Is expansion necessary for this quadratic equation?

AI Thread Summary
The equation (x+3)(x-4)(x-2)(x+1) = 24 represents a quartic polynomial, not a quadratic, due to its degree. It is impossible to transform it into a quadratic equation without multiplying the expressions, as the coefficients of x^4 and x^3 cannot be canceled out. The right-hand side of the equation is a constant, further confirming that expansion is necessary. Additionally, the product of the constants in the brackets equals 24, reinforcing the need to expand the equation. Therefore, expansion is essential to analyze the equation properly.
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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