A factorization of 
is 
.
<h3>What are the properties of roots of a polynomial?</h3>
- The maximum number of roots of a polynomial of degree
is . - For a polynomial with real coefficients, the roots can be real or complex.
- The complex roots of a polynomial with real coefficients always exist in a pair of conjugate numbers i.e., if
is a root, then 
is also a root.
If the roots of the polynomial 
are 
, then it can be factorized as 
.
Here, we are to find a factorization of 
. Also, given that 
and 
are roots of the polynomial.
Since is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.
Hence, 
and 
are also roots of the given polynomial.
Thus, all the four roots of the polynomial , are: 
.
So, the polynomial can be factorized as follows:
![\{x-(-2+i\sqrt{7})\}\{x-(-2-i\sqrt{7})\}\{x-(1-i\sqrt{3})\}\{x-(1+i\sqrt{3})\}\\=(x+2-i\sqrt{7})(x+2+i\sqrt{7})(x-1+i\sqrt{3})(x-1-i\sqrt{3})\\=\{(x+2)^2+7\}\{(x-1)^2+3\}\hspace{1cm} [\because (a+b)(a-b)=a^2-b^2]\\=(x^2+4x+4+7)(x^2-2x+1+3)\\=(x^2+4x+11)(x^2-2x+4)](https://tex.z-dn.net/?f=%5C%7Bx-%28-2%2Bi%5Csqrt%7B7%7D%29%5C%7D%5C%7Bx-%28-2-i%5Csqrt%7B7%7D%29%5C%7D%5C%7Bx-%281-i%5Csqrt%7B3%7D%29%5C%7D%5C%7Bx-%281%2Bi%5Csqrt%7B3%7D%29%5C%7D%5C%5C%3D%28x%2B2-i%5Csqrt%7B7%7D%29%28x%2B2%2Bi%5Csqrt%7B7%7D%29%28x-1%2Bi%5Csqrt%7B3%7D%29%28x-1-i%5Csqrt%7B3%7D%29%5C%5C%3D%5C%7B%28x%2B2%29%5E2%2B7%5C%7D%5C%7B%28x-1%29%5E2%2B3%5C%7D%5Chspace%7B1cm%7D%20%5B%5Cbecause%20%28a%2Bb%29%28a-b%29%3Da%5E2-b%5E2%5D%5C%5C%3D%28x%5E2%2B4x%2B4%2B7%29%28x%5E2-2x%2B1%2B3%29%5C%5C%3D%28x%5E2%2B4x%2B11%29%28x%5E2-2x%2B4%29)
Therefore, a factorization of is .
To know more about factorization, refer: brainly.com/question/25829061
#SPJ9
Answer:
a
Step-by-step explanation:
=3a + a + 2a - 5a
=4a - 3a
= a
hope it helps u tate!
Answer:
A. 228.5
B. 10
Step-by-step explanation:
A. Since <em>x</em> represents the number of months, replace <em>x</em> with 6 in the equation. Then multiply 29x6, which equals 174. Then add 174+54.5, which equals 228.5.
B. You need to solve for <em>x</em> by switching the signs in the equation<em>. </em>Set the original equation (29x+54.5) equal to 344.50. To solve for <em>x, </em>first subtract 344.50-54.5, which equals 290 (you subtract because it's the opposite of adding). Then divide 290÷29, which equals 10. You can check your work by replacing <em>x</em> in the original equation with 10, and if you get 344.5, your answer is correct.
Good luck :)
What is the mean, median, mode, and range of this data set, 2,3,2,4,3,3,3,4,2,3,4,2,4,4,9,3,4,4
slava [35]
Answer:
Mean: 3.5
Median: 3
Mode: 4
Range: 7
Step-by-step explanation:
Answer:
12 inches per foot.
Step-by-step explanation:
It's just like how the question was stated from above! No need to over think this question. .ω.
Hope this helps!
