To find a dimension of Vincent's rectangular poster given that the area is \( x^2 - 17x - 60 \), we need to factor the quadratic expression.
We need to find two numbers that multiply to \(-60\) (the constant term) and add up to \(-17\) (the coefficient of the linear term).
After checking the possible pairs of factors of \(-60\), we find that:
- The pair \(-20\) and \(3\) works because: \(-20 + 3 = -17\) \(-20 \times 3 = -60\)
Thus, we can factor the quadratic as:
\[ x^2 - 17x - 60 = (x - 20)(x + 3) \]
Now, we see that the factors are \( (x - 20) \) and \( (x + 3) \).
The possible dimensions of the poster, according to the answer choices given, are:
- \( (x - 3) \)
- \( (x + 12) \)
- \( (x - 5) \)
- \( (x - 20) \)
Among these, \( (x - 20) \) matches one of the factors we found.
Therefore, the dimension of the poster is:
(x - 20).
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