To correctly demonstrate polynomial subtraction, we need to subtract each corresponding term in the two polynomials. Let's break down the expression (2x² + 6x + 1) − (3x² + 3x + 9):
-
Subtracting the \(x^2\) terms:
\(2x² - 3x² = -1x²\) or \(-x²\) -
Subtracting the \(x\) terms:
\(6x - 3x = 3x\) -
Subtracting the constant terms:
\(1 - 9 = -8\)
Putting it all together, we get:
\((-x² + 3x - 8)\)
Now let's compare this with the given options:
- First option: \((2x² + 6x + 1) − (3x² + 3x + 9) = −x² + 3x − 8\) (This is correct)
- Second option: \((2x² + 6x + 1) − (3x² + 3x+9) = 5x + 29 + 10\) (This is incorrect)
- Third option: \((2x² + 6x + 1) − (3x² + 3x+9) = x² + 3x + 8\) (This is incorrect)
- Fourth option: \((2x² + 6x + 1) − (3x² + 3x+9) = -5x² + 3x - 8\) (This is incorrect)
Therefore, the correct example that demonstrates polynomial subtraction is:
(2x² + 6x + 1) − (3x² + 3x + 9) = −x² + 3x − 8.