Question 2

We will substitute the given values of $s$ into the polynomial $7s^2 - 4s + 6$.

Step 1 — Evaluate for s = 0

Let's find the value of the polynomial when $s$ is 0. We replace every $s$ in the polynomial with 0.

$7s^2 - 4s + 6 = 7(0)^2 - 4(0) + 6$

$= 7(0) - 0 + 6$

$= 0 - 0 + 6$

$\boxed{6}$

Step 2 — Evaluate for s = -3

Now, let's find the value when $s$ is -3. We will substitute -3 in place of $s$.

$7s^2 - 4s + 6 = 7(-3)^2 - 4(-3) + 6$

$= 7(9) - (-12) + 6$

$= 63 + 12 + 6$

$= 75 + 6$

$\boxed{81}$

Step 3 — Evaluate for s = 4

Finally, let's find the value when $s$ is 4. We will substitute 4 for $s$.

$7s^2 - 4s + 6 = 7(4)^2 - 4(4) + 6$

$= 7(16) - 16 + 6$

$= 112 - 16 + 6$

$= 96 + 6$

$\boxed{102}$

Answer

(i) The value of the polynomial when $s = 0$ is 6. (ii) The value of the polynomial when $s = -3$ is 81. (iii) The value of the polynomial when $s = 4$ is 102.