# Find the binomials that is a factor of x^{3} + 4x^{2 }+ x - 6.

Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial, or an algebraic expression.

## Answer: The binomial factors of x^{3} + 4x^{2 }+ x - 6 are (x + 2), (x + 3) and (x - 1).

Let's look into the steps below

**Explanation:**

Given: A cubic polynomial, x^{3} + 4x^{2 }+ x - 6

Let's use splitting and grouping the terms

x^{3} + 4x^{2 }+ x - 6

= x^{3} + 2x^{2 }+ 2x^{2} + x - 6 [Splitting 4x^{2} = 2x^{2 }+ 2x^{2}]

= (x^{3} + 2x^{2}) + (2x^{2} + x - 6)

= x^{2} (x + 2) + (2x^{2} + 4x - 3x - 6)

= x^{2} (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x^{2} (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x^{2} + 2x - 3)

= (x + 2) ( x^{2} + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

We can use Cuemath's online factorization calculator to find the factors of a polynomial.

### Hence, the binomial factors are (x + 2), (x + 3) and (x - 1).

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