Let’s find the value of the polynomial [tex]\( p(x) = 4x^2 - 3x + 7 \)[/tex] when [tex]\( x = 1 \)[/tex].
1. Start by substituting [tex]\( x = 1 \)[/tex] into the polynomial:
[tex]\[
p(1) = 4(1)^2 - 3(1) + 7
\][/tex]
2. Calculate the value of each term:
- [tex]\( 4(1)^2 = 4 \times 1^2 = 4 \)[/tex],
- [tex]\( -3(1) = -3 \times 1 = -3 \)[/tex].
3. Substitute these values back into the polynomial:
[tex]\[
p(1) = 4 - 3 + 7
\][/tex]
4. Perform the addition and subtraction:
[tex]\[
p(1) = 4 - 3 + 7 = 1 + 7 = 8
\][/tex]
Thus, the value of the polynomial [tex]\( p(x) \)[/tex] when [tex]\( x = 1 \)[/tex] is [tex]\( 8 \)[/tex].
