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 – 5)

(x – 20)

1 answer

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).