What is the first step when factorising a cubic polynomial by hand?
ADivide by the constant term
BGuess a root and test it
CComplete the square first
DTake out the highest power
Answer & Solution
Correct answer: B. Guess a root and test it
1. A cubic cannot be factorised by inspection in one move, so one factor has to be found first.
2. Looking at the coefficients suggests small values that might be roots.
3. Each guess is tested by substituting it into the polynomial and checking whether the result is zero.
4. A zero result confirms a root, and the factor theorem then supplies the matching linear factor.
5. Dividing the whole polynomial by its constant term does not produce a factor at all.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 5: Polynomials_
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