Question

please Ans needed of this q, fast...... also needed detailed explanation​

Answer 1

Answer:

Let p(x) = 3x3 + x2 - 22x + 9

and q(x) = 3x2 + 7x - 6

We know if p(x) is divided by q(x) which is quadratic polynomial therefore if p(x) is not exactly divisible by q(x) then the remainder be r(x) and degree of r(x) is less than q(x) (or Divisor)

∴By long division method Let we added ax + b (linear polynomial) is p(x), so that p(x) + ax + b is exactly divisible by 3x2 + 7x - 6.

Hence p(X) + ax + b = s(x)

= 3x3 + x2 - 22x + 9 ax + b = 3x3 + x2 - x(22 - a) + (9 + b)

Hence, x(a – 2 + b – 3 = 0. x+0)

⇒ a - 2 = 0 & b - 3 = 0 ⇒ a = 2 or b = 3

Hence, if we add ax + b or 2x + 3 in p(x) then it is exactly divisible by 3x2 + 7x - 6