Polynomials Calculator

An Algebraic expression is of the form axn is called a monomial. The variable a is called the coefficient of xn and n, the degree of monomial. For example, 7x3 is monomial in x of degree 3 and 7 is the coefficient of x3. The combination of two monomials is called a binomial and the combination of three monomials is called a trinomial. For example, 2x3 + 3x is a binomial and 2x5 – 3x2 + 3 is trinomial. The sum of n number of monomials, where n is finite and x is called a polynomial in x.
Illustration to Polynomials:

Polynomial Calculator Example 1:

The polynomial calculator of the equation x2 + ax + b gives the remainder 18, when divided by x – 2 and leaves the polynomial calculator of remainder –2 when that is been divided by (x + 3).

Find the values of a and b.

Solution to the polynomial calculator:

P(x) = x2 + ax + b.

In tyh is polynomial calculator,

When x – 2 divides P(x) then the remainder is P (2).

∴P (2) = 4 + 2a + b.

But remainder = 18 ⇒ 4 + 2a + b = 18;

2a + b = 14 (1)

When (x + 3) divides P(x)

, the remainder is P (–3).     ∴ P (–3) = (–3)2 + a (–3) + b

= 9 – 3a + b.

But remainder = –2;      ∴ 9 – 3a + b = –2;

⇒ –3a + b = –11 (2)

(1) ⇒   2a + b = 14

(2) ⇒ –3a + b = –11 (subtracting)

5a        = 25

(Or) a     = 5

Substituting a = 5 in equation (1) we get

10 + b = 14; b = 4, ∴ a = 5, b = 4
Subtraction of Polynomials Calculator:

Example for Polynomials calculator:

Subtract        2x3 – 3x2 – 1 from x3 + 5x2 – 4x – 6.

Solution:

Using associative and distributive properties, we have

( x3 + 5x2 – 4x – 6) – (2x3 – 3x2 – 1) = x3 + 5x2 – 4x – 6 – 2x3 + 3x2 + 1

= x3 – 2x3 + 5x2 + 3x2 – 4x – 6 + 1

= (x3 – 2x3) + (5x2 + 3x2) + (–4x) + (–6+1)

= –x3 + 8x2 – 4x – 5.

The subtraction can also be performed in the following way:

Line (1): x3 + 5x2 – 4x – 6.

Line (2): 2x3 – 3x2 – 1.

Changing the signs of the polynomial in Line (2), we get

Line (3): –2x3 + 3x2 + 1.

Adding the polynomials in Line (1) and Line (3), we get

–x3 + 8x2 – 4x – 5.