2018 · Q17
If f(x) and g(x) are polynomials of degree p and q respectively, then the degree of f(x) ± g(x) (if it is non-zero) is
Elementary MathematicsAlgebra
- AGreater than min(p, q)
- BGreater than max(p, q)
- CLess than or equal to max(p, q)
- DEqual to min(p, q)
Explanation
Adding or subtracting polynomials can only cancel the leading terms; it can never create a term of higher degree than both summands. Hence the degree of f(x) ± g(x) is at most max(p, q), option (C). The trap is option (B), which ignores cancellation.