Question

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. When the polynomial f(x) = 4x³ − 7x + 3 is divided by x − 1, the remainder is 0.
2. x − a is a factor of the polynomial f(x) if f(a) = 0.

Options

• Only (i)

• Only(ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

i. We check the remainder by evaluating:

x − 1 = 0

x = 1

f(1) = 4(1)³ − 7(1) + 3

= 4 − 7 + 3

= 0
Therefore, statement (i) is valid.

ii. The Factor Theorem, which states that when you substitute x = a in a polynomial and get zero, it means the polynomial is exactly divisible by x − a.