Question

The area of Vincent’s rectangular poster is x2 – 17x – 60. Which of the following represents a dimension of the poster?

Group of answer choices

(x – 3)

(x + 12)

(x – 20)

(x – 5)

Answer 1

To determine which expression represents a dimension of Vincent's rectangular poster, we first need to factor the area expression \( x^2 - 17x - 60 \).

To factor \( x^2 - 17x - 60 \), we need to find two numbers that multiply to \(-60\) (the constant term) and add to \(-17\) (the coefficient of the linear term).

The pairs of factors of \(-60\) are:
- \(1, -60\)
- \(-1, 60\)
- \(2, -30\)
- \(-2, 30\)
- \(3, -20\)
- \(-3, 20\)
- \(4, -15\)
- \(-4, 15\)
- \(5, -12\)
- \(-5, 12\)
- \(6, -10\)
- \(-6, 10\)

Among these pairs, the numbers \(-20\) and \(3\) multiply to \(-60\) and add to \(-17\).

Thus, we can factor the expression as follows:

\[
x^2 - 17x - 60 = (x - 20)(x + 3)
\]

Now, we can see that the dimensions of the poster can be represented by the factors \( (x - 20) \) and \( (x + 3) \).

Reviewing the answer choices, we find:

- \((x - 3)\)
- \((x + 12)\)
- \((x - 20)\)
- \((x - 5)\)

Among these, \((x - 20)\) is the only factor we found when we factored the area.

Therefore, a dimension of the poster is represented by \((x - 20)\).