Factorising with Negatives

When the first term of an expression is negative, it is usual to take out a negative highest common factor so that the bracket starts with a positive term. In NSW Year 8 maths this means \(-6x + 15\) becomes \(-3(2x - 5)\) (NESA outcome MA4‑ALG‑C‑01).

You will factorise expressions with numbers, pronumerals and powers, such as \(-8xy^2 + 4x^2y\), remembering that dividing by a negative changes the sign of every term in the bracket. You will check each answer by expanding it and correct a student's error. Negative terms turn up whenever money is owed, a tank drains or a temperature falls. It is part of Year 8 Algebra.