➕ Algebra 1 · Exponents and Polynomials
Adding and Subtracting Polynomials cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
Words
- Monomial: 1 term. Binomial: 2 terms. Trinomial: 3 terms.
- Degree: the highest degree of any term (one variable: the highest exponent; several variables: add the exponents in each term). Coefficient: the number in front.
- Standard form: highest power first, constant last
- Not polynomials: 5/x, √x, x−2
Adding
- Group like terms and add the coefficients
- Vertical: line up like terms in columns, use 0 as a placeholder
- Adding like terms changes the coefficients, never the exponents
Subtracting
- A − B = A + (−B)
- Flip the sign of EVERY term in B
- −(4x2 − 7x + 3) = −4x2 + 7x − 3
Checking
- Same test value in the original and the answer, such as x = 3
- Avoid 0, 1 and 2, which can hide mistakes
- One match is a good sign, not a proof
Applications
- Perimeter: add the sides
- Missing side: perimeter minus the known sides
- Area of a part left over: whole minus the removed part
Formulas
- Adding: (ax2 + bx + c) + (dx2 + ex + f) = (a + d)x2 + (b + e)x + (c + f)
- Subtracting: (ax2 + bx + c) − (dx2 + ex + f) = (a − d)x2 + (b − e)x + (c − f)
- Minus sign in front: −(ax2 + bx + c) = −ax2 − bx − c
- Subtracting is adding the opposite: A − B = A + (−B)
- Degree of a sum or difference: At most the larger of the two degrees (it can be smaller if leading terms cancel)
Adding and Subtracting Polynomials cheat sheet from HighSchoolQ.com, for personal study use.