Introduction to dividing polynomials with exponents:
Dividing polynomials with exponents is nothing but if the polynomials are having the degree we have to expand the polynomials and we have to divide the polynomials. Normally polynomials mean we are having power more than one. We will see some example problems for dividing polynomials. It is better to understand the division of polynomials with exponents. We can use the basic algebraic formulas and using the factorization method we can divide the polynomials.I like to share this Divide Exponents with you all through my article.
Examples for Dividing Polynomials with Exponents:
Example 1: Divide the following polynomials: `((x^2 + 3x + 2)^2) / ((x^2 - 4)^2)`
Solution:
The given polynomials are `((x^2 + 3x + 2)^2) / ((x^2 - 4)^2)`
Here the exponents of the polynomials are 2.
First we have to find the factors of the polynomials of the numerator.
x2 + 3x + 2 = x2 + 2x + x + 2 = x (x + 2) + (x + 2) = (x + 2) (x + 1)
Next we have to find the factors of the denominators.
x2 – 4 = x2 – 22 = (x +2) (x – 2)
Now we have to plug the values.
= ` (((x + 2) (x + 1))^2) / (((x + 2) (x - 2))^2)`
= `((x + 2)^2 (x + 1)^2) / ((x + 2)^2 (x - 2)^2)`
From this we get `(x + 1)^2 / (x - 2)^2`
Example 2: Divide the following polynomials: `((x^2 - 5x + 4)^2) / (x^2 - 1)`
Solution:
The given polynomials are `((x^2 - 5x + 4)^2) / (x^2 - 1)`
Here the exponents of the polynomials in numerator are 2 and the denominator exponents is 1.
First we have to find the factors of the polynomials of the numerator.
x2 – 5x + 4 = x2 - 4x - x + 4 = x (x - 4) - (x - 4) = (x - 4) (x - 1)
Next we have to find the factors of the denominators.
x2 – 1 = x2 – 12 = (x +1) (x - 1)
Now we have to plug the values.
` = (((x - 4) (x - 1))^2) / ((x +1) (x - 1))`
`= ((x - 4)^2 (x - 1)^2) / ((x + 1) (x - 1))`
From this we get `((x - 4)^2(x - 1)) / (x + 1)^2`
These are some of the examples for dividing polynomials with exponents. First we have to expand the polynomials and we have to divide.
Dividing polynomials with exponents is nothing but if the polynomials are having the degree we have to expand the polynomials and we have to divide the polynomials. Normally polynomials mean we are having power more than one. We will see some example problems for dividing polynomials. It is better to understand the division of polynomials with exponents. We can use the basic algebraic formulas and using the factorization method we can divide the polynomials.I like to share this Divide Exponents with you all through my article.
Examples for Dividing Polynomials with Exponents:
Example 1: Divide the following polynomials: `((x^2 + 3x + 2)^2) / ((x^2 - 4)^2)`
Solution:
The given polynomials are `((x^2 + 3x + 2)^2) / ((x^2 - 4)^2)`
Here the exponents of the polynomials are 2.
First we have to find the factors of the polynomials of the numerator.
x2 + 3x + 2 = x2 + 2x + x + 2 = x (x + 2) + (x + 2) = (x + 2) (x + 1)
Next we have to find the factors of the denominators.
x2 – 4 = x2 – 22 = (x +2) (x – 2)
Now we have to plug the values.
= ` (((x + 2) (x + 1))^2) / (((x + 2) (x - 2))^2)`
= `((x + 2)^2 (x + 1)^2) / ((x + 2)^2 (x - 2)^2)`
From this we get `(x + 1)^2 / (x - 2)^2`
Example 2: Divide the following polynomials: `((x^2 - 5x + 4)^2) / (x^2 - 1)`
Solution:
The given polynomials are `((x^2 - 5x + 4)^2) / (x^2 - 1)`
Here the exponents of the polynomials in numerator are 2 and the denominator exponents is 1.
First we have to find the factors of the polynomials of the numerator.
x2 – 5x + 4 = x2 - 4x - x + 4 = x (x - 4) - (x - 4) = (x - 4) (x - 1)
Next we have to find the factors of the denominators.
x2 – 1 = x2 – 12 = (x +1) (x - 1)
Now we have to plug the values.
` = (((x - 4) (x - 1))^2) / ((x +1) (x - 1))`
`= ((x - 4)^2 (x - 1)^2) / ((x + 1) (x - 1))`
From this we get `((x - 4)^2(x - 1)) / (x + 1)^2`
These are some of the examples for dividing polynomials with exponents. First we have to expand the polynomials and we have to divide.
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