The expression 4x2 - 4 has the following as its factors EXCEPT

Analyze the question: We need to factorise 4x² − 4 completely and find which option is NOT a factor.

Concept: Take out the common factor first, then use the difference of two squares: a² − b² = (a − b)(a + b).

Solution:

4x² − 4 = 4(x² − 1) = 4(x − 1)(x + 1)

So the factors include: 4, (x − 1), (x + 1), (x² − 1), and also combinations such as 4(x − 1) = 4x − 4 and 4(x + 1) = 4x + 4.

Checking each option:

• A. x − 1 → a factor ✔
• B. x + 1 → a factor ✔
• C. x² − 1 → a factor, since 4x² − 4 = 4(x² − 1) ✔
• D. 4x + 1 → not a factor ✘. The factor would be 4x + 4, not 4x + 1. Check: at x = −1/4, 4x² − 4 = 4(1/16) − 4 = −15/4 ≠ 0, so (4x + 1) does not divide the expression.
• E. 4x − 4 → a factor, since 4(x − 1) = 4x − 4 ✔

Tip: In "EXCEPT" questions, factorise fully first, then test each option. Always take out the common factor before using the difference of two squares. A quick check is to substitute the root of an option (for example, x = −1/4 for 4x + 1) into the expression. If the result is not zero, it is not a factor.