Answer:
-22x +5
Explanation:
You want to know what must be subtracted from (4x⁴ -2x³ -6x² +x -5) to make it exactly divisible by (2x² +3x -2).
Remainder
The quartic expression will be exactly divisible by the quadratic expression if the division results in a remainder of zero. This tells us that the amount that needs to be subtracted can be found by determining the remainder from the division of the expressions as they are.
The first attachment shows the long division of the quartic by the quadratic. The resulting remainder is (-22x +5).
The amount that must be subtracted is (-22x +5).
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Additional comment
The second attachment shows verification that the remainder is zero when the quantity (-22x +5) is subtracted from the quartic.
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