Is expansion necessary for this quadratic equation?

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SUMMARY

The expression (x+3)(x-4)(x-2)(x+1) = 24 cannot be transformed into a quadratic equation without expanding the factors. This expression is inherently quartic due to its four linear factors, which results in a fourth-degree polynomial. The only way to achieve a quadratic form would require the cancellation of the x^4 and x^3 coefficients, which is impossible given that the right-hand side is a constant. Therefore, expansion is necessary to analyze the equation properly.

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Kartik.
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(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?
 
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Kartik. said:
(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?

No, this will be a quartic (4th degree in x) whichever way you play with it. You can easily see this because the only way for it to become a quadratic is if the LHS x4 and x3 coefficients are cancelled, which isn't going to happen since the RHS only has a constant.
 
Kartik. said:
(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?

You should realize that 3 times 4 times 2 is equal to 24, so you definitely want to expand.
 

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