Answer:
7x -1 is correct after combining like terms
Step-by-step explanation:
6+8x-7-x
To simplify algebraic expression we combine like terms
In the given expression
-x or -1x are same
8x and -1x are like terms
6 and -7 are also like terms
8x-1x= 7x
6 - 7 = -1
So 7x -1 is correct after combining like terms
12a + 6 + 3a = 15a + 2
15a = 15a - 4
0 = - 4
Answer:
2x+5
Step-by-step explanation:
X represents the number in "2 times a number." You could insert any number into x.
Answer:
, for ![r_{1} = 0](https://tex.z-dn.net/?f=r_%7B1%7D%20%3D%200)
Step-by-step explanation:
The general form of quintic-order polynomial is:
![p_{5}(t) = a\cdot x^{5} + b\cdot x^{4} + c\cdot x^{3} + d\cdot x^{2} + e \cdot x + f](https://tex.z-dn.net/?f=p_%7B5%7D%28t%29%20%3D%20a%5Ccdot%20x%5E%7B5%7D%20%2B%20b%5Ccdot%20x%5E%7B4%7D%20%2B%20c%5Ccdot%20x%5E%7B3%7D%20%2B%20d%5Ccdot%20x%5E%7B2%7D%20%2B%20e%20%5Ccdot%20x%20%2B%20f)
According to the statement of the problem, the polynomial has the following roots:
![p_{5} (t) = (x - r_{1})\cdot (x-3)^{2}\cdot x^{2} \cdot (x+1)](https://tex.z-dn.net/?f=p_%7B5%7D%20%28t%29%20%3D%20%28x%20-%20r_%7B1%7D%29%5Ccdot%20%28x-3%29%5E%7B2%7D%5Ccdot%20x%5E%7B2%7D%20%5Ccdot%20%28x%2B1%29)
Then, some algebraic handling is done to expand the polynomial:
![p_{5} (t) = (x - r_{1}) \cdot (x^{3}-6\cdot x^{2}+9\cdot x) \cdot (x+1)\\p_{5} (t) = (x - r_{1}) \cdot (x^{4}-5\cdot x^{3} + 3 \cdot x^{2} + 9 \cdot x)](https://tex.z-dn.net/?f=p_%7B5%7D%20%28t%29%20%3D%20%28x%20-%20r_%7B1%7D%29%20%5Ccdot%20%28x%5E%7B3%7D-6%5Ccdot%20x%5E%7B2%7D%2B9%5Ccdot%20x%29%20%5Ccdot%20%28x%2B1%29%5C%5Cp_%7B5%7D%20%28t%29%20%3D%20%28x%20-%20r_%7B1%7D%29%20%5Ccdot%20%28x%5E%7B4%7D-5%5Ccdot%20x%5E%7B3%7D%20%2B%203%20%5Ccdot%20x%5E%7B2%7D%20%2B%209%20%5Ccdot%20x%29)
![p_{5} (t) = x^{5} - (5+r_{1})\cdot x^{4} + (3 + 5\cdot r_{1})\cdot x^{3} +(9-3\cdot r_{1})\cdot x^{2} - 9 \cdot r_{1}\cdot x](https://tex.z-dn.net/?f=p_%7B5%7D%20%28t%29%20%3D%20x%5E%7B5%7D%20-%20%285%2Br_%7B1%7D%29%5Ccdot%20x%5E%7B4%7D%20%2B%20%283%20%2B%205%5Ccdot%20r_%7B1%7D%29%5Ccdot%20x%5E%7B3%7D%20%2B%289-3%5Ccdot%20r_%7B1%7D%29%5Ccdot%20x%5E%7B2%7D%20-%209%20%5Ccdot%20r_%7B1%7D%5Ccdot%20x)
If
, then:
![p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}](https://tex.z-dn.net/?f=p_%7B5%7D%20%28t%29%20%3D%20x%5E%7B5%7D%20-%205%5Ccdot%20x%5E%7B4%7D%20%2B%203%5Ccdot%20x%5E%7B3%7D%20%2B9%5Ccdot%20x%5E%7B2%7D)