If two polynomials F(x) and G(x) are equal for all x, which of the following is correct? i. their equality is called an identity ii. the polynomials can be written as F(x) ≡ G(x) iii. their degrees are unequal

Mymensingh Board 2023

If two polynomials F(x) and G(x) are equal for all x, which of the following is correct?

Think it through first, then pick an option.

Answer and explanation

Correct answer: a i and ii

i and ii are true: it is called an identity and written F(x) ≡ G(x); iii is false, polynomials equal for all x have equal degrees.

Why the other options are wrong

b i and iii: iii is false, so the pair i and iii is wrong; the coefficients are equal, so the degrees are equal.
c ii and iii: iii is false, so the pair ii and iii is wrong.
d i, ii and iii: Because iii is false, the three cannot all be correct.