Certainly! Let's evaluate the polynomial [tex]\( p(y) = y^2 - 5y + 6 \)[/tex] at [tex]\( y = -3 \)[/tex] step-by-step.
1. Start by writing the polynomial [tex]\( p(y) \)[/tex]:
[tex]\[
p(y) = y^2 - 5y + 6
\][/tex]
2. Substitute [tex]\( y = -3 \)[/tex] into the polynomial:
[tex]\[
p(-3) = (-3)^2 - 5(-3) + 6
\][/tex]
3. Compute [tex]\( (-3)^2 \)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
So, the equation now looks like:
[tex]\[
p(-3) = 9 - 5(-3) + 6
\][/tex]
4. Next, calculate [tex]\( -5(-3) \)[/tex]:
[tex]\[
-5(-3) = 15
\][/tex]
Updating the equation:
[tex]\[
p(-3) = 9 + 15 + 6
\][/tex]
5. Finally, add the results together:
[tex]\[
p(-3) = 9 + 15 + 6 = 30
\][/tex]
Therefore, the value of [tex]\( p(-3) \)[/tex] is:
[tex]\[
p(-3) = 30
\][/tex]
