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Danii70go
Answered

What is the complete factorization of the polynomial below?
x^3 + 3x^2 + 9x + 27
A. (x-3)(x+3)(x +31)
B. (x-3)(x+31)(x-31)
C. (x+3)(x + 31)(x+31)
D. (x+3)(x+3)(x-31)

Answer :

BasketballEinsteingo

Answer:

[tex]\displaystyle (x + 3)(x^2 + 9)[/tex]

Step-by-step explanation:

[tex]\displaystyle x^3 + 3x^2 + 9x + 27 \hookrightarrow x^2(x + 3)\:9(x + 3) \\ \\ \boxed{(x^2 + 9)(x + 3)}[/tex]

Perhaps there is a typographical errour in your answer choises.

Still, I am joyous to assist you at any time.

Eduard22slygo

When we factorise the polynomial x³ + 3x² + 9x + 27 completely, the result obtained is (x² + 9)(x + 3)

Data obtained from the question

  • polynomial = x³ + 3x² + 9x + 27
  • Factorisation =?

How to factorise x³ + 3x² + 9x + 27

x³ + 3x² + 9x + 27

Group the terms

(x³ + 3x²) + (9x + 27)

Factorise

x²(x + 3) + 9(x + 3)

Since the same entity appear in both brackets, we shall pick one as follow

(x² + 9)(x + 3)

Thus,

x³ + 3x² + 9x + 27 = (x² + 9)(x + 3)

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