Find the binomials that is a factor of x³ + 4x² + x - 6.

Solution:

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

Given: A cubic polynomial, x³ + 4x² + x - 6

Let's use splitting and grouping the terms

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)] 

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 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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Find the binomials that is a factor of x³ + 4x² + x - 6.

Summary:

The binomial factors of x³ + 4x² + x - 6 are (x + 2), (x + 3) and (x - 1).