3(1) + b = 5 \implies b = 2.

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• 3a + b &= 5, \\
• 5a + b &= 7.
• Substitute \( a = 1 \) back into \( 3a + b = 5 \):
• Substitute \( a = 1 \) and \( b = 2 \) into \( a + b + c = 6 \):
• + 2 + c = 6 \implies c = 3.
• Thus, the polynomial is \( f(x) = x^2 + 2x + 3 \).

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