The image shows the first few steps of the polynomial division (3x4+9x2−13)÷(x2−5x). Complete the division process and find the remainder of this polynomial division.

Answer 1

The polynomial division of (3x^4 + 9x^2 - 13) ÷ (x^2 - 5x) can be completed as follows:

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x^2 - 5x | 3x^4 + 9x^2 + 0x - 13
- (3x^4 - 15x^3)
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24x^3 + 0x^2

Now, we continue with the division:

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x^2 - 5x | 3x^4 + 9x^2 + 0x - 13
- (3x^4 - 15x^3)
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24x^3 + 0x^2 - 13
- (24x^3 - 120x^2)
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120x^2 - 13

Since no further division is possible, we can conclude that the remainder of the polynomial division is 120x^2 - 13.