Addition, subtraction, multiplication and division of polynomials
Algebra in Maths is as important as the water required to a plant for the process of photosynthesis. Without it, nobody imagines getting a hold in advance maths and problems in science, accounts, economics, and technology. Here in this post, we are going to discuss polynomial. The contents of this post contain the Introduction of polynomial, addition, subtraction, multiplication, and division of the polynomial.
Polynomials are the algebraic expression in which the power of the variable is a whole number. Find out the degree of the following polynomials. The highest degree of the variable in a polynomial is known as the degree of the polynomial.
(a) 2 (b) x + 2 (c)x² + 1
(d)√x + 2 (e) x/2 + 2
Here in (a) power of 2 is 0, so it is a polynomial of the degree 0.
In (b) x + 2, the power of x is 1 so it is a polynomial of the degree 1.
In (c) x² + 1, the power of x is 2, so this is a polynomial of the degree 2.
(d) √x + 2 , is not a polynomial because √x = x½, degree of the polynomial is not a whole number.
(e) 1/x + 2, is not a polynomial because 1/x = x─1
degree of the polynomial is not a whole number.
Addition of the polynomial:
Ex. Add the following polynomials.
(3x² + 3x + 4) and (x² + 4x ─ 8)
(3x² + 3x + 4) + (x² + 4x ─ 8)
3x² + x² + 3x + 4x + 4 ─ 8
4x² + 7x ─4
Subtraction of the polynomials →
Ex.Subtract (x² + 4x ─ 8 ) from (3x² + 3x + 4)
(3x² + 3x + 4) ─ (x² + 4x ─ 8)
3x² + 3x + 4 ─ x² ─ 4x + 8
3x² ─ x² + 3x ─ 4x + 4 + 8
2x² ─ x + 12
Multiplication of the polynomial →
Ex: (x + 2)× (3x² – 2) = ?
= x(3x² – 2) +2(3x² – 2)
=3xᶾ – 2x + 6x² – 4
= 3xᶾ + 6x² – 2x – 4
Division of the polynomial →
Ex:(3xᶾ + 6x² – 2x – 4) ÷ (3x² – 2)
Therefore the quotient is x +2