Given:
The expression is:
It leaves the same remainder when divided by x -2 or by x+1.
To prove:
Solution:
Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).
Let the given polynomial is:
It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that
...(i)
Substituting 
in the given polynomial.
Substituting 
in the given polynomial.
Now, substitute the values of P(2) and P(-1) in (i), we get
Divide both sides by 3.
Hence proved.
Answer:
3xy² - 14y²
Step-by-step explanation:
I hope that this is the problem
- x²y + [ - (x²y - 2xy² + y²) + (xy² - 3y² + x²y)] - (10y² - x²y)
= - x²y + [ - x²y + 2xy² - y² + xy² - 3y² + x²y] - 10y² + x²y
Now combine like terms in the [ ].
= - x²y + [ -x²y + x²y + 2xy² + xy² - y² - 3y² ] - 10y² + x²y
= - x²y + [ 0 + 3xy² - 4y²] - 10y² + x²y
= - x²y + 3xy² - 4y² -10y² + x²y Now combine like terms
= (-x²y + x²y) + 3xy² + (-4y² - 10y²)
= 0 + 3xy² - 14y²
= 3xy² - 14y² or y²(3x - 14)
6x-12=4x+10
2x-12=10
2x=22
x=11
Answer: The four integers are: 6,8,11 and 14
Step-by-step explanation:
The attachments below contains step-by-step explanations of the guessing and checking approach that would be used to arrive at the answer.
The calculations on the attachments is from left to right.
