Final answer:
The sum of the polynomials 2x^(2)+5x+7 and -10x^(2)-7x+1 is -8x^2 - 2x + 8, which is found by combining like terms.
Step-by-step explanation:
To find the sum of 2x^(2)+5x+7 and -10x^(2)-7x+1, you need to combine like terms. The coefficients of the x2 terms (2 and -10), the x terms (5 and -7), and the constant terms (7 and 1) are added together separately.
Combining the x2 terms: 2x2 - 10x2 = (-8x2)
Combining the x terms: 5x - 7x = (-2x)
Combining the constant terms: 7 + 1 = 8
So, the sum of the two polynomials is -8x2 - 2x + 8.