Answer: - 235
<u>Step-by-step explanation:</u>
f(x) = -3x² + 13x + 3
f(-7) = -3(-7)² + 13(-7) + 3
= -3(49) - 91 + 3
= -147 - 88
= -235
The standard equation for a circle with center at (h,k) and radius r is
(x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle.
The formula for the circumference of a circle is C = 2pi*r. In this particular problem, we need to determine the radius of the circle. That radius is: r = C/[2pi]. Here, C = 22pi, so we get r = 22pi/[2pi], and so r^2 = 11^2.
Putting to use the given info, we have:
(x+14)^2 + (y-5)^2 = 11^2
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
160in 5x8=40x4=160 is the answer to ur question
