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p(x) = \frac{(x^22 - 33x - 4040)}{(x^22 + 1616x + 6464)}

Full solution

Q. p(x) = \frac{(x^22 - 33x - 4040)}{(x^22 + 1616x + 6464)}
  1. Factorization: Factor the numerator and denominator.\newline Numerator: x23x40x^2 - 3x - 40 factors to (x8)(x+5)(x - 8)(x + 5).\newline Denominator: x2+16x+64x^2 + 16x + 64 factors to (x+8)(x+8)(x + 8)(x + 8).
  2. Rewrite with Factored Forms: Rewrite the expression with the factored forms. p(x)=(x8)(x+5)(x+8)(x+8)p(x) = \dfrac{(x - 8)(x + 5)}{(x + 8)(x + 8)}
  3. Check for Common Factors: Check for common factors in the numerator \text{numerator} and denominator \text{denominator} . There are no common factors to cancel out.
  4. Simplified Form: The simplified form of the expression is already in its simplest form.