explain polynomials of 10 standard
Answers
Step-by-step explanation:
Polynomial
An algebraic expression can have exponents that are rational numbers. However, a polynomial is an algebraic expression in which the exponent on any variable is a whole number.
5x3+3x+1 is an example of a polynomial. It is an algebraic expression as well
2x+3√x is an algebraic expression, but not a polynomial. – since the exponent on x is 1/2 which is not a whole number.
Degree of a Polynomial
For a polynomial in one variable – the highest exponent on the variable in a polynomial is the degree of the polynomial.
Example: The degree of the polynomial x2+2x+3 is 2, as the highest power of x in the given expression is x2.
TYPES OF POLYNOMIALS
Polynomials can be classified based on
a) Number of terms
b) Degree of the polynomial.
Types of polynomials based on the number of terms
a) Monomial – A polynomial with just one term. Example – 2x, 6x2, 9xy
b) Binomial – A polynomial with two terms. Example – 4x2+x, 5x+4
a) Trinomial – A polynomial with three terms. Example – x2+3x+4
Types of Polynomials based on Degree
Linear Polynomial
A polynomial whose degree is one is called a linear polynomial.
For example, 2x+1 is a linear polynomial.
Quadratic Polynomial
A polynomial of degree two is called a quadratic polynomial.
For example, 3x2+8x+5 is a quadratic polynomial.
Cubic Polynomial
A polynomial of degree three is called a cubic polynomial.
For example, 2x3+5x2+9x+15 is a cubic polynomial.
Graphical Representations
Representing Equations on a Graph
Any equation can be represented as a graph on the Cartesian plane, where each point on the graph represents the x and y coordinates of the point that satisfies the equation. An equation can be seen as a constraint placed on the x and y coordinates of a point, and any point that satisfies that constraint will lie on the curve
For example, the equation y = x, on a graph, will be a straight line that joins all the points which have their x coordinate equal to their y coordinate. Example – (1,1), (2,2) and so on.
Polynomials for class 10 -1
Visualization of a Polynomial
Geometrical Representation of a Linear Polynomial
The graph of a linear polynomial is a straight line. It cuts the X-axis at exactly one point.
Polynomials for class 10-2
Linear graph
Geometrical Representation of a Quadratic Polynomial
The graph of a quadratic polynomial is a parabola.
It looks like a U which either opens upwards or opens downwards depending on the value of a in ax2+bx+c.
If a is positive then parabola opens upwards and if a is negative then it opens downwards.
It can cut the x-axis at 0, 1 or two points.
Polynomials for class 10 -3
Graph of a polynomial which cuts the x-axis in two distinct points (a>0)
Polynomials for class 10 -4
Graph of a Quadratic polynomial which touches the x-axis at one point (a>0)
Polynomials for class 10 -5
Graph of a Quadratic polynomial that doesn’t touch the x-axis (a<0)