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- 1. SUBMITTED TO:- SUBMITTED BY:-VINOD PATIL KRISHNA GUPTASAMYAK JAINPRADHUM PATHAKClass:- 10th BSESSION: 2013-2014Subject :-Mathematics
- 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. 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. 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. 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. 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. 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. 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. 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. Function Of PolynomialFor 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. 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. 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. 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. 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. Write the polynomials in standard form and identify thepolynomial by degree and number of terms.23237 xx1.2. xx 231 2
- 16. 23237 xx23237 xx33x 22x 77231 23xx723 23xxThis is a 3rd degree, or cubic, trinomial.
- 17. xx 231 2xx 231 223x x2 1This is a 2nd degree, or quadratic, trinomial.

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