Grade 9 › G9U03 Polynomials

Grade 9 › G9U03 Polynomials › L1
GRADE 9 · ALBERTAOUTCOME AB-G9-9A1

L1 · Polynomial language: terms, coefficients, degree (single variable)

Learning goal

“I can take any single-variable polynomial apart: name its terms and coefficients, state its degree, classify it by its terms and its degree, and rewrite it in descending order.”

Term (monomial) — the product of a coefficient and a power of the variable, e.g. 4x^2, -3x, 7. A polynomial is a sum of terms.
Coefficient — the number multiplying the variable part of a term. The sign in front belongs to the term: in -3x, the coefficient is -3.
Degree — of a term: the exponent on its variable (a constant term has degree 0). Of a polynomial: the greatest degree of any one term - never a sum of exponents.
Like terms — terms with the same variable raised to the same degree, e.g. 4x^2 and 2x^2. Only like terms can be combined (L2).
Worked example

Take apart 4x^2 - 3x + 7. Step 1: Split it into terms. The + and - signs are the cuts, and each sign travels with the term after it: the terms are 4x^2, -3x, and 7. Step 2: Read each coefficient: 4x^2 has coefficient 4; -3x has coefficient -3 (not 3 - the sign is part of the term); the constant term 7 has coefficient 7 and degree 0. Step 3: Read each degree: 4x^2 has degree 2; -3x has degree 1 (x means x^1); 7 has degree 0. Step 4: The degree of the polynomial is the greatest single degree: 2. It is a quadratic. Say it plainly: degree is a "biggest wins" rule. You never add the exponents of different terms - they live on different terms.

Check yourself — explain it

In 4x^2 - 3x + 7, why is the coefficient of the x-term -3 and not 3?

Paired problem — example still visible

Take apart 2x^3 + 5x - 9: list the terms, coefficients, and the degree of the polynomial. -> Terms 2x^3, 5x, -9; coefficients 2, 5, -9; degree 3

Faded completion — last step is yours

"In 6x^2 - x + 4, the coefficient of x is ___ and the degree of the polynomial is ___." -> -1; 2 (a bare x has coefficient 1, and here the term is -x, so -1)

Ready to practise?

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

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