A factor of 2x³-7x²-5x+4 is

To find a factor of the polynomial 2x³-7x²-5x+4, we can use the Rational Root Theorem. This theorem states that any rational root of the polynomial, expressed in lowest terms, has a numerator that is a factor of the constant term (4 in this case) and a denominator that is a factor of the leading coefficient (2 in this case).

The factors of 4 are ±1, ±2, ±4 and the factors of 2 are ±1, ±2. So, the possible rational roots of the polynomial are ±1, ±2, ±4, ±1/2, ±2/2, ±4/2 which simplifies to ±1, ±2, ±4, ±1/2, ±1, ±2.

We can test these possible roots by substituting them into the polynomial and checking if the result is zero. If the result is zero, then that value is a root of the polynomial and (x - that value) is a factor of the polynomial.

After testing all the possible roots, we find that x = 1 is a root of the polynomial because 2(1)³ - 7(1)² - 5(1) + 4 = 0. Therefore, (x - 1) is a factor of the polynomial 2x³ - 7x² - 5x + 4.

To find the other factors, we can perform polynomial division or use synthetic division to divide the original polynomial by (x - 1). The quotient will be the other factor of the polynomial.

Using synthetic division, we get the other factor as 2x² - 5x - 4.

So, the factors of the polynomial 2x³ - 7x² - 5x + 4 are (x - 1) and (2x² - 5x - 4).