Explain the step by step of this factoring polynomials. 8x^3+1. This problem is the sum of 2 perfect cubes.

Amari Flowers

Amari Flowers

Answered question

2021-09-08

Explain the step by step of this factoring polynomials.
8x3+1
This problem is the sum of 2 perfect cubes.
8x3+1=(2x)3+(1)3
and so we know that it is the fourth special form from above. Here is the factor for this polynomials.
8x3+1=(2x+1)(4x22x+1)

Answer & Explanation

Daphne Broadhurst

Daphne Broadhurst

Skilled2021-09-09Added 109 answers

Given polynomial is, 8x3+1
The objective is to factorize the polynomial.
The polynomial 8x3+1 is written as, (2x)3+13
Now,
Apply the sum of cubes formula, x3+y3=(x+y)(x2xy+y2), by taking 2x as x and 1 as y.
8x3+1=(2x)3+13
=(2x+1)(22x22x+1)
This is the required answer.

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