Certainly! The expression given is a polynomial in terms of [tex]\( x \)[/tex]. Let's break it down and simplify step by step:
The expression is:
[tex]\[ 27x^6 - 19x^3 - 8 \][/tex]
This is a polynomial of degree 6 since the highest power of [tex]\( x \)[/tex] is 6. The variables and constants in the polynomial are:
- [tex]\( 27x^6 \)[/tex], which is a term involving [tex]\( x \)[/tex] raised to the power of 6 and multiplied by 27,
- [tex]\( -19x^3 \)[/tex], which is a term involving [tex]\( x \)[/tex] raised to the power of 3 and multiplied by -19,
- [tex]\( -8 \)[/tex], which is a constant term.
Let's analyze each term individually:
1. [tex]\( 27x^6 \)[/tex]: This term indicates that [tex]\( x \)[/tex] is raised to the 6th power and then multiplied by 27.
2. [tex]\( -19x^3 \)[/tex]: This term indicates that [tex]\( x \)[/tex] is raised to the 3rd power and then multiplied by -19.
3. [tex]\( -8 \)[/tex]: This is a constant term and does not depend on [tex]\( x \)[/tex].
To evaluate this polynomial for a specific value of [tex]\( x \)[/tex], you would substitute that value into the polynomial and compute the result. For example, if you want to evaluate the polynomial at [tex]\( x = a \)[/tex]:
[tex]\[ 27(a)^6 - 19(a)^3 - 8 \][/tex]
The steps to evaluate would be:
1. Calculate [tex]\( (a)^6 \)[/tex] and multiply it by 27.
2. Calculate [tex]\( (a)^3 \)[/tex] and multiply it by -19.
3. Add these results along with the constant term -8.
4. Summing all these will give you the value of the polynomial at [tex]\( x = a \)[/tex].
However, without a specific value for [tex]\( x \)[/tex], the polynomial simply remains as stated:
[tex]\[ 27x^6 - 19x^3 - 8 \][/tex]
There are no further simplifications possible for this general polynomial expression without specific values or additional constraints.
