Question

Solve This Problem please it's urgent

Answer 1

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P(X) = 6X⁴ + 8X³ + 17X² + 21X + 7





Remainder = AX + B


And,




G(X) = 3X² + 4X + 1





On dividing P(X) by G(X) we get,







3X²+4X+1 )6X⁴+8X³+17X² +21X + 7(2X² +5






*************6X⁴ + 8X³ + 2X²





----------------------------------------------------



***********************+15X² + 21X + 7





***********************+15X² + 20X + 5





------------------------------------------------------





Remainder = X + 2





According to question,



When polynomial 6X⁴ + 8X³ +17X² +21X + 7 is divided by another polynomial 3X²+4X+1 , the remainder comes AX+B.




So,




Remainder = Remainder

X + 2 = AX + 2








Clearly,





Coefficient of X is 1 and constant term is 2.



Therefore,



A = 1 and B = 2






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