Which is a factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35?
2x - 7, 2x + 7, 3x - 7, 3x + 7

Solution:

Given: Polynomial function is f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35.

By rational roots theorem,

From the options given above, the factors can be

1. If (2x -7) is a factor i.e. x = 7/2, then f(7/2) = 0

f(7/2) = 6(7/2)⁴ - 21(7/2)³ - 4(7/2)² + 24(7/2) - 35

f(7/2) = 900.375 - 900.375 - 49 + 84 - 35

f(7/2) = 0

2. If (2x + 7) is a factor i.e. x = -7/2, then f(-7/2) = 0

f(-7/2) = 6(-7/2)⁴ - 21(-7/2)³ - 4(-7/2)² + 24(-7/2) - 35

f(-7/2) = -900.375 + 900.375 -49 -84 -35

f(-7/2) = -168 ≠ 0

Therefore, the factor of the polynomial is (2x - 7).

Which is a factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35?

Summary:

The factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is (2x - 7).