Problem preview
A-APR.1 Warmup M3-001-A01-V01

Add, subtract, and multiply polynomials beyond quadratic cases.

Add higher-degree polynomials by combining like terms

Problem

Simplify \((3x^4~-~2x^2~+~5)~+~(x^4~+~7x^2~-~9)\).

Big Picture

What this problem is really about

This is a polynomial addition problem, so the structure comes from matching terms with exactly the same power of x. We’ll group the fourth-power terms, squared terms, and constants, then add only the coefficients inside each group while keeping each exponent unchanged. That produces one simplified polynomial without mixing unlike degrees.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
A-APR.1
Category
Algebra
Domain
Arithmetic with Polynomials and Rational Expressions
Objective
Add, subtract, and multiply polynomials beyond quadratic cases.
Problem type
Add higher-degree polynomials by combining like terms