Adding (3x² + 2x - 5) + (x² - 4x + 3)

Algebra 1 · Axiom Academy

EXAMPLE Adding Polynomials (vertical & horizontal) Add two polynomials by combining like terms — shown both the vertical (aligned-column) way and the horizontal way. Add the polynomials (3x^2 + 2x - 5) + (x^2 - 4x + 3) . We will work it two ways — stacking like terms in aligned columns (vertical), and combining like terms inline (horizontal) — and confirm both give the same result. Nice work — you added two polynomials and saw the vertical and horizontal methods land on the same answer. Like terms share the same variable raised to the same power; only like terms can be combined. Vertical vs. horizontal: stacking into aligned columns and grouping inline are the same idea — line up like terms, then add their coefficients. Keep the variable part: 3x^2 + x^2 = 4x^2 , not 4x^4 — adding like terms never changes the exponent. Mind the signs: 2x + (-4x) = -2x and -5 + 3 = -2 ; rewrite + (-2x) as - 2x to clean up. (3x^2 + 2x - 5) + (x^2 - 4x + 3) = 4x^2 - 2x - 2 . The same routine works for any polynomial sum.

This is the written version of the interactive lesson above. See the full Algebra 1 course.