decompose the polynomial x^3 -13x^2 +43x-25 into two factors, given that x-5 is a factor

Answer 1

To find the other factor, we can perform long division.

x^2 - 8x + 5
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x - 5 | x^3 - 13x^2 + 43x - 25
- (x^3 - 5x^2)
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- 8x^2 + 43x
- (-8x^2 + 40x)
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3x - 25
- (3x - 15)
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- 10

Therefore, we have (x^3 - 13x^2 + 43x - 25) = (x - 5)(x^2 - 8x + 5).

Thus, the polynomial can be decomposed as: x^3 - 13x^2 + 43x - 25 = (x - 5)(x^2 - 8x + 5).