Question

The polynomial x3 - 3x² + 4x - 12 is exactly divisible by
a) (x - 2)
b) (x-3)
c) x + 2
d)all​

Answer 1

I solved this a different way from the elegant solutions provided

. Because I was looking for a result that had x-3 as a factor, I attempted to find an equation that nearly matches the stated target

result: x^3 - 3x^2 + 4x - 13.

Starting with (x^2 - n)(x - 3) = x^3 - 3x^2 - nx + 3n, I notice the signs for the last 2 elements need to be reversed, so (x^2 + n)(x - 3) = x^3 - 3x^2 + nx - 3n.

Now, eliminating common components, the differences between target and model require that nx - 3n ~= 4x - 13. Taking n = 4,

we now have (x^2 + 4)(x - 3) = x^3 - 3x^2 + 4x - 12.

Striking the equivalent components, we see -13 + m = -12. [m represents the amount to add to the original equation to result in x - 3 being a factor of the polynomial.]

Isolating m by subtracting 13 from both sides,

we get m = 13 - 12. m = 1.

Answer 2

Answer:

(x-3)

Step-by-step explanation:

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