Final answer:
To add and simplify (2x^2 − 11x) + (3x^2 + 10x − 4), we combine like terms to get 5x^2 − x − 4. This corresponds to option B.
Step-by-step explanation:
Step-by-Step Simplification
To add and simplify the expression (2x2 − 11x) + (3x2 + 10x − 4), we combine like terms. We add the coefficients of the terms with the same variable exponents.
Combine the x2 terms: 2x2 + 3x2 = 5x2.
Combine the x terms: -11x + 10x = -x. Notice that when adding a negative number and a positive number, we subtract the absolute values and keep the sign of the larger absolute value which in this case is negative.
Combine the constant terms: -4 is alone, so it remains as it is.
Our final answer is 5x2 − x − 4, which corresponds to option B.
Reasoning
We follow the rules of addition where like terms are combined and subtraction is treated as the addition of a negative number. When two terms are multiplied, the sign of the product follows multiplication rules for sign.