SOLUTION: The polynomial ax^3+bx^2+cx+d is factored at 3(x-2)(x+3)(x-4). What are the values of "a" and "d"?

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Question 1180342: The polynomial ax^3+bx^2+cx+d is factored at 3(x-2)(x+3)(x-4). What are the values of "a" and "d"?
Found 3 solutions by greenestamps, Edwin McCravy, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


"a" is the coefficient of the x^3 term; it is the constant 3, multiplied by the coefficients of the x terms in the three binomial factors.

ANSWER: a = 3(1)(1)(1) = 3

"d" is the constant term; it is the constant 3, multiplied by the constant terms in the three binomial factors.

ANSWER: d = 3(-2)(3)(-4)=72
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Greenestamps made an arithmetic error on d.

Or you could muliply it out and find b and c as well.



Multiply the last two binomials:



Multiply the binomial and the trinomial:



Combine like terms:



Distribute the 3:



Compare to 





Edwin
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

It can be easily answered  MENTALLY,  without making  FOIL. 

    The leading coefficient  " a "  at x^3 is 3 (obviously).


    The constant term " d "  is three times the product of the numbers (-2), 3 and (-4);


    so,  d = 3 * (-2)*3*(-4) = 3 * (24) = 72.     ANSWER

Solved.



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