To find the value of the polynomial [tex]\(8x^3 - 6x^2 + 2\)[/tex] at [tex]\(x = 1\)[/tex], you substitute [tex]\(x = 1\)[/tex] into the polynomial and simplify.
Step-by-Step Solution:
1. Substitute [tex]\(x = 1\)[/tex] into the polynomial:
[tex]\[
8(1)^3 - 6(1)^2 + 2
\][/tex]
2. Calculate each term individually:
- [tex]\( (1)^3 = 1 \)[/tex]
- So, [tex]\( 8 \cdot 1 = 8 \)[/tex]
- Next, [tex]\( (1)^2 = 1 \)[/tex]
- So, [tex]\( 6 \cdot 1 = 6 \)[/tex]
3. Simplify the expression:
- [tex]\( 8 - 6 + 2 \)[/tex]
4. Perform the addition and subtraction:
- [tex]\( 8 - 6 = 2 \)[/tex]
- Finally, [tex]\( 2 + 2 = 4 \)[/tex]
Therefore, the value of the polynomial [tex]\(8x^3 - 6x^2 + 2\)[/tex] at [tex]\(x = 1\)[/tex] is [tex]\(4\)[/tex].
