Question

Question 14 of 25What is the complete factorization of the polynomial below?x³+x² + 4x+4O A. (x-1)(x+2)(x+2)B. (x + 1)(x + 2)(x + 2)O C. (x + 1)(x + 2)(x-2)O D. (x-1)(x + 2)(x-2)SUBMIT

Answer 1

GIVEN:

We are given the following polynomial;

`x^3+x^2+4x+4`

Required;

We are required to factorize this polynomial completely.

Step-by-step explanation;

To factorize this polynomial, we start by grouping;

`(x^3+x^2)+(4x+4)`

We now take the common factor in each group;

`\begin{gathered} x^2(x+1)+4(x+1) \\ \\ (x^2+4)(x+1) \end{gathered}`

Next, we factorize the first parenthesis. To do this we set the equation equal to zero and solve for x as follows;

`\begin{gathered} x^2+4=0 \\ \\ Subtract\text{ }4\text{ }from\text{ }both\text{ }sides: \\ \\ x^2=-4 \\ \\ Take\text{ }the\text{ }square\text{ }root\text{ }of\text{ }both\text{ }sides: \\ \\ x=\pm√(-4) \\ \\ x=(\pm√(-1)*√(4)) \\ \\ x=\pm2i \end{gathered}`

Therefore, the factors of the other parenthesis are;

`(x+2i)(x-2i)`

Therefore, the complete factorization of the polynomial is;

ANSWER:

`(x+1)(x+2i)(x-2i)`

Option C is the correct answer.