Learn Online Polynomials

Learn polynomials in online very easy. Online polynomials are mathematical expression, which comprises of sum of terms each and every term including a single variable or more variables raised to the powers and it is multiplied by coefficients. A simple online polynomial has only one variable. Polynomials are of different types that is two, three, or more variables. A two-variable polynomial is called bi-variate and three-variable polynomial is called trivariate.


Learning problems on polynomials online:


Learn an Example For Factor Polynomial online:

Factorize 3x3 – 4x2 – 13x – 6.

Solution for factor polynomial:

Sum of the coefficients of all terms: 3 – 4 – 13 – 6 = 20 ≠ 0.

Therefore, learn (x – 1) is not a factor.

Sum of the coefficients of even degree terms = –4 – 6 = –10.

Sum of the coefficients of odd degree terms = 3 – 13 = –10.

Since they are equal (x + 1) is a factor.

By synthetic division,

-1   |      3    -4    -13     -6

|            -3     +7    +6

|____________________

3      -7     -6   | 0

|_____

Remainder is 0.

Therefore the online polynomials (x + 1) is a factor.

Factorizing the quotient,

3x2 – 7x – 6 = 3x2 – 9x + 2x – 6

= 3x (x–3) + 2 (x–3) = (x–3) (3x+2)

Therefore 3x3 – 4x2 – 13x – 6 = (x+1) (x–3) (3x+2)

I like to share this Inequalities Calculator with you all through my article.

Learn sample problems on polynomials online:


Example:

Find out the G.C.D. of the following online polynomials x3 – 9x2 + 23x – 15 and

4x2 – 16x + 12

Solution:

Let f(x) = x3 – 5x2 + 13x – 10 and g(x) = 4x2 – 16x + 12 = 4 (x2 – 4x + 3)



x-5

____________________

x2 – 4x + 3 |      x3 – 9x2 + 23x – 15

|      x3 – 4x2 + 3x

| ___________________

|          – 5x2 + 20x – 15

|          – 5x2 + 20x – 15

| ____________________

0

_____________________

G.C.D. = x2 – 4x + 3

Problem for factorization:

Determine the value of m and learn the factorization, if x + 1 is a factor of x3 + mx2 + 20x + 13

Solution:

Let P(x) = x3 + mx2 + 20x + 13

P(–1) = (–1)3 + m(–1)2 + 20(–1) + 13 = –8 + m

By learn factor theorem since the polynomial (x + 1) is a factor P(–1) = 0 or –8 + m = 0 or m=8