Q12 of 84 Page 55

Polynomials bx2 + x + 5 and bx3 – 2x + 5 are divided by polynomial x – 3 and the remainders are and respectively. If m – n =0 then find the value of b.

Put x = 3 in the first polynomial:

b× (3)2 + 3 + 5 = m


9b + 8 = m ………………………………….. (i)


Put x = 3 in the second polynomial


b× (3)3 -2× 3 + 5 = n


27b -6 + 5 = n


27b -1 = n …………………………………. (ii)


Equation (i) – (ii)


m –n = 9b + 8 – (27b -1)


but m-n = 0


9b + 8 -27b + 1 = 0


-18b + 9 = 0


18b = 9


b = 9/18


b = 1/2


More from this chapter

All 84 →
10

For which the value of x + 3 is the factor of the polynomial x3 – 2mx + 21?

 11

At the end of the year 2016, the population of villages Kovad, Varud, Chikhali is 5x2 – 3y2, 7y2 + 2xy and 9x2 + 4xy respectively. At the beginning of the year 2017, x2 + xy – y2,5xy and 3x2 + xy persons from each of the three villages respectively went to another village for education then what is the remaining total population of these three villages?

 13

Simplify.

(8m2 + 3m – 6) - (9m-7) + (3m2 – 2m + 4)

 14

Which polynomial is to be subtracted from x2 + 13x + 7 to get the polynomial 3x2 + 5x – 4?