Find the value of the linear polynomial 5x − 3 if:
- (i) x = 0
- (ii) x = −1
- (iii) x = 2
Answer: (i) −3 (ii) −8 (iii) 7
Step-by-step solution
Idea: To find the value, put the given number in place of x (use brackets for negative numbers) and simplify.
(i) x = 0
- 5x − 3 = 5(0) − 3½ mark
- = 0 − 3 = −3½ mark
−3
(ii) x = −1
- 5x − 3 = 5(−1) − 3½ mark
- = −5 − 3 = −8½ mark
−8
(iii) x = 2
- 5x − 3 = 5(2) − 3½ mark
- = 10 − 3 = 7½ mark
7
(i) −3 (ii) −8 (iii) 7
Check: The values go up by 5 each time x goes up by 1: from x = −1 to 0 the value rises from −8 to −3 (+5), and from 0 to 2 it rises by 10 = 2 × 5 ✓. That is what a linear polynomial with coefficient 5 should do.
Answer to write in the exam
(i)
5(0) − 3 = 0 − 3
∴ Value = −3
(ii)
5(−1) − 3 = −5 − 3
∴ Value = −8
(iii)
5(2) − 3 = 10 − 3
∴ Value = 7
Common mistakes that cost marks
- Writing 5x at x = −1 as 5 − 1 = 4. 5x means 5 × x = 5 × (−1) = −5.
- Getting −5 − 3 = −2. Two negatives add up: −5 − 3 = −8.
- Writing 5(0) = 5. Anything multiplied by 0 is 0.
How this can come in the exam
MCQ (1 mark)
The value of 4 − 7y at y = −2 is
- −10
- 18
- 10
- −18
Show answer
(B) 18
4 − 7(−2) = 4 + 14 = 18.
Short answer (2 marks)
If p(x) = 3x + 8, find p(−4) and p(23).
Show answer
p(−4) = −12 + 8 = −4 (1 mark). p(23) = 2 + 8 = 10 (1 mark).Try one yourself
Find the value of 6x + 1 at x = −3, x = 0 and x = 1.5.
Show answer
−17, 1 and 10.
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