Monomials and Polynomials

Introduction to monomial and polynomials:

Monomials

The monomial is a product of powers of variables, or formally any value obtained from 1 by finitely many multiplications by a variable. If only a single variable x is to be considered this means that any monomial is either 1 or a power xn of x, with n a positive integer.

Polynomials

In mathematics, a polynomials is an expression of the finite length constructed from variables (also known as indeterminate) and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents.(Source in Wikipedia ).

 

Problems in Monomials:

 

Solving Monomials Examples:

Example 1:

Simplify the lowest number and find out the GCF. (Using the Concept of monomials)

                    96y, 12x, -8y

Solution:

96y, 12x, -8y

Factor out the GCF of 4 from each term,

4(24y) + 4(3x) + 4(-2y)

            = 4(24y + 3x – 2y)

                  GCF = 4

 Example 2:

Solving Problems on multiplying the monomials. (Using the Concept of monomials):

  (2x2y)(3x4y2)

Solution:

Step 1: First Multiply the Coefficient first

  2 * 3 = 6

Step 2: Multiply the variable with the base of x. If the bases are same add exponent.

             (x2 * x4) à (x2+4=x6)

Step 3: Multiply the variable with the base of y. If the bases are same add exponent.

(y1 * y2) à (y1+2= y3)

      The Final answer is 6x6y3

I am planning to write more post on Regression Definition with example, math test 6th grade. Keep checking my blog.
 

Problems in polynomials

 

Solving Polynomials problems:

Example 1:

Simplify (7x2 – x – 5) + (x2 – 2x – 4) + (–2x2 + 3x + 6) (concept using Polynomials)

  (7x2 – x – 5) + (x2 – 2x – 4) + (–2x2 + 3x + 6)

After clearing the parentheses and then we want to group the like terms and simplify the given polynomial which is done on the basis of coefficients of the terms,

= 7x2 – x – 5 + x2 – 2x – 4 + –2x2 + 3x +6

        = 7x2 + 1x2 – 2x2 – 1x – 2x + 3x – 5 – 4 + 6

        = 8x2 – 2x2 – 3x + 3x – 9 +6

         = 6x2 – 3

 Example 2:

(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4) (concept using Polynomials)

 Solution:

Step 1: (3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4).

Step 2: It can be written as 3x3 + 3x2 – 4x + 5 + x3 – 2x2 + x – 4.

Step 3: now we need to simplify this, so.

Step 4: 3x3 + x3 + 3x2 – 2x2 – 4x + x + 5 – 4.

Step 5: So, the answer is 4x3 + 1x2 – 3x + 1.

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