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The terms in x in the factorisation must be 3 and 1, the whole numbers must be factors of 48 ie 1/48, 2/24, 3/16, 4/12, or 6/8. The only ones which can combine with the 3 to give a sum of 24 are 4 and 12 viz:

(3x + 12)(x + 4)

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What number is needed to complete the square x squared plus 24x equals 0?

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