• services@thehomeworkhelp.co.uk
Call Us Now: 8185279935
Call Us Now: 8185279935
Homework Help
Homework Help
Homework Help
View Details
Homework Help
Assignment Help
Homework Help
Assignment Help
View Details
Assignment Help
Online Tutoring
Online Tutoring
Online Tutoring
View Details
Online Tutoring
Home » Math Homework Help » Algebra Homework Help » Rational, Integral Polynomial
Rational, Integral Polynomial
An expression of the form ƒ(x) = a0xn + a1xn-1 + …. + an-1 + an, where (i) a0, a1, …., an are constants, real or imaginary, (ii) x is a variable, and (iii) n is a positive integer, is called a rational integral function of x or a polynomial in x. If the coefficients a0, a1, a2, …., an are real number then the equation is called an equation with real coefficients.

Coefficients: The constants a0, a1, ….., an are called the coefficients of the polynomial of ƒ(x).

Degree of polynomial:
If a0 ≠ 0, then the polynomial ƒ(x) is of degree n, i.e. it is the highest power of the variable x in the polynomial.

Identically vanishing polynomial: A polynomial all of whose coefficients are equal to zero is called an identically vanishing polynomial and is represented by 0, i.e. the polynomial a0xn + a1xn-1 + …. + an will be an identically vanishing polynomial if ai = 0, ∀ 1 ≤ i ≤ n.

Note 1:
No degree is assigned to an identically vanishing polynomial.

Note 2: Constants (other than zero) are polynomial of degree zero.

Equality of polynomials: Two polynomials ƒ(x) = a0xn + a1xn-1 + …. + an, a0 ≠ 0 and g(x) = b0xm + b1xm-1 + …. + bm b0 ≠ 0, are said to be equal if
   
(i) They are of the same degree, i.e. m = n.
   
(ii) Their corresponding coefficients are equal, i.e. ai = bi, ∀ 1 ≤ i ≤ m.

Equation: If two different polynomials in the same variable x become equal for some values of x or a polynomial is equated to zero, then such a relation is called an equation, i.e. the polynomial  ƒ(x) = a0xn + a1xn-1 + …. + an, a0 ≠ 0, will be an equation if ƒ(x) = a0xn + a1xn-1 + …. + an, a0 = 0, for some values of x.

Degree of an equation: The degree of an equation is the highest power of the variable in the equation, when it is expressed as a rational and integral function of the variable.

For example, consider the following equations:



(ii) x-3/2 + 4x2 = 3x1/2

The equation (i) when expressed in rational and integral form is 6x8 + 5x6 + 6x5 + 6x2 + 1 = 0 and thus its degree is 8 and the equation (ii) when expressed in rational integral form is of degree 3 for

9x3 – 6x2 + x – 16 = 0.

Note 3:
The equation of degree two, three and four are called quadratic, cubic and biquadratic respectively.

Services: -
Rational, Integral Polynomial Homework | Rational, Integral Polynomial Homework Help | Rational, Integral Polynomial Homework Help Services | Live Rational, Integral Polynomial Homework Help | Rational, Integral Polynomial Homework Tutors | Online Rational, Integral Polynomial Homework Help | Rational, Integral Polynomial Tutors | Online Rational, Integral Polynomial Tutors | Rational, Integral Polynomial Homework Services | Rational, Integral Polynomial

Submit Your Query ???
Topics
Real Number Absolute Value Addition Of Matrices Square Matrix Adjoint Algebraic Structures Alternating Series Linear Equations Determinants Archimedean Real Numbers Binary Operation Binary Relation In A Set Bounded, Unbounded Sets Cauchy Root Test Caylay Hamiltion Theorem Circular Permutation Common Roots Complex Numbers Complex Number Conjugate Conjugate Of A Matrix Constant Sequences Convergence Of A Sequence Cosets Cubic, Biquadratic Equations De Moivre Theorem Real Number Denseness Order 3 Determinants Differences Of Matrices Direct Sum Of Vector Subspaces Eigen Vector Elementary Matrices Matrix Elem. Transformations Equal Matrices Equal Roots Two Permutations Equity Equivalent Matrices Trigonometry Function Expansion Field Function Algebra Fundamental Theorem Gaussian Integer Geometric Series Group Ideals Quantity Increasing Roots Infinite Series Convergent Integers Inverse Of Square Matrix Inverses Of Elementary Matrices Iota, Imaginary Numbers Left-Right Identity Sequence Limit Points Linear Combination Vectors Span Linear Dependence, Independence Linear Homogeneous Equations Two Subspaces Linear Sum Matric Polynomial Matrix Linear Equation Matrix Inverse Matrix Multiplication Matrix Scalar Multiplication Method Of Difference Minors And Co-factors Multiplication Modulo P Normal Sub-Group Normalizer Or Centalizer Orbit Of Permutation Peano Axioms Permutation Function Pigeon Hole Principle Matrices Integral Powers Mathematical Induction Principal Two Determinants Product Two Permutations Product Properties Of Modulus Rank Of A Matrix Rational Numbers Rational, Integral Polynomial Reciprocal Roots Relation Of Sets Rings Of A Set Row By Column Matrix Sequence Series Series Of Positive Terms Series Partial Sum Sequence Subrings Sum Of A Series Cosine Series Sum Sum Of Sine Series Symmetric/Skew Symm. Matrices Roots Symmetric Functions Symmetric Set Degree N Synthetic Division Transformation In General Transformations Of Equations Transpose Of A Matrix Matrix Transposed Conjugate Transposition Complex Numbers Representation Vector Space Vector Sub-spaces Whole Numbers

 

To book a free session write to:- tutoring@thehomeworkhelp.co.uk or call 8185279935