GIVEN:
We are given the following polynomial;
![x^3+x^2+4x+4](https://tex.z-dn.net/?f=x%5E3%2Bx%5E2%2B4x%2B4)
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)](https://tex.z-dn.net/?f=%28x%5E3%2Bx%5E2%29%2B%284x%2B4%29)
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}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%28x%2B1%29%2B4%28x%2B1%29%20%5C%5C%20%20%5C%5C%20%28x%5E2%2B4%29%28x%2B1%29%20%5Cend%7Bgathered%7D)
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}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%2B4%3D0%20%5C%5C%20%20%5C%5C%20Subtract%5Ctext%7B%20%7D4%5Ctext%7B%20%7Dfrom%5Ctext%7B%20%7Dboth%5Ctext%7B%20%7Dsides%3A%20%5C%5C%20%20%5C%5C%20x%5E2%3D-4%20%5C%5C%20%20%5C%5C%20Take%5Ctext%7B%20%7Dthe%5Ctext%7B%20%7Dsquare%5Ctext%7B%20%7Droot%5Ctext%7B%20%7Dof%5Ctext%7B%20%7Dboth%5Ctext%7B%20%7Dsides%3A%20%5C%5C%20%20%5C%5C%20x%3D%5Cpm%5Csqrt%7B-4%7D%20%5C%5C%20%20%5C%5C%20x%3D%28%5Cpm%5Csqrt%7B-1%7D%5Ctimes%5Csqrt%7B4%7D%29%20%5C%5C%20%20%5C%5C%20x%3D%5Cpm2i%20%5Cend%7Bgathered%7D)
Therefore, the factors of the other parenthesis are;
![(x+2i)(x-2i)](https://tex.z-dn.net/?f=%28x%2B2i%29%28x-2i%29)
Therefore, the complete factorization of the polynomial is;
ANSWER:
![(x+1)(x+2i)(x-2i)](https://tex.z-dn.net/?f=%28x%2B1%29%28x%2B2i%29%28x-2i%29)
Option C is the correct answer.
Answer:
a=6
Step-by-step explanation:
-6(2+(6)=-48
-6(2+6)=-48
(-6X2)+(-6+6)=-48
(-12)+(-36)=-48
-48=-48
They are equal. Tell me if I made a mistake. Thanks!
Answer:
3x+y=5x-y
Step-by-step explanation:
Answer:
x=7
Step-by-step explanation:
Answer:
A (in millions) B (in millions) C D E F G
Total Market Value Total Shares Issued Value Per Share Amount Invested Charge D minus E Shares Purchased
$47 2 $
23.50
$4,000 $250 $
3,750
159.6
$25 4 $
6.25
$4,000 $250 $
3,750
600
$31 3 $
10.33
$4,000 $250 $
3,750
363
$12 12 $
1.00
$4,000 $300 $
3,700
3,700
$90 18 $
5.00
$4,000 $300 $
3,700
740
$26 3 $
8.67
$4,000 $300 $
3,700
426.8
$84 22 $
3.82
$4,000 none $
4,000
1,047.1
$32 5 $
6.40
$4,000 none $
4,000
625
$25 3 $
8.33
$4,000 $275 $
3,725
447.20
$27 3 $
9.00
$4,000 $275 $
3,725
413.9
Step-by-step explanation:
Those are the answers, copy and pastes- good luck though : ))