Unit 3
5 marks · Normal(a) Express 96 as a product of its prime factors in index form.
(b) The product of two numbers is 288. One of the numbers is 16. Using prime factors, find the other number.
(c) Factorise the expression completely.
Express 96 as a product of its prime factors in index form.
The product of two numbers is 288. One of the numbers is 16. Using prime factors, find the other number.
Factorise the expression completely.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) · must show 2^5, 3
(b) 18 · must show 18
(c) · must show 10x(x-4)
Common mistakes: Not writing in index form; Only taking out x in part c
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Attempts to write 96 as a product of factors.
A1 (a) · 1 mark · Correct final answer in index form.
M2 (b) · 1 mark · Divides 288 by 16 correctly or uses prime factors to find the missing number.
M3 (c) · 1 mark · Takes out the common factor (e.g., 10x or x).
A2 (c) · 1 mark · Fully factorised answer .
Worked solution
(a) 96 = 2 × 48 = 2 × 2 × 24 = 2 × 2 × 2 × 12 = 2 × 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 2 × 3 = .
(b) 288 ÷ 16 = 18, so the other number is 18.
(c) 10x^2 - 40x = 10x(x - 4).