Respuesta :
Given:
The polynomial,
[tex]12x^2+6-7x^5+3x^3+7x^4-5x[/tex]
To find:
The standard form, leading coefficient, degree, and number of terms for the given polynomial.
Solution:
Consider the polynomial,
[tex]P(x)=12x^2+6-7x^5+3x^3+7x^4-5x[/tex]
Arrange the terms according to their powers from largest to smallest.
[tex]P(x)=-7x^5+7x^4+3x^3+12x^2-5x+6[/tex]
Therefore, the standard form of given polynomial is [tex]P(x)=-7x^5+7x^4+3x^3+12x^2-5x+6[/tex].
Here, the highest power of the variable is 5.
So, degree of the polynomial is 5.
Leading term is [tex]-7x^5[/tex].
So, leading coefficient is -7.
Terms in the polynomial are [tex]-7x^5,7x^4,3x^3,12x^2,-5x,[/tex] and 6.
So, the number of terms is 6.
The rewrite of the given equation is [tex]-7x^5 + 7x^4 +3x^3+12x^2-5x + 6[/tex]
Given that,
- The polynomial is [tex]12x^2 + 6 - 7x^5 + 3x^3 + 7x^4 - 5x[/tex].
Based on the above information, the rewritten of the polynomial is as follows:
Here we have to write from the highest to smallest
So, it is
[tex]-7x^5 + 7x^4 +3x^3+12x^2-5x + 6[/tex]
Therefore we can conclude that The rewrite of the given equation is [tex]-7x^5 + 7x^4 +3x^3+12x^2-5x + 6[/tex]
Learn more: brainly.com/question/6201432
