What is the constant term of the polynomial 9x3 + 5x2 − 8x −10?
Answer: The constant term is −10.
Step-by-step solution
Idea: The constant term is the term with no variable in it (the coefficient of x0). Its sign is part of it.
- Terms: 9x3, 5x2, −8x and −10. Only −10 has no x in it.½ mark
- So the constant term is −10 (not 10: the minus sign belongs to the term).½ mark
The constant term is −10.
Answer to write in the exam
Terms: 9x3, 5x2, −8x, −10
∴ Constant term = −10
Common mistakes that cost marks
- Writing 10 instead of −10, dropping the sign in front of the term.
- Giving −8 (the coefficient of x) because it is the last number next to a letter.
- Thinking the constant term is the coefficient of the highest power (9).
How this can come in the exam
MCQ (1 mark)
The constant term of 4 − 7t + t2 is
- −7
- 1
- 4
- 0
Show answer
(C) 4
The term without t is 4, even though it is written first.
Short answer (2 marks)
For the polynomial p(x) = 2x2 − 5x − 3, find the constant term and show that it equals p(0).
Show answer
Constant term = −3 (1 mark). p(0) = 2(0) − 5(0) − 3 = −3, the same (1 mark): putting x = 0 removes every term except the constant.Try one yourself
Write the constant term of 6y2 − y − 12.
Show answer
−12.
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