Question

What number should be subtracted from 2x^3-5x^2+5x so that the resulting polynomial has 2x-3 as the factor

Answer 1

We divide 2x3−5x2+5x by 2x−3 by long division method

\text{By division algorithm, we have}By division algorithm, we have

2x^3-5x^2+5x=(2x-3)(x2-x+1)+32x

3

−5x

2

+5x=(2x−3)(x2−x+1)+3

\therefore\textbf{3 should be subtracted from $\bf\,2x3-5x2+5x$}∴3 should be subtracted from 2x3−5x2+5x

\textbf{so that the resulting polynomial has factor $\bf\,2x-3$}so that the resulting polynomial h