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

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Answer 1 · 2018-06-22T11:41:38

$(x - 2)$ $(x-2)$ .

We know that,

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

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

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

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

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

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

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

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

What polynomial yields a quotient of 2x-32x−32x-3 and a remainder of 3 when it divides 2x^2-7x+92x2−7x+92x^2-7x+9?