To determine if Oliver's work is accurate, let's first break down the equation he is solving:
Given:
\[ (x + 3)(x + 4) = 0 \]
According to the Zero Product Property, if the product of two factors equals zero, at least one of the factors must be equal to zero. Therefore, we can set each factor equal to zero:
- \(x + 3 = 0\)
- \(x + 4 = 0\)
Now, solving each of these equations:
-
From \(x + 3 = 0\): \[ x = -3 \]
-
From \(x + 4 = 0\): \[ x = -4 \]
Now, looking over the options given regarding Oliver's work:
- No.30 in the second row should be x3-0: This does not represent a correct interpretation of the Zero Product Property.
- No. 2+40 in the second row should be 24-0: This also does not correctly relate to solving the factors \(x + 3\) and \(x + 4\).
- Yes, the work is accurate: This option would only be correct if the work done was accurately reflecting the method of solving through the Zero Product Property.
- No, he should have a third column where he should set = 0: This could be a valid suggestion, as outlining each step clearly helps avoid confusion.
Based on these evaluations, Oliver's work is indeed not accurate if he did not properly identify the factors and equate them to zero.
Thus, the correct answer is: No, he should have a third column where he should set = 0.