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"?

Algebra ->  Polynomials-and-rational-expressions -> 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"?      Log On


   

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) About Me  (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) About Me  (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.

3%28x-2%29%28x%2B3%29%28x-4%29

Multiply the last two binomials:

3%28x-2%29%28x%5E2-x-12%29

Multiply the binomial and the trinomial:

3%28x%5E3-x%5E2-12x-2x%5E2%2B2x%2B24%29%29

Combine like terms:

3%28x%5E3-3x%5E2-10x%2B24%29%29

Distribute the 3:

3+x%5E3+-+9+x%5E2+-+30+x+%2B+72

Compare to 

ax%5E3%2Bbx%5E2%2Bcx%2Bd



Edwin

Answer by ikleyn(52803) About Me  (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.