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Select ALL of the following for which there exist nonzero constants which can be

ID: 3031395 • Letter: S

Question

Select ALL of the following for which there exist nonzero constants which can be substituted into the equation to make it true. [Hint: compare the left and right sides as x goes to infinity.]

Submission 1 (0/0.7 points) Saturday, October 15 2016 11:21 PM EDT Select ALL of the following for which there exist nonzero constants which can be substituted into the equation to make it true [Hint: compare the left and right sides as x goes to infinity.] (x + 1)(x +4)(x +9) x+1 x + 4 x 9 ax (x + 1)(x + 4) (x +9) x+1 x + 4 x9 ax (x + 1)(x + 4)(x +9) X+1 x + 4 x 9 4 ax (x + 1)(x + 4)(x +9) X+1 x + 4 X9 None of the Above

Explanation / Answer

Multiplying each case with (x+1)(x+4)(x+9) on both sides

1) a(x+1)(x+4)(x+9) = b(x+4)(x+9) + c(x+1)(x+9) +d (x+1)(x+4)

LHS a   (x^2 + 5x +4)(x+9) = a(x^3 +9x^2 +5x^2 +45x +4x +36) = a(x^3 +14x^2 +49x +36)

RHS b(x^2 +13x + 36) + c(x^2 +10x +36) + d(x^2 +5x +4)

all constants exist on comaoring LHS and RHS

2) ax = b(x+4)(x+9) + c(x+1)(x+9) +d (x+1)(x+4)

all constants exist on comaoring LHS and RHS

3) ax^2 = b(x+4)(x+9) + c(x+1)(x+9) +d (x+1)(x+4)

all constants exist on comaoring LHS and RHS

4) ax^3 = b(x+4)(x+9) + c(x+1)(x+9) +d (x+1)(x+4)

constant a does not exist as there are no x^3 terms on RHS

So, all constants do not exist

5) ax^4 = b(x+4)(x+9) + c(x+1)(x+9) +d (x+1)(x+4)

constant a does not exist as there are no x^4 terms on RHS

So, all constants do not exist

Option 1,2,3