Grade 9 › G9U03 Polynomials

Grade 9 › G9U03 Polynomials › L2
GRADE 9 · ALBERTAOUTCOME AB-G9-9A1

L2 · Adding and subtracting polynomials

Learning goal

“I can add polynomials by combining like terms, and subtract polynomials by adding the additive inverse - flipping every sign in the polynomial being subtracted.”

Combine like terms — add the coefficients of like terms (same variable, same degree) and keep the variable part unchanged: 3x^2 + x^2 = 4x^2, never 4x^4.
Additive inverse — the polynomial with every sign flipped: the additive inverse of 2x^2 + 3x - 5 is -2x^2 - 3x + 5. A polynomial plus its additive inverse is 0.
Simplify — write a polynomial with all like terms combined, in descending order (the canonical form for this unit).
Worked example

Simplify (3x^2 + 2x - 5) + (x^2 - 4x + 1). Step 1: Addition means the brackets come off unchanged: 3x^2 + 2x - 5 + x^2 - 4x + 1. Step 2: Group like terms: x^2 terms: 3x^2 + x^2. x terms: 2x - 4x. Constants: -5 + 1. Step 3: Combine each group by adding coefficients: 4x^2; -2x; -4. Result: 4x^2 - 2x - 4. Say it plainly: combining like terms changes only the coefficient. The variable part - x^2 stays x^2 - is untouched.

Check yourself — explain it

In the sum above, why can 3x^2 and x^2 be combined, but 2x and -5 cannot?

Paired problem — example still visible

Simplify (5x^2 - 3x + 2) + (2x^2 + 6x - 8). -> 7x^2 + 3x - 6 (5x^2 + 2x^2 = 7x^2; -3x + 6x = 3x; 2 - 8 = -6)

Faded completion — last step is yours

"(4x^2 + x - 7) + (___ + 2x + 3) = 6x^2 + 3x - 4. What is the missing term?" -> 2x^2 (the x^2 group must total 6x^2, and 4x^2 + 2x^2 = 6x^2; check the rest: x + 2x = 3x, -7 + 3 = -4)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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