Find The Binomials That Is A Factor Of X3 + 4x2 + X - 6. - Cuemath

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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).

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).

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