Absolute value and factorising, in the words your course notes use. Use these words in your answers.
Absolute value: the distance of a number from zero, so never negative; written |x|. Avoid: “modulus” (same thing, the notes mention it once).
Restriction: a condition an answer must satisfy, e.g. RHS ≥ 0 when |…| equals an expression in x. Answers that break it are rejected.
No solution: when the absolute value equals a negative number, or every case breaks the restriction.
Salient point: the sharp corner (p; q) of the graph of y = a|x − p| + q. Avoid: “vertex”, “turning point” (other sources use these).
Form: which standard shape the equation matches: y = a|x| + q or y = a|x − p|.
Factorise fully: write as a product of brackets that cannot be factorised any further.
Common factor (HCF): the biggest number, letter or bracket in every term; always taken out first.
Difference of squares: A² − B² = (A − B)(A + B).
Trinomial: a three-term quadratic ax² + bx + c, factorised into two brackets.
Grouping: splitting four terms into groups that share a common factor or bracket.
Sum and difference of cubes: A³ ± B³ = (A ± B)(A² ∓ AB + B²).
Factor theorem: if f(d/a) = 0 then (ax − d) is a factor of f(x) (term1 p.24).
Synthetic division: the short method from the notes for dividing a polynomial by a factor (x − k).
Cubic: a polynomial ax³ + bx² + cx + d.