1Cademy - Finding the Sum $$(7x^2 - 4x + 5) + (x^2

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Adding and Subtracting Polynomials

Example

Finding the Sum $(7x^2 - 4x + 5) + (x^2 - 7x + 3)$

Find the sum of the polynomials:

$(7x^2 - 4x + 5) + (x^2 - 7x + 3)$

First, identify the like terms. The $x^2$ -terms are $7x^2$ and $x^2$ ; the $x$ -terms are $-4x$ and $-7x$ ; the constants are $5$ and $3$ .

Next, rearrange the terms to group them together:

$7x^2 + x^2 - 4x - 7x + 5 + 3$

Finally, combine the like terms by adding their coefficients: $7 + 1 = 8$ gives $8x^2$ ; $-4 + (-7) = -11$ gives $-11x$ ; and $5 + 3 = 8$ .

The sum is $8x^2 - 11x + 8$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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Intermediate Algebra @ OpenStax

Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax

Algebra

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