Factor completely 3x2 − x − 4
Factorization simply means expressing a number as a multiplication of two other numbers.
Answer: The factorization of 3x2 − x − 4 is (x+1)(3x-4)
The given expression is a quadratic expression.
Let's explore the factorization of a quadratic expression.
The given quadratic expression can be factorized by splitting the middle term.
3x2 − x − 4
=> 3x2 + 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 x2 is same as (3 x2)(-4)= -12 x2
⇒ 3x2 − x − 4
= 3x2 + 3x - 4x − 4
= 3x(x+1) - 4(x+1) = (3x-4)(x+1)
So, 3x2 − x − 4 when factored completely gives (3x-4)(x+1)