Answer:
![x=4+-2\sqrt{7}](https://tex.z-dn.net/?f=x%3D4%2B-2%5Csqrt%7B7%7D)
Step-by-step explanation:
To solve, we need to take square root of both sides first:
![(x-4)^2=28\\\sqrt{(x-4)^2} =+-\sqrt{28} \\x-4=+-\sqrt{28}](https://tex.z-dn.net/?f=%28x-4%29%5E2%3D28%5C%5C%5Csqrt%7B%28x-4%29%5E2%7D%20%3D%2B-%5Csqrt%7B28%7D%20%5C%5Cx-4%3D%2B-%5Csqrt%7B28%7D)
Now we use the property of radical shown below to simplify square root of 28:
Property: ![\sqrt{x*y}=\sqrt{x} \sqrt{y}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2Ay%7D%3D%5Csqrt%7Bx%7D%20%5Csqrt%7By%7D)
Now, we have:
![x-4=+-\sqrt{28}\\x-4=+-\sqrt{4*7}\\x-4=+-\sqrt{4}\sqrt{7}\\x-4=+-2\sqrt{7}](https://tex.z-dn.net/?f=x-4%3D%2B-%5Csqrt%7B28%7D%5C%5Cx-4%3D%2B-%5Csqrt%7B4%2A7%7D%5C%5Cx-4%3D%2B-%5Csqrt%7B4%7D%5Csqrt%7B7%7D%5C%5Cx-4%3D%2B-2%5Csqrt%7B7%7D)
Now we take 4 to the other side and isolate x:
![x-4=+-2\sqrt{7} \\x=4+-2\sqrt{7}](https://tex.z-dn.net/?f=x-4%3D%2B-2%5Csqrt%7B7%7D%20%5C%5Cx%3D4%2B-2%5Csqrt%7B7%7D)
first answer choice is right.
Function is p(x)=(x-4)^5(x^2-16)(x^2-5x+4)(x^3-64)
first factor into (x-r1)(x-r2)... form
p(x)=(x-4)^5(x-4)(x+4)(x-4)(x-1)(x-4)(x^2+4x+16)
group the like ones
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
multiplicity is how many times the root repeats in the function
for a root r₁, the root r₁ multiplicity 1 would be (x-r₁)^1, multility 2 would be (x-r₁)^2
so
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
(x^2+4x+16) is not on the real plane, but the roots are -2+2i√3 and -2-2i√3, each multiplicity 1 (but don't count them because they aren't real
baseically
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
Answer:
Step-by-step explanation to be honest probably 12 if not i’m so sorry