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17 June, 15:26

Find the largest value of n such that 3x^2 + nx + 72 can be factored as the product of two linear factors with integer coefficients.

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  1. 17 June, 15:54
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    n = 217

    Step-by-step explanation:

    The quadratic expression that we have to factorize is 3x² + nx + 72.

    So, we have to find factors of (3 * 72) i. e. 216.

    Now, we can write 216 as

    (1 * 216), Hence, 1 + 216) = 217

    (2 * 108), Hence, 2 + 108 = 110

    (3 * 72), Hence, 3 + 72 = 75

    (4 * 54), Hence, 4 + 54 = 58

    So on.

    Therefore, to factorize 3x² + nx + 72, the maximum value of n which can be put in place of n to factorize the expression is 217. (Answer)
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