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# (3x + 2) (2x - 5) = ax² + kx + n . What is the value of a - n + k ?

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Re: (3x + 2) (2x - 5) = ax² + kx + n . What is the value of a - n + k ? [#permalink]
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Bunuel wrote:
(3x + 2) (2x - 5) = ax^2 + kx + n . What is the value of a - n + k ?

A. 5
B. 8
C. 9
D. 10
E. 11

Given: $$(3x + 2)(2x - 5) = ax^2 + kx + n$$
Use FOIL to expand the left side: $$6x^2 - 15x + 4x - 10 = ax^2 + kx + n$$
Simplify: $$6x^2 - 11x - 10 = ax^2 + kx + n$$
At this point we can see that $$a=6$$, $$k = -11$$, and $$n = -10$$, which means $$a - n + k = 6 - (-10) + (-11) = 5$$