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factor the expression

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2 Answers

To factor the equation, you must first list the multiples of 14, which are +/-1 & 14 and +/- 2 & 7. Usually, you would need to only add the multiple pair together and that would give you the number next to the x, but since there is a 3 next to the x2, you must multiply one multiple by 3d and one by d. Try it both ways. If it was (3d+7)(d+2), that would only be 3d2+13d+14. If you switch the 7 and 2 to be (3d+2)(d+7), you will get 3d2+23d+14.

3d2+23d+14

We can start with one of the factors to have a coefficient of 3 on the variable d and the other coefficient to be one because of the coefficient on d2.

(3d+?)(d+?)

We know the ?'s have to multiply to 14, so we can try 1 and 14 or 2 and 7.  We see that when we use 2 and 7 in the following manner, when multiplied and added, we obtain the expected coefficient of d, 23, in the original expression.

(3d+7)(d+2)