Question

(a) 5 calculators for 6125: 24
calculators for 24,000
(b) 21 staplers for 399; 14 staplers
for 238
(c) 3 litres for 180; 10 litres for
690.
(d) 96 for 8 batteries : 475 for 38
batteries.​

Answer 1

f(x) = (2x3 + 9x2 + x + k)

x – 1 = 0  ⇒ x = 1

∴ f(1) = 2 × 13 + 9 × 12 + 1 + k

= 2 + 9 + 1 + k

= 12 + k

Given that (x – 1) is a factor of f(x).

By the Factor Theorem, (x – a) will be a factor of f(x) if f(a) = 0 and therefore f(1) = 0.

⇒ f(1) = 12 + k = 0

⇒ k = -12.