# Factor Completely 3x2 − X − 4. (3x − 1)(X + 4) (3x + 4)(X − 1) (3x − 2)(X + 2) (3x − 4)(X + 1)

## Question: Factor completely 3x^{2} − x − 4

Factorization simply means expressing a number as a multiplication of two other numbers.

## Answer: The factorization of 3x^{2} − x − 4 is (x+1)(3x-4)

The given expression is a quadratic expression.

Let's explore the factorization of a quadratic expression.

## Explanation:

The given quadratic expression can be factorized by splitting the middle term.

3x^{2} − x − 4

=> 3x^{2} + 3x -4x − 4. (Since, the middle term -x can be split as +3x - 4x)

The middle term should be split in such a way that the product of the split terms is the same as that of the first term and the constant

Here, (3x)(-4x) = -12 x^{2} is same as (3 x^{2})(-4)= -12 x^{2}

⇒ 3x^{2} − x − 4

= 3x^{2} + 3x -4x − 4

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

So, 3x^{2} − x − 4 when factored completerly we get (3x-4)(x+1)

### Thus, the factorization of 3x^{2} − x − 4 is (x+1)(3x-4)

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