0848[Yr11 Ext1] Polynomials - Identical Polynomials and the Identity (Congruence) Symbol ≡

Let P(x) and Q(x) represent two polynomials. P(x) is identical to Q(x) if P(x) x Q(x) for all values of x.

The symbol for "is identical to" is the congruence, or identity, symbol ≡.

For two polynomials P(x) and Q(x) to be identical, i.e. P(x) ≡ Q(x), the corresponding terms of each polynomial must be identical.
e.g. Let P(x) = 3x^2 + 5x - 9 and Q(x) = (A + 1)x^2 + (B - 3)x + C. P(x) ≡ Q(x) if and only if:

(A + 1)x^2 ≡ 3x^2 which means A = 2

(B - 3)x ≡ 5x which means B = 8 and C = -9 since C corresponds to the constant term.

Therefore, if P(x) ≡ Q(x), then A = 2, B = 8 and C = -9

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