# Polynomials

Poonam SinghG.L.T S.B.M
1 von 31

Algebraic expressions von
Algebraic expressionsOrlando Calderon
43.6K views16 Folien
Polynomials von
PolynomialsVer Louie Gautani
24.6K views33 Folien
Algebraic expressions von
Algebraic expressionsChristie Harp
42.7K views20 Folien
POLYNOMIALS von
6.9K views50 Folien
Relations and functions von
Relations and functions Leslie Amoguis
54.4K views79 Folien
Multiplying polynomials von
Multiplying polynomialschrystal_brinson
9.9K views18 Folien

## Was ist angesagt?

2.2K views13 Folien
Solving systems of Linear Equations von
Solving systems of Linear Equationsswartzje
30.4K views33 Folien
Slope of a Line von
Slope of a Linekaren wagoner
8.2K views23 Folien
Introduction to Function, Domain and Range - Mohd Noor von
Introduction to Function, Domain and Range - Mohd Noor Mohd. Noor Abdul Hamid
11.2K views24 Folien
Linear Equations in Two Variables von
Linear Equations in Two Variablessheisirenebkm
15.6K views14 Folien
Real Numbers von
Real NumbersKavya Singhal
54K views19 Folien

### Was ist angesagt?(20)

Albert Go2.2K views
Solving systems of Linear Equations von swartzje
Solving systems of Linear Equations
swartzje30.4K views
Introduction to Function, Domain and Range - Mohd Noor von Mohd. Noor Abdul Hamid
Introduction to Function, Domain and Range - Mohd Noor
Linear Equations in Two Variables von sheisirenebkm
Linear Equations in Two Variables
sheisirenebkm15.6K views
Brian Mary11.3K views
Linear equations in two variables von Vinisha Pathak
Linear equations in two variables
Vinisha Pathak7.2K views
Factoring Polynomials von itutor
Factoring Polynomials
itutor24.9K views
Algebraic expressions and terms von panchmahal
Algebraic expressions and terms
panchmahal11.4K views
Rational algebraic expressions von myla gambalan
Rational algebraic expressions
myla gambalan2.9K views
Laws Of Exponents von Phil Saraspe
Laws Of Exponents
Phil Saraspe178.1K views
Factoring Trinomials von Don Simmons
Factoring Trinomials
Don Simmons7.4K views
Algebraic expressions and identities von Deepansha Singh
Algebraic expressions and identities
Deepansha Singh47.2K views
Evaluating Algebraic Expressions von bizarregirl
Evaluating Algebraic Expressions
bizarregirl41.3K views

WATER CRISIS “Prediction of 3rd world war” von
WATER CRISIS “Prediction of 3rd world war”Poonam Singh
3K views35 Folien
Diabetes von
DiabetesPoonam Singh
2.7K views28 Folien
Polynomials von
Polynomialspartikpures3
107.1K views10 Folien
Polynomials And Linear Equation of Two Variables von
Polynomials And Linear Equation of Two VariablesAnkur Patel
27.3K views47 Folien
Polynomials von
25.9K views18 Folien
Polynomial  von
Polynomial anushkachdcity
2.5K views17 Folien

WATER CRISIS “Prediction of 3rd world war” von Poonam Singh
WATER CRISIS “Prediction of 3rd world war”
Poonam Singh3K views
Polynomials And Linear Equation of Two Variables von Ankur Patel
Polynomials And Linear Equation of Two Variables
Ankur Patel27.3K views
Quiz acc ppt akhil bhartiya vidya sansthan samarth shiksha samiti von gltsbm bal mandir
Quiz acc ppt akhil bhartiya vidya sansthan samarth shiksha samiti
gltsbm bal mandir474 views
Maths polynomials von avimehta14
Maths polynomials
avimehta143.9K views
Polynomials CLASS 10 von Nihas Nichu
Polynomials CLASS 10
Nihas Nichu25.4K views
Ani agustina (a1 c011007) polynomial von Ani_Agustina
Ani agustina (a1 c011007) polynomial
Ani_Agustina2.2K views
6.4 binomials containing radicals von andreagoings
andreagoings277 views
12 x1 t08 02 general binomial expansions (2012) von Nigel Simmons
12 x1 t08 02 general binomial expansions (2012)
Nigel Simmons1.1K views
CIS Anaesthesia Software von steensgaard
CIS Anaesthesia Software
steensgaard537 views

## Similar a Polynomials

3. Polynomials von
3. PolynomialsKanchan Gupta
49 views15 Folien
Algebra and functions review von
Algebra and functions reviewInstitute of Applied Technology
315 views30 Folien
Algebra and functions review von
Algebra and functions reviewInstitute of Applied Technology
807 views30 Folien
Algebra and functions review von
Algebra and functions reviewInstitute of Applied Technology
615 views30 Folien
ALGEBRA (3).pptx von
ALGEBRA (3).pptxThangathilakaManju1
12 views29 Folien
1.8K views18 Folien

### Similar a Polynomials(20)

Hari narayan class 9-a von Kartik Kumar
Hari narayan class 9-a
Kartik Kumar829 views
Polinomials in cd von Adi Sharma
Polinomials in cd
polynomial von 9420476359
polynomial
9420476359748 views
Maths portfolio manvi von Manvigangwar
Maths portfolio manvi
Manvigangwar26.8K views
5.4 long division von leblance
5.4 long division
leblance1.6K views
Equations Complex Numbers Quadratic Expressions Inequalities Absolute Value E... von Telenor
Equations Complex Numbers Quadratic Expressions Inequalities Absolute Value E...
Telenor1.8K views

## Más de Poonam Singh

627 views32 Folien
old age von
old agePoonam Singh
19.3K views30 Folien
Chemistry von
ChemistryPoonam Singh
497 views25 Folien
Diabetes mellitus von
Diabetes mellitusPoonam Singh
507 views28 Folien
Issue of Shares von
Issue of SharesPoonam Singh
37.4K views37 Folien
My experience my values 7th von
My experience my values 7thPoonam Singh
477 views42 Folien

## Último

Create a Structure in VBNet.pptx von
Create a Structure in VBNet.pptxBreach_P
70 views8 Folien
Dance KS5 Breakdown von
Dance KS5 BreakdownWestHatch
68 views2 Folien
Narration lesson plan.docx von
Narration lesson plan.docxTARIQ KHAN
104 views11 Folien
The Open Access Community Framework (OACF) 2023 (1).pptx von
The Open Access Community Framework (OACF) 2023 (1).pptxJisc
85 views7 Folien
Are we onboard yet University of Sussex.pptx von
Are we onboard yet University of Sussex.pptxJisc
77 views7 Folien
11.28.23 Social Capital and Social Exclusion.pptx von
11.28.23 Social Capital and Social Exclusion.pptxmary850239
281 views25 Folien

### Último(20)

Create a Structure in VBNet.pptx von Breach_P
Create a Structure in VBNet.pptx
Breach_P70 views
Dance KS5 Breakdown von WestHatch
Dance KS5 Breakdown
WestHatch68 views
Narration lesson plan.docx von TARIQ KHAN
Narration lesson plan.docx
TARIQ KHAN104 views
The Open Access Community Framework (OACF) 2023 (1).pptx von Jisc
The Open Access Community Framework (OACF) 2023 (1).pptx
Jisc85 views
Are we onboard yet University of Sussex.pptx von Jisc
Are we onboard yet University of Sussex.pptx
Jisc77 views
11.28.23 Social Capital and Social Exclusion.pptx von mary850239
11.28.23 Social Capital and Social Exclusion.pptx
mary850239281 views
Class 10 English notes 23-24.pptx von TARIQ KHAN
Class 10 English notes 23-24.pptx
TARIQ KHAN107 views
Classification of crude drugs.pptx von GayatriPatra14
Classification of crude drugs.pptx
GayatriPatra1477 views
The basics - information, data, technology and systems.pdf von JonathanCovena1
The basics - information, data, technology and systems.pdf
JonathanCovena188 views
Use of Probiotics in Aquaculture.pptx von AKSHAY MANDAL
Use of Probiotics in Aquaculture.pptx
AKSHAY MANDAL89 views
Solar System and Galaxies.pptx von DrHafizKosar
Solar System and Galaxies.pptx
DrHafizKosar85 views
The Accursed House by Émile Gaboriau von DivyaSheta
The Accursed House by Émile Gaboriau
DivyaSheta158 views
11.30.23 Poverty and Inequality in America.pptx von mary850239
11.30.23 Poverty and Inequality in America.pptx
mary850239144 views
7 NOVEL DRUG DELIVERY SYSTEM.pptx von Sachin Nitave
7 NOVEL DRUG DELIVERY SYSTEM.pptx
Sachin Nitave58 views
ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively von PECB
ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively
PECB 545 views

### Polynomials

• 2. Table Of Contents - • Introduction • History 1. History Of Notation • Terms • Types Of Polynomials • Uses • Zeroes Of Polynomial • Degree • Graphs Of Polynomial Function • Table • Algebraic Identities • Arithmetic Of Polynomials • Think Tanker ? ?
• 3. Introduction….. ~ What Is a Polynomial ?? In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer-exponents. Example : x2 − 3x + 6, which is a quadratic polynomial.
• 4. History Of Notation • He popularized the use of letters from the beginning of the alphabet to denote constants and letters from the end of the alphabet to denote variables. • As can be seen above, in the general formula for a polynomial in one variable, where the a's denote constants and x denotes a variable. • Descartes introduced the use of superscripts to denote exponents as well.
• 6. Types Of Polynomials... Monomial In mathematics, A monomial is a polynomial with just one term. For Example: 3x,4xy is a monomial. Binomial In algebra, A binomial is a polynomial, which is the sum of two monomials. For Example: 2x+5 is a Binomial. Trinomial In elementary algebra, A trinomial is a polynomial consisting of three terms or monomials. For Example : 3x+5y+7z is a Trinomial.
• 8. Uses... • Polynomials appear in a wide variety of areas of mathematics and science. ~ For example, they are used to form “Polynomial” equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences. • They are used to define “Polynomial Functions”, which appear in settings ranging from basic chemistry and physics to economics and social science. • They are used in calculus and numerical analysis to approximate other functions.
• 9. Zeroes Of Polynomial • Consider the polynomial p(x) = 5x3 – 2x3+ 3x – 2. If we replace x by 1 everywhere in p(x), we get p(1) = 5 × (1)3 – 2 × (1)2 + 3 × (1) – 2 = 5 – 2 + 3 –2 = 4 So, we say that the value of p(x) at x = 1 is 4. Similarly, p(0) = 5(0)3 – 2(0)2 + 3(0) –2 = –2
• 10. Degree • The degree of a polynomial is the highest degree of its terms, when the polynomial is expressed in canonical form (i.e., as a linear combination of monomials). The degree of a term is the sum of the exponents of the variables that appear in it.
• 11. DEGREE OF POLYNOMIAL • Degree 0 – constant • Degree 1 – linear • Degree 2 – quadratic • Degree 3 – cubic • Degree 4 – quartic (or, less commonly, biquadratic)
• 13. Look at each term, whoever has the most letters wins! x2 – 4x4 + x6 This is a 8th degree polynomial: xy4 + x4y4 + 12 This guy has 6 letters… The degree is 6. This guy has 8 letters… The degree is 8 Here’s how you find the degree of a polynomial :
• 14. The graph of the zero polynomial f(x) = 0 is the x-axis. Graphs Of Polynomial Functions ..
• 15. The graph of the polynomial of degree 2 Graphs Of Polynomial Functions ..
• 16. Table Polynomial Degree Name Using Degree Nos. Of Terms Name Using Nos Of Terms 4 0 Constant 1 Monomial 3x+6 1 Linear 2 Binomial 3x2+2x+1 2 Quadratic 3 Trinomial 2x3 3 Cubic 1 Monomial 6x4 + 3x 4 Biquadratic 2 Binomial
• 17. Algebraic Identities (a + b ) 2 = a 2 + b 2 + 2 ab (a - b ) 2 = a 2 + b 2 - 2 ab (a 2 - b 2 )= (a + b)(a - b) (x - a)(x - b )= x2 +(a+b)x - ab
• 18. Arithmetic Of Polynomials • Addition ( + ) • Subtraction( - ) • Division ( / )
• 19. Addition Of Polynomials….. • Polynomials can be added using the associative law of addition (grouping all their terms together into a single sum), possibly followed by reordering, and combining of like terms. For example, if Method 1: Line up like terms. Then add the coefficients. P = 3x + 7 Q = 2x + 3 P + Q = 5x + 10
• 20. Addition Of Polynomials….. Method 2 : Group like terms. Then add the coefficients. 4x2 + 6x + 7 + 2x2 – 9x + 1 = (4x2 + 2x2)+(6x – 9x)+ (7+1) = 6x2 – 3x + 8 » The sum of two polynomials is also a polynomial.
• 21. Subtraction Of Polynomials • Earlier you learned that subtraction means to add the opposite. So when you subtract a polynomial, change the signs of each of the terms to its opposite. Then add the coefficients. Method 1: Line up like terms. Change the signs of the second polynomial, then add. For Example: 4x - 7 4x - 7 -(2x + 3)  -2x – 3 2x - 10
• 22. Subtraction Of Polynomials Method 2: Simplify: (5x2 – 3x) – (-8x2 + 11) Write the opposite of each term : 5x2 – 3x + 8x2 – 11 Group like terms : (5x2 + 8x2) + (3x + 0) + (-11 + 0) = 13x2 + 3x – 11 »The difference of two polynomials is also a polynomial
• 23. Division Of Polynomials • The Methods Used For Finding Divison Of Polynomials Are: 1. Long Division Method 2. Factor Theorem
• 24. Long- Division Method • In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand. • It breaks down a division problem into a series of easier steps. • As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. Dividend = (Divisor × Quotient) + Remainder
• 25. Long- Division Method Dividend = (Divisor × Quotient) + Remainder
• 26. Factorisation • Factor Theorem : If p(x) is a polynomial of degree n > 1 and a is any real number, Then : (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x).
• 28. Q.1 What is the simplified form of : 2x-3x+2?? A. -x+2 B. -5x+2 C. -10x+2 D. -2x+2
• 29. Q.2 What is the value of x when x+3=10 ?? A. 7 B. 4 C. 2 D. 9
• 30. Q 3. Solve 2x+4=108 ?? A. 32 B. 56 C. 52 D. 23
Aktuelle SpracheEnglish
Español
Portugues
Français
Deutsche