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📅 May 14, 2026 👤 scraface

May 14, 2026

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3a + b &= 5, \\
5a + b &= 7.
Substitute \( a = 1 \) back into \( 3a + b = 5 \):
3(1) + b = 5 \implies b = 2.
Substitute \( a = 1 \) and \( b = 2 \) into \( a + b + c = 6 \):
+ 2 + c = 6 \implies c = 3.
Thus, the polynomial is \( f(x) = x^2 + 2x + 3 \).
Now, calculate \( f(x+1) \):
f(x+1) = (x+1)^2 + 2(x+1) + 3.
= x^2 + 2x + 1 + 2x + 2 + 3 = x^2 + 4x + 6.

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