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Polynomials1
This document discusses polynomials. It defines polynomials as expressions formed by adding or subtracting terms, where terms are coefficients multiplied by variables raised to powers. It provides examples of expressions that are and are not polynomials. It also discusses the degree of a polynomial, which is the highest power of the variable. Polynomials are classified based on their degree as constant, linear, quadratic, cubic, etc. The document shows how to identify the degree and type of different polynomials. It also introduces the concept of zeroes of a polynomial and how the number of zeroes relates to its degree.
Polynomials1
- 1. Lets start witha new topic today..
- 2. Take this expression 2x2– 3x + 5 Here 2x2 , 3x, 5 are called as ‘terms’. When we add or subtract terms, it is called a polynomial.
- 3. 2x2 – 3√x+ 5 Let us check on few expressions… 3y2 – 2y + 4 Is this a polynomial? Yes..it is a proper combo of y terms and number terms Is this a polynomial? No..it is not a polynomial as x is in roots 2x3 – 3 + 4 x Is this a polynomial? No..it is not a polynomial as x becomes x -1 when taken to the numerator.
- 4. So, what isnot a polynomial? Any polynomial expression with • Roots in the x terms, eg:- 5√x • Negative powers in the x term, eg:- x-2 • x term in the denominator, eg :- 1 x ARE “NOT POLYNOMIALS”
- 5. Now let ussee whether you are able to figure out whether an expression is a polynomial or not.. Go on to the next page..
- 6. Is this apolynomial? 3x – 2
- 7. Next one…Is thisa polynomial.. 2x2 – 3√x + 5
- 8. What about thisone? Is it a polynomial.. 1 x2 – 2x + 5
- 9. Check this out.. 4x3+ 2x2 – 3x + 1
- 11. Let us nowcheck out the degree of a polynomial
- 12. Check this expression 4x3+ 2x2 – 3x + 1 Can you see the powers of x ? 4x3 has the power of x as 3 2x2 has the power of x as 2 3x has the power of x as 1 Here The highest power of x is 3. Hence, 3 is the degree of the polynomial
- 13. The highest powerof x or y or z in a polynomial is called the degree of the polynomial. 4x3 + 2x2 – 3x + 1
- 14. Try to figureout the degrees of the polynomial… 3x + 1 2y2 – 2y + 7 5x3 – 3x2 + x – 1 9u3 – 2u4 + u2 – 1 Degree 1 Degree 3 Degree 2 Degree 3 What 3? No..See properly..The highest degree is 4..Just to check whether you are reading smart..
- 15. After having seenthe degrees of a polynomial, let us see how to classify them according to their degree 3x + 1 Constant Polynomial Linear Polynomial Quadratic Polynomial Cubic Polynomial Eg: - 7 8 3 – x2 4x3 + 2x - 1 If the degree of x is zero or if there is no x term, then it is a constant polynomial If the degree of x is 1, then it is a linear polynomial If the degree of x is 2, then it is a quadratic polynomial If the degree of x is 3, then it is a cubic polynomial
- 16. Let us tryto figure out the polynomial types according to their degrees….Ready?
- 17. Click the correctpolynomial type.. 3-x2
- 18. Click the correctpolynomial type.. 3-x2
- 19. Click the correctpolynomial type.. 3-x2
- 20. Click the correctpolynomial type.. 3-x2
- 21. Click the correctpolynomial type.. 3-x2
- 23. Click the correctpolynomial type.. √3x2 - 4/3x + ½
- 24. Click the correctpolynomial type.. 2/3u - 5/2
- 25. Click the correctpolynomial type.. 9/5x3 – 2x2 + 7/3x – 1/5
- 26. Click the correctpolynomial type.. 2y3 + 5y – 7
- 27. Click the correctpolynomial type.. -3/2
- 28. Click the correctpolynomial type.. 4x – 3
- 29. Click the correctpolynomial type.. 3y
- 30. Click the correctpolynomial type.. 4x – 3
- 31. Click the correctpolynomial type.. 3-x2
- 32. 3-x2 √3x2 - 4/3x+ ½ 2/3u - 5/2 9/5x3 – 2x2 + 7/3x – 1/5 2y4 + 3 2y3 + 5y – 7 3y 2y2 – 3 4x – 3 -3/2 Quadratic Quadratic Quadratic Linear Linear Linear Cubic Cubic Constant Bi quadratic
- 33. Linear polynomial 3x +2 ax + b Quadratic polynomial 3x2 + 2x + 5 ax2 + bx + c Cubic polynomial 2y3 + 3x2 + 4x + 5 ax3 + bx2 + cx + d
- 34. Graph of apolynomial
- 35. Y X Y’ X’ ax 2 +bx + c Zeroes of the polynomial Number of zeroes - 2
- 36. Find the numberof zeroes
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