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How to multiply my raster by factors depending on each polygon

sadaoui 
Hello,

I want to correct my raster with correction factors for each polygon.
each polygon I have to correct it with its own correction factor.

Is it possible to make the manipulation at once:  import my raster and my
polygons, then I will multiply my raster with a factor of each polygon.

or I must to cut my raster according to all polygons and then I multiply
each raster by its factor,  one by one (it is too long)

Best regards



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