Question

If the polynomial x⁴-6x³+16x²-25x+10 is divided by anothe polynomial x²-2x+k

Remainder comes out to be x+a ,Find k and a
Please solve​

Answer 1

Hi there!

Please refer the the attachment for answer..

Answer 2

x²-2x+k)x⁴-6x³-16x²+25x+10(x²-4x-(24+k)

             x⁴-2x³+kx²

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               -4x³-(16+k)x²+25x

               -4x³+8x² - 4kx

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             -(24+k)x²+(25+4k)x+10

             -(24+k)x² +2(24+k)x-k(24+k)

___________________________

                  (25+4k-48-2k)x+10+k(24+k)

Remainder = ( -23+2k)x + (k²+24k+10)

Remainder = ( x + a ) [ Given ]

-23 + 2k = 1

=> 2k = 1 + 23

=> 2k = 24

=> k = 12

and

k²+24k+10 = a

=> 12²+24×12+10 = a

=> 144+288+10 = a

=> 442 = a

Therefore ,

a = 442 ,

k = 12