What is the coefficient of z in the polynomial 4z3 + 5z2 − 11?
Answer: The coefficient of z is 0, because there is no z term.
Step-by-step solution
Idea: If a power of the variable does not appear, its coefficient is 0. We can always add a “missing” term with coefficient 0 without changing the polynomial.
- Write the polynomial with every power of z shown: 4z3 + 5z2 + 0z − 11. Adding 0z = 0 changes nothing.½ mark
- So the number multiplying z is 0. The coefficient of z is 0.½ mark
The coefficient of z is 0.
Answer to write in the exam
4z3 + 5z2 − 11 = 4z3 + 5z2 + 0z − 11
∴ Coefficient of z = 0
Common mistakes that cost marks
- Answering 1. A coefficient of 1 would mean the term +z is present; here there is no z term at all.
- Answering −11. That is the constant term (the coefficient of z0), not the coefficient of z.
- Saying “no coefficient” or “does not exist”. The correct answer is the number 0.
How this can come in the exam
MCQ (1 mark)
The coefficient of x2 in x3 − 6x + 2 is
- 1
- −6
- 0
- 2
Show answer
(C) 0
There is no x2 term: x3 + 0x2 − 6x + 2. So the coefficient is 0.
Short answer (2 marks)
For p(y) = 3y4 − 2y + 9, write the coefficients of y4, y3, y2 and y.
Show answer
Write 3y4 + 0y3 + 0y2 − 2y + 9 (1 mark). Coefficients: 3, 0, 0, −2 (1 mark).Try one yourself
What is the coefficient of m2 in 7m3 − m + 4?
Show answer
0 (there is no m2 term).
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