Year 7: Coefficients and Constants (Advanced)

Quick Reference

Coefficient: The number multiplied by a variable
Constant: A standalone number in an expression
Polynomial: An expression with multiple terms and different powers

Identifying Coefficients in Polynomial Expressions

In more complex algebraic expressions, coefficients appear with different powers and multiple variables.

Examples with various structures:

In $7 x^{2} + 3 x - 5$ , the coefficients are 7 (for x²) and 3 (for x), with constant -5
In $- 4 a^{3} + 2 a^{2} - a + 8$ , the coefficients are -4, 2, -1, with constant 8
In $5 x y + 3 x + 2 y + 1$ , coefficient of xy is 5, coefficient of x is 3, coefficient of y is 2, constant is 1

Understanding Variables and Powers

Important: Each unique variable or power combination has its own coefficient:

Different variables: x and y are different, so $3 x + 5 y$ has two separate coefficients
Different powers: x and x² are different terms, so their coefficients are separate
Constant term: Always has coefficient 1 in the expression's constant value

Key Insight: To find ALL coefficients in an expression, identify each unique term (variable and power combination), then note the number multiplying each.

Common Mistakes:

Confusing the coefficient with the power: In 2x³, the coefficient is 2 (not 3)
Forgetting implicit coefficients: x means 1x, not 0x
Mixing up coefficients of different variables: In $3 x + 5 y$ , they're separate coefficients