LEMMA

Polynomials & quadratics

Add and subtract polynomials

ALEKS placement

Add polynomials by combining like terms; subtract by distributing the minus sign first.

What this covers

  • Write both polynomials in descending order.
  • For subtraction, change the sign of every term in the second polynomial.
  • Combine terms with matching variable and exponent.
  • The degree stays the same unless the leading terms cancel.

Worked example

Worked example

Subtract (3x² - 5x + 2) - (x² + 4x - 7).

  1. 3x2−5x+2−x2−4x+7The minus flips every sign in the second group.
  2. 2x2−9x+9Combine like terms.
Another worked example

Add (2x² + 4x + 1) + (x² − 6x + 5).

  1. (2+1)x2+(4−6)x+(1+5)Addition keeps every sign. Group the x² terms, the x terms, and the numbers.
  2. 3x2−2x+6Combine the coefficients in each lane. The powers themselves do not change.

A common mistake

A mistake Lemma catches

From (3x2−5x+2)−(x2+4x−7)

3x2−5x+2−x2−4x−73x2−5x+2−x2−4x+7

“The minus sign in front of the second bracket changes the sign of all three terms: −(x²) = −x², −(4x) = −4x and −(−7) = +7. The last one was left as −7.”

Try one

Sample problem

Add and simplify.

(3x2+7x)+(2x2−7x)

Practice polynomial sums free

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