64.8k views
1 vote
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

A student correctly evaluated an expression with P = -2 and a = 3 and got 3 as the-example-1
User Txizzle
by
7.6k points

1 Answer

5 votes

Answer:

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.

User Lior Dahan
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories