In the following question, two statements (i) and (ii) are given. Choose the valid statement. i. When the polynomial f(x) = 4x3 − 7x + 3 is divided by x − 1, the remainder is 0. ii. x − a is a factor of the polynomial f(x) if f(a) = 0.

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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.

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