Q3. - Algebra 2

Question

FIND THE ERROR Teisha and Molly are finding $g\left(2a\right)$ for the function $g\left(x\right)=x^2+x-1$.

Teisha                                                           Molly

$\begin{array}{c}g\left(2a\right)=2(a^2+a-1)\\ =2a^2+2a-2\end{array}$                            $\begin{array}{c}g\left(2a\right)={\left(2a\right)}^2+2a-1\\ =4a^2+2a-1\end{array}$

Who is correct? Explain your reasoning.

Step-by-Step Solution

Answer

The solution of Molly is correct.

Step 1 – Order of operations.

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

Step 2 – Substitute the given value in the given function.

The given function is:

$g\left(x\right)=x^2+x-1$

Substitute $x=2a$ in the function $g\left(x\right)$.

$g\left(2a\right)={\left(2a\right)}^2+\left(2a\right)-1$

Step 3 – Calculate the value by simplification.

$\begin{array}{c}g\left(2a\right)={\left(2a\right)}^2+2a-1\\ =2^2{a}^2+2a-1\\ =4a^2+2a-1\end{array}$

So, Molly is correct.

In Teisha’s solution, she writes 2 outside the parenthesis and then substitutes x=a instead of substituting x=2a.

Thus, the solution of Molly is correct.