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 7x² + 3x - 5, the coefficients are 7 (for x²) and 3 (for x), with constant -5
In -4a³ + 2a² - a + 8, the coefficients are -4, 2, -1, with constant 8
In 5xy + 3x + 2y + 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 3x + 5y 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 3x + 5y, they're separate coefficients