Factor completely 3x² - x - 4.
(3x - 1)(x + 4), (3x + 4)(x - 1), (3x - 2)(x + 2), (3x - 4)(x + 1)

Solution:

Given is a quadratic polynomial.

Step 1: Identify the values of a, b and c.

In the above equation, a is coefficient ofx² = 3,

b is the coefficient of x = -1 and

c is the constant term = - 4.

Step 2: Solve for x by factoring polynomial 

Multiply a and c and find the factors that add up to b.

3 × (- 4) = 12

⇒ 3 and -4 are the factors of 12 that add up to b.

Step 3: Let us factorize the polynomial to find the value of x by splitting the middle term.

Split bx into two terms.

3x² + 3x - 4x - 4

Step 4: Take out the common factors by grouping.

3x(x + 1) -4(x + 1)

= (x + 1) (3x - 4)

Therefore, the factors of the given polynomial are (x + 1) (3x - 4)

Factor completely 3x² - x - 4.
(3x - 1)(x + 4), (3x + 4)(x - 1), (3x - 2)(x + 2), (3x - 4)(x + 1)

Summary:

The factors of the equation 3x² - x - 4 are (x + 1) (3x - 4).