Question

Factories completely 2x * (2x + 1) ^ 2 + (2x + 1)(4x ^ 2 - 3)

Answer 1

The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).

How to factor an algebraic equation

In this question we have an algebraic expression to be expanded by means of algebraic properties, the purpose of this handling is to modify the polynomial until its standard form is finally obtained and later we find its factor form by Cardano's method. Now we proceed to show the procedure in detail:

2 · x · (2 · x + 1)² + (2 · x + 1) · (4 · x² - 3)     Given

2 · x · (4 · x² + 4 · x + 1) + (2 · x + 1) · (4 · x²) + (2 · x + 1) · (- 3)      Perfect square trinomial/Distributive property

8 · x³ + 4 · x² + 2 · x + 8 · x³ + 4 · x² - 6 · x - 3     Distributive property/(- 1) · a = - a

16 · x³ + 8 · x² - 4 · x - 3     Distributive property/Definitions of addition and subtraction

(x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242)      Cardano's method/Result

The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).

To learn more on polynomials: brainly.com/question/11536910

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