alleryIf p(x) is a polynomial and p(a) = 0 for some number a, then which first-degree polynomial is a factor of p(x)?
Ax + a
Ba − x
Cax + 1
Dx − a
Answer & Solution
Correct answer: D. x − a
1. The factor theorem links roots of p(x) to first-degree factors.
2. If p(a) = 0, then x − a is a factor of p(x).
3. This is the unit's Factor Theorem statement.
4. Conversely, if x − a is a factor of p(x), then p(a) = 0.
5. So the correct factor is x − a, not x + a or a − x.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
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