Given the equation:

\[(3x + 2)(2x - 5) = ax^2 + kx + n\]

What is the value of \(a - n + k\)?

( 3 x + 2 ) ( 2 x − 5 ) = a x 2 + k x + n = 3 x ⋅ 2 x − 3 x ⋅ 5 + 2 ⋅ 2 x − 2 ⋅ 5 = = 6 x 2 − 15 x + 4 x − 10 = = 6 x 2 − 11 x − 10 a = 6 , n = − 10 , k = − 11 a − n + k = 6 − ( − 10 ) + ( − 11 ) = 6 + 10 − 11 = 5

Answered by Lilith | 2024-06-10

The value of a − n + k is 5 , calculated by expanding the given expression and identifying the coefficients. After finding a = 6 , k = − 11 , and n = − 10 , the substitution yields the final result. This demonstrates how to manipulate and simplify polynomial expressions effectively.
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Answered by Lilith | 2024-12-17