What polynomial yields a quotient of #2x-3# and a remainder of 3 when it divides #2x^2-7x+9#?

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Answer 1 · 2018-06-22T11:41:38

# (x-2)#.

We know that,

The Dividend=(The Divisor)(The Quotient)+The Remainder.

So, if the Divisor Polynomial is #p(x)#, then,

#:. (2x^2-7x+9)=(2x-3)*p(x)+3#.

#:. 2x^2-7x+9-3=(2x-3)*p(x)#,

# i.e., 2x^2-7x+6=(2x-3)*p(x)#.

#:. p(x)=(2x^2-7x+6)/(2x-3)#,

#={(x-2)cancel((2x-3))}/cancel((2x-3))#.

# rArr" The Divisor Poly. is "(x-2)#.