The LCM of two expressions is 3x ^ 3 + 18x ^ 2 + 30x + 12 and their HCF is x + 2 One of the expressions is x + 2 What is the sum of the coefficients (a,b), if the other expression can be represented as k(x ^ 2 + ax + b) ?

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Quintessence Classes · Accepted Answer

The correct answer is 6. To find the other expression, divide the Lowest Common Multiple by the Highest Common Factor.Dividing three x cubed plus eighteen x squared plus thirty x plus twelve by x plus two gives three x squared plus twelve x plus six.Factoring out the constant three from this expression gives three times the quantity x squared plus four x plus two.Comparing this to the form k times the quantity x squared plus a x plus b, we get:The constant k equals threeThe coefficient a equals fourThe constant b equals twoThe sum of the coefficients a and b is four plus two, which equals six.

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3

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4

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5

The LCM of two expressions is 3x ^ 3 + 18x ^ 2 + 30x + 12 and their HCF is x + 2 One of the expressions is x + 2 What is the sum of the coefficients (a,b), if the other expression can be represented as k(x ^ 2 + ax + b) ?

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