Math

Question Find the sum of 2x2+3x+22x^2 + 3x + 2 and 3x25x13x^2 - 5x - 1.

Studdy Solution

STEP 1

Assumptions
1. We are given two polynomials: 2x2+3x+22x^2 + 3x + 2 and 3x25x13x^2 - 5x - 1.
2. We need to find the sum of these polynomials by adding like terms.

STEP 2

To add polynomials, we combine like terms. Like terms are terms that have the same variable raised to the same power.

STEP 3

Identify the like terms in the given polynomials. In this case, the like terms are those that contain x2x^2, xx, and the constant terms.

STEP 4

Add the coefficients of the x2x^2 terms from both polynomials.
2x2+3x22x^2 + 3x^2

STEP 5

Calculate the sum of the x2x^2 terms.
2x2+3x2=5x22x^2 + 3x^2 = 5x^2

STEP 6

Add the coefficients of the xx terms from both polynomials.
3x5x3x - 5x

STEP 7

Calculate the sum of the xx terms.
3x5x=2x3x - 5x = -2x

STEP 8

Add the constant terms from both polynomials.
212 - 1

STEP 9

Calculate the sum of the constant terms.
21=12 - 1 = 1

STEP 10

Combine the sums of the like terms to get the sum of the polynomials.
5x22x+15x^2 - 2x + 1
The sum of the polynomials is 5x22x+15x^2 - 2x + 1.

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