What must be added to 3x^3+x^2-22x+9 …
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Posted by Geeta Bohra 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
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.
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