Question

Find the sum of the following expressions:

(x^2 + 3x + 5) + (2x^2 - 4x - 1).
a) 3x^2 - x - 4
b) 3x^2 - x + 4
c) 3x^2 - x + 6
d) 4x^2 - 7x + 4

Answer 1

The sum of the two algebraic expressions (x^2 + 3x + 5) and (2x^2 - 4x - 1) is 3x^2 - x + 4, obtained by adding the like terms from each expression.

Step-by-step explanation:

The sum of the expressions (x^2 + 3x + 5) and (2x^2 - 4x - 1) involves combining like terms. We add the coefficients of the terms that have the same degree of x. Here's a step-by-step explanation:

• Identify the like terms: x^2 terms, x terms, and constant terms.
• Add the coefficients of x^2 terms: 1x^2 + 2x^2 = 3x^2.
• Add the coefficients of x terms: 3x + (-4x) = -x.
• Add the constants: 5 + (-1) = 4.

So, the sum of the two expressions is 3x^2 - x + 4.