<span> First, reduce the fraction to lowest terms, e.g. 8/6 = 4/3.

Look at the denominator. Split it into its prime factors. If its prime factors only consist of 2's and 5's, then it will be terminating.

Examples:
16 = 2 x 2 x 2 x 2, so terminating
25 = 5 x 5, so terminating
2000 = 2 x 1000 = 2 x (2 x 5) x (2 x 5) x (2 x 5), so terminating
12 = 2 x 3, so repeating (has prime factor 3, which is not 2 or 5)
13 = 13, so repeating (has prime factor 13, which is not 2 or 5) Hope this helps!!

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3 years ago

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

mote1985 [20]

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;

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

Therefore, the factors of the other parenthesis are;