Factoring Trinomials Worksheet – When a = 1

Factor a trinomial of the form x² + bx + c by finding the integer pair whose product is c and whose sum is b

Work confidently with all four sign combinations, including cases such as x² − 11x − 12 where the constant is negative and the middle term negative

Find factor pairs of larger constants such as 55, 56, 77 and 84 rather than relying on small numbers

The two pages are self-contained — problems 1 to 9 use letters A to I and problems 10 to 18 use J to R — so one can be classwork and the other homework without breaking the matching

Tell students to work the whole block before writing any letters; the check only works once all nine are placed and every letter has been used once

Problems 5, 12 and 17 lean on factor pairs of 77, 55 and 84, so a quick review of divisibility is worth doing before the sheet goes out Students ready to move beyond a leading coefficient of one can try factoring trinomials when a is not 1.

Factoring trinomials when a = 1 — students turn eighteen expressions such as x² − 18x + 77 into (x − 11)(x − 7) by finding the integer pair that multiplies to the constant and adds to the middle coefficient.

Handling every sign pattern — the set deliberately mixes x² + 11x + 18, x² + 7x − 60, x² − 13x + 30 and x² − 11x − 12, so both signs in a factor pair have to be reasoned about rather than guessed.

Factor pairs of larger numbers — x² + 5x − 84, x² + 16x + 55 and x² + 15x + 56 push students past the small constants that make trial and error easy.