As the expression is not equal to zero on x=3, x-3 is not a factor of given expression
Step-by-step explanation:
Given expression is:
![x^3+2x^2-5x-6](https://tex.z-dn.net/?f=x%5E3%2B2x%5E2-5x-6)
We have to check if x-3 is a factor of given expression
In order for x-3 to be a factor of expression, we have to put x-3 = 0 => x=3 in expression.
If the expression is zero at x=3 then x-3 is a factor of expression otherwise not.
So putting x=333 in expression
![=(3)^3+2(3)^2-5(3)-6\\= 27+2(9) - 15-6\\= 27+18-15-6\\= 45-21\\=24 \neq 0](https://tex.z-dn.net/?f=%3D%283%29%5E3%2B2%283%29%5E2-5%283%29-6%5C%5C%3D%2027%2B2%289%29%20-%2015-6%5C%5C%3D%2027%2B18-15-6%5C%5C%3D%2045-21%5C%5C%3D24%20%5Cneq%200)
As the expression is not equal to zero on x=3, x-3 is not a factor of given expression
Keywords: Polynomials, expressions
Learn more about polynomials at:
#LearnwithBrainly
<h3>Given:</h3>
- Hemisphere ×2 or sphere
- Cylinder
<h3>Solution:</h3><h3>Volume of the sphere:</h3>
![v = \frac{4}{3} \pi {r}^{3}](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5Cpi%20%7Br%7D%5E%7B3%7D%20)
![v = \frac{4}{3} \times \pi \times {2}^{3}](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5Ctimes%20%5Cpi%20%5Ctimes%20%20%7B2%7D%5E%7B3%7D%20)
![v = 33.51 \: {m}^{3}](https://tex.z-dn.net/?f=v%20%3D%2033.51%20%5C%3A%20%20%7Bm%7D%5E%7B3%7D%20)
<h3>Volume of the cylinder:</h3>
![v = \pi {r}^{2} h](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%7Br%7D%5E%7B2%7D%20h)
![v = \pi \times {2}^{2} \times 6](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%5Ctimes%20%20%7B2%7D%5E%7B2%7D%20%20%5Ctimes%206)
![v = 75.40 \: {m}^{3}](https://tex.z-dn.net/?f=v%20%3D%2075.40%20%5C%3A%20%20%7Bm%7D%5E%7B3%7D%20)
<h3>Total volume:</h3>
![v = 75.40 + 33.51](https://tex.z-dn.net/?f=v%20%3D%2075.40%20%2B%2033.51)
![v = 108.91 \: {m}^{3}](https://tex.z-dn.net/?f=v%20%3D%20108.91%20%5C%3A%20%20%7Bm%7D%5E%7B3%7D%20)
<u>Hence</u><u>,</u><u> </u><u>the</u><u> </u><u>volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>given</u><u> </u><u>compound</u><u> </u><u>shape</u><u> </u><u>is</u><u> </u><u>108.91</u><u> </u><u>cubic</u><u> </u><u>meters</u><u>.</u>
Answer:The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from
π
π
to find the solution in the third quadrant.
Step-by-step explanation: