Final answer:
The second polynomial that Cindy added to 2x³+x+4 to get the sum 6x³-4x²+x+7 is 4x³ - 4x² + 3.
Step-by-step explanation:
To find the second polynomial that Cindy added to 2x³+x+4 to obtain the sum 6x³-4x²+x+7, we need to perform polynomial subtraction. We subtract Cindy's initial polynomial from the final sum, which will give us the second polynomial.
Starting with the sum, 6x³-4x²+x+7, we subtract the initial polynomial Cindy had, which is 2x³+x+4. We do this term by term:
- For the x³ term: 6x³ - 2x³ = 4x³
- For the x² term: The initial polynomial does not have an x² term, so we just bring down the -4x² term from the sum, which is -4x²
- For the x term: x - x = 0x, which means we don't have an x term in the second polynomial
- For the constant term: 7 - 4 = 3
So, the second polynomial that Cindy added is 4x³ - 4x² + 3.