Question

A student correctly evaluated an expression with P = -2 and a = 3 and got 3 as the result. Which of the following expressions could she have been evaluating

Answer 1

B

Explanation:

A student correctly evaluated an expression where p = -2 and q = 3 and acquired 3 as the result.

And we want to determine which expression could the student have been evaluating.

Thus, we simply need to check each expression by letting p = -2 and q = 3 and see which one equals 3.

Checking the first one:

`\displaystyle \begin{aligned} 3p^2 +2pq - 6q +2 &= 3(-2)^2+2(-2)(3)-6(3) + 2\\ &= (12)+(-12) +(-18) + 2 \\ &=-16\end{aligned}`

The result is not 3. Hence, A is not correct.

The second expression:

`\displaystyle \begin{aligned} p^3 + 2p^2q-p^2+2pq+q &= (-2)^3+2(-2)^2(3)-(-2)^2+2(-2)(3)+(3)\\ &= (-8)+(24)-(4)+(-12)+(3) \\ &= 3\stackrel{\checkmark}{=}3\end{aligned}`

Therefore, we can conclude that our answer is B.

We can check the other two regardless.

The third expression:

`\begin{aligned} p^2+q-4q^2 &= (-2)^2 + (3) - 4(3)^2 \\ &= (4) + (3) -(36) \\ &= -29\end{aligned}`

And the fourth:

`\displaystyle \begin{aligned} p^2+3q^2-q^2+p &= (-2)^2+3(3)^2-(3)^2+(-2) \\ &= (4) + (27) - (9) + (-2) \\ &= 20\end{aligned}`

Thus, neither the third expression nor the fourth is also correct.

In conclusion, our answer is B.