Question

Which of the following is a factor of (x - 27) - 14x + 120?

Option 1: (x - 30)
Option 2: (x + 2)
Option 3: (x - 5)
Option 4: (x + 6)

Answer 1

To determine the factor of the given expression, we use the factor theorem.

Step-by-step explanation:

In order to determine which of the given options is a factor of the expression (x - 27) - 14x + 120, we can use the factor theorem. If a polynomial expression, f(x), has a factor (x - a), then f(a) = 0.

Let's test each option by substituting the value and simplifying:

1. (x - 30): Substituting x = 30 gives (30 - 27) - 14(30) + 120 = 3 - 420 + 120 = -297
2. (x + 2): Substituting x = -2 gives (-2 - 27) - 14(-2) + 120 = -29 + 28 + 120 = 119
3. (x - 5): Substituting x = 5 gives (5 - 27) - 14(5) + 120 = -22 - 70 + 120 = 28
4. (x + 6): Substituting x = -6 gives (-6 - 27) - 14(-6) + 120 = -33 + 84 + 120 = 171

Only option 3, (x - 5), gives a result of zero when substituted into the expression. Therefore, option 3 is a factor of (x - 27) - 14x + 120.