Question

Given a polynomial f(x), if (x − 4) is a factor, what else must be true? f(0) = 4 f(0) = −4 f(4) = 0 f(−4) = 0

Answer 1

Question:

Given a polynomial f(x), if (x − 4) is a factor, what else must be true?

• f(0) = 4
• f(0) = −4
• f(4) = 0
• f(−4) = 0

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Solution:

f(x) is a polynomial.

(x - 4) is a polynomial of f(x).

By converse of factor theorem: If (x - a) is a factor of f(x), then, f(a) = 0.

On comparing (x - 4) with (x - a), we get,

• a = 4

So,

f(a) = 0

=> f(4) = 0