Grade9 polynomials, linear relations and equations
Terms represent complete algebraic quantities
A polynomial is built from terms with coefficients and whole-number variable exponents. Combine like terms only when their variable parts match. Three x terms and two x terms make five x terms; three x terms and two x-squared terms cannot be collapsed into five x-cubed. The degree of a one-variable polynomial is the greatest exponent with a nonzero coefficient, not the number of written terms.
Distribution applies to every term inside a group. In(x+3)(x+2), multiply each term in one factor by each term in the other, then combine: x-squared plus five x plus six. Checking a numerical substitution can reveal a missing cross product. When dividing terms by a monomial, divide coefficients and apply exponent laws separately, while keeping restrictions on any variable denominator.
Equations preserve equality
To solve a linear equation, apply equal operations to both sides and check the proposed value in the original expression. Removing a denominator requires multiplying the entire relevant side, not only the first term. In x/2+x/3=5, a common denominator gives 5 x/6=5 and therefore x=6. Substitution gives 3+2=5.
An inequality describes a set of permitted values. Reversing its direction when multiplying or dividing by a negative number preserves the same ordered relationship. Interpret a boundary and inclusive symbol in context instead of treating every inequality as a single-value equation.
Relate tables, graphs and equations
A linear relationship has a constant rate of change over equal input changes. A vertical intercept describes the output when the input is zero in a model where that input is meaningful. In y=−3 x+7, the rate is−3 and the vertical intercept is 7. A negative rate means the output decreases as input increases; it does not automatically make every output negative.
A table's pattern should be tested across several rows before extrapolating. Define variables and units in a word problem, identify whether there is a starting amount and distinguish rate from total. Related school sources can reinforce these foundations, but higher quadratic, exponential, trigonometric or calculus problems are not substituted indiscriminately for Saskatchewan grade 9 linear and polynomial work.