answer! 2x and 3xwill fill our Punnett Square.2x3x
• x262x3xFirst let’s look atcolumns for commonfactors. Remember,the sign on the x termis the sign for thatfactor.x +3In the first column, x is commonto both terms. In the secondcolumn, positive 3 is common toboth terms.We have foundour first factor!It is(x + 3)
• x22x3x6x +3Now let’s look at rows.Remember, the sign onthe x term is the signfor that factorIn the first row, x is common toboth terms. In the second row,positive 2 is common to bothterms.x+2We have found oursecond factor! It is(x + 2)
• Finally, it’s time toput it all together!The trinomial x262x3xx +3x+2X2 + 5x + 6Factors as(x + 3) (x + 2)
• Factoring Trinomialswith aLeading CoefficientOther Than 1We can use Punnett Squares tofactor trinomials with a leadingcoefficient other than one. It’sreally easy!
• The first step is tomake sure thetrinomial is indescending order.8x2 - 2x - 3Seconddegree FirstdegreeConstantThis trinomialis already inthe properorder.
• 8x2 - 2x - 3The next step is to checkfor a common factor thatcan be factored out. Whatare the coefficents of eachterm?823Is there a numbercommon to all threethat can be dividedout? Not on thisparticular polynomial.
• 8x2 - 2x - 3We’re ready to begin!8x2-3Now we’re readyto figure out themiddle terms.
• First we multiply thecoefficient of the x2term and the constanttogether.8x2 - 2x - 38(3) = 248x2-3This sign tells usthe factors aredifferent signsThis signtells us thelarger factoris negativeNow we check thesigns, looking at thesecond sign first,then at the first sign.
• 8x2 -2x - 3Now we need to determinethe factors of 24 because wewill find the difference toequal the x term.8x2-31 * 24 = 242 * 12 = 243 * 8 = 244 * 6 = 241 - 24 = -23 24 – 1 = 232 – 12 = -10 12 – 2 = 103 – 8 = -5 8 – 3 = -54 - 6 = -2 6 – 4 = 2There’s our answer! -6x and4x will fill our Punnett Square.4x-6x
• 8x2-34x-6xFirst let’s look atcolumns for commonfactors. Remember,the sign on the x termis the sign for thatfactor.4x -3In the first column, 4x iscommon to both terms. In thesecond column, negative 3 iscommon to both terms.We have foundour first factor!It is(4x - 3)
• 8x24x-6x-34x -3Now let’s look at rows.Remember, the sign onthe x term is the signfor that factorIn the first row, 2x is commonto both terms. In the secondrow, positive 1 is common toboth terms.2x+1We have found oursecond factor! It is(2x + 1)
• Finally, it’s time toput it all together!The trinomial 8x2-34x-6x4x -3x+18x2 - 2x - 3Factors as(4x - 3) (2x + 1)
• Remember, Punnett Squares are an easy way tomultiply and factor polynomials, but they are not theonly way. If you have already learned to do thesetasks with other methods and can use thosemethods successfully, you may prefer to stick withthe “tried and true”. Even if you prefer to do that,give Punnett Squares a chance. They might justmake the job easier!Success!