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10 b krishna


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10 b krishna

  2. 2. Monomial: A number, a variable or the product of a number andone or more variables.Polynomial: A monomial or a sum of monomials.Binomial: A polynomial with exactly two terms.Trinomial: A polynomial with exactly three terms.Coefficient: A numerical factor in a term of an algebraicexpression.
  3. 3. Degree of a monomial: The sum of the exponents of all of thevariables in the monomial.Degree of a polynomial in one variable: The largest exponent ofthat variable.Standard form: When the terms of a polynomial are arrangedfrom the largest exponent to the smallest exponent in decreasingorder.
  4. 4. What is the degree of the monomial?245 bxThe degree of a monomial is the sum of the exponents ofthe variables in the monomial.The exponents of each variable are 4 and 2. 4+2 = 6.The degree of the monomial is 6.The monomial can be referred to as a sixth degreemonomial.
  5. 5. A polynomial is a monomial or the sum of monomials24x 83 3x 1425 2xxEach monomial in a polynomial is a term of the polynomial.The number factor of a term is called the coefficient.The coefficient of the first term in a polynomial is the leadcoefficient.A polynomial with two terms is called a binomial.A polynomial with three terms is called a trinomial.
  6. 6. A real number α is a zero of apolynomial f(x), if f(α) = 0.e.g. f(x) = x³ - 6x² +11x -6f(2) = 2³ -6 X 2² +11 X 2 – 6= 0 .Hence 2 is a zero of f(x).The number of zeroes of thepolynomial is the degree ofthe polynomial. Therefore aquadratic polynomial has 2zeroes and cubic 3 zeroes.
  7. 7. 14x83 3x1425 2xxThe degree of a polynomial in one variable is the largestexponent of that variable.2 A constant has no variable. It is a 0 degree polynomial.This is a 1st degree polynomial. 1st degree polynomials are linear.This is a 2nd degree polynomial. 2nd degreepolynomials are quadratic.This is a 3rd degree polynomial. 3rd degree polynomials arecubic.
  8. 8. Classify the polynomials by degree and number of terms.Polynomiala.b.c.d.542xxx2314 23xxDegreeClassify bydegreeClassify bynumber oftermsZero Constant MonomialFirst Linear BinomialSecond Quadratic BinomialThird Cubic Trinomial
  9. 9. To rewrite a polynomial in standard form, rearrangethe terms of the polynomial starting with the largestdegree term and ending with the lowest degree term.The leading coefficient, the coefficient of thefirst term in a polynomial written in standard form,should be positive.
  10. 10. Function Of PolynomialFor it to be a Polynomial Function theexponent has to be positive and whole.There are 2 forms. Standard Formwhere it’s all multiplied out. FactoredForm where it has parenthesis.
  11. 11. Degree- the highest power of x whenit’s in Standard Form.Leading Coefficient- the firstcoefficient when the polynomial is inStandard Form and in order. To find theleading coefficient you have to put thepolynomial in order by exponent, fromhighest to lowest.
  12. 12. The x-intercept of the graph and thezero of its function are opposites.If 2 of the factors are the same thenthere is only one x-intercept. 2 of thesame factors is called multiplicity.The number of x-intercepts can equal orbe less than the number of factors.Never more.
  13. 13. First degree polynomials have one set ofparenthesis.Second degree polynomials have twosets of parenthesis.Third degree polynomials have threesets of parenthesis.Fourth degree polynomials have foursets of parenthesis.
  14. 14. 745 24xxxx544x 2x 7Write the polynomials in standard form.2435572 xxxx32x4x 7x525x)7552(1 234xxxx32x4x 7x525xRemember: The leadcoefficient should bepositive in standardform.To do this, multiply thepolynomial by –1 usingthe distributiveproperty.
  15. 15. Write the polynomials in standard form and identify thepolynomial by degree and number of terms.23237 xx1.2. xx 231 2
  16. 16. 23237 xx23237 xx33x 22x 77231 23xx723 23xxThis is a 3rd degree, or cubic, trinomial.
  17. 17. xx 231 2xx 231 223x x2 1This is a 2nd degree, or quadratic, trinomial.