Class 10 Maths Polynomials | Polynomials |

**Polynomials**

The deal in the family is that, if Rosy gets x marks in her exam, her brother will give her 2x chocolates, her mother promised to give her x^{2} chocolates, her dad promised to give her x^{3} chocolates? How many chocolates will get?

Number of Chocolates Rosy will get, if she scored x marks is p(x) = 2x + x^{2} + x^{3}

Number of Chocolates Rosy will get, if she scored 1 mark is p(1) = 2*1 + 1^{2} + 1^{3} = 4

Number of Chocolates Rosy will get, if she scored 2 mark is p(2) = 2*2 + 2^{2} + 2^{3} = 16

Number of Chocolates Rosy will get, if she scored 3 mark is p(3) = 2*3 + 3^{2} + 3^{3} = 42

The general expression p(x) = 2x + x^{2} + x^{3} is a polynomial.

Use of Polynomial in day to day life: We come across polynomial when we have to find area of a figure with variable dimensions. Also the formula to calculate compound interest on your money deposited in bank is a polynomial. It is also used in Physics, Chemistry & other field of science. Distance travelled by a ball on throw or bullet on fire can be calculated using a polynomial formula, S= ut + ½ at^{2 }

What we already know:

- Polynomials in one variable and their degrees. E.g. p(x)=3x
^{2}+4x + 2 - If p(x) is a polynomial in x, highest power of x in p(x) is called degree of p(x). g. for polynomial p(x)= 3x
^{2}+4x + 2, highest power is 2, & thus degree is 2. - A polynomial of degree 1 is called a linear polynomial. E.g. p(x)=3x +4
- A polynomial of degree 2 is called a quadratic polynomial E.g. p(x)=3x
^{2}+4 - A quadratic polynomial in x with real coefficients is of the form ax
^{2}+ bx + c, where a, b, are real numbers with a ≠ 0. - A polynomial of degree 3 is called a cubic polynomial. E.g. p(x)=3x
^{3}+4 - If p(x) is a polynomial in x, and if k is any real number, then the value obtained by replacing x by k in p(x), is called the value of p(x) at x = k, and is denoted by p(k).g. p(x)=3x +4 , p(2) = 3*2 + 4 = 10.
- A real number k is said to be a zero of a polynomial p(x), if p(k) = 0. g. p(x) =x
^{3}-27, p(3)=0, thus 3 is said to be Zero of polynomial . p(x)=x^{3}-27

.