FIRST PROBLEM AS GENIUS!!!
The 45-45-90 triangle theorem states that each leg equals x, and the hypotenuse equals

. Using this, we can find that the height is 10. Take the average of the lengths to get l = 27.
The area = 270.
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.
<span>[x + 2 - (5x + 5)] ² =
[x + 2 - 5x - 5]² =
[x - 5x + 2 - 5]² =
[-4x - 3]² =
(-4x)² - 2.(-4x).3 + (-3)² =
16x² + 24x + 9
Answer:
</span>

<span>
</span>
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