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 is not 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 us see whether you are able
to figure out whether an expression is
a polynomial or not..
Go on to the next page..
10.
Let us now check out the degree of a
polynomial
11.
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
12.
The highest power of x or y or z in a
polynomial is called the degree of the
polynomial.
4x3 + 2x2 – 3x + 1
13.
Try to figure out 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..
14.
After having seen the 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
15.
Let us try to figure out the polynomial
types according to their
degrees….Ready?
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