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what must be subtracted from x^3 - 4x^2 + 3x - 9 to obtain a polynomial which is exactly divisible by (x-2)?

User Sa
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Answer: If we divide a polynomial by (x - 2) and obtain a quotient without a remainder, then (x - 2) must be a factor of the polynomial. Therefore, we need to find the factor of (x - 2) that will evenly divide the polynomial x^3 - 4x^2 + 3x - 9.

To do this, we can use long division or synthetic division. Let's use synthetic division:

2 | 1 - 4 + 3 - 9

| 2 - 4 - 2

|---------------

| 1 - 2 - 1 - 11

The result is a quotient of x^2 - 2x - 1 with a remainder of -11.

Since we want to obtain a polynomial that is exactly divisible by (x - 2), we need to subtract the remainder from the original polynomial, which gives:

x^3 - 4x^2 + 3x - 9 - (-11) = x^3 - 4x^2 + 3x + 2

Therefore, we need to subtract 11 from x^3 - 4x^2 + 3x - 9 to obtain a polynomial which is exactly divisible by (x-2). The resulting polynomial is x^3 - 4x^2 + 3x + 2.

Explanation:

User Yufei Zhao
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