Solution:
3-7-5
3 9 -42 19 70 2596 -7 -42 19-42 496 -14 -5 -30 70 25-30 70 250Therefore, 9 x^4 − 42 x^3 + 19 x^2 + 70 x+ 25 =3x^2 − 7 x− 5
In the above example, the coefficients viz., 9, -42, 19, 70 and 25 are detached from
the polynominal and written in order horizontally. Consider the first coeffecient 9.
Since 9 is a perfect square write its square root 3 in the place meant for quotient and
also to the left of 9. Multiply 3 with 3 and write the product 9 below 9 and subtract.
The result is zero. Now take the next two coeffecients -42 and 19. Double the
quotient 3 and write the value 6 to the left of -42. Identify a suitable number which
when multiplied by 6, gives -42. In this case the number is -7. Write -7 in the
quotient and to the left of -42 also. Now multiply and subtract -7 x 6 = -42 and -7 x
-7 = 49. Subtract -42 and 49 from -42 and 19 respectively. Repeat the procedure till
the remainder is zero. Note that if the remainder is zero then the polynominal is a
perfect square. Otherwise, the polynominal is imperfect.