Adding + Subtracting Polynomials – Leveled Worksheet

Add polynomials by combining like terms, as in 3x² − 4x + (2x² + 5x) = 5x² + x

Subtract a polynomial by distributing the negative across every term inside the bracket, as in x² − 7 − (2x² + 2) = −x² − 9

Judge whether a supplied answer to a polynomial problem is correct, and justify the judgement with written working

Introduce the matching, answer-checking and independent-solving formats one at a time.

Ask students to show how subtraction changes each term inside parentheses before combining like terms.

Use a selected answer as a starting point for discussing the working, rather than assuming why the student chose it.

Adding polynomials — Set A combines like terms across sums such as 3x² − 4x + (2x² + 5x) and x² + 5x + (3x² + 6x − 7).

Subtracting polynomials — Sets B, C and D all require distributing a negative across a bracket, as in x − 12 − (x² + 16x − 12), which the key expands term by term before simplifying.

Setting out working — Sets C and D both instruct students to show all work, and the key models intermediate lines in Sets B–D.