Q. 44.4( 324 Votes )
On dividing x3 - 3x2 + x + 2 by a polynomial g(x) the quotient and remainder were (x - 2) and (-2x + 4), respectively. Find g(x).
Polynomial, p(x) = x3 - 3x2 + x + 2 (dividend)
Quotient = (x − 2)
Remainder = (− 2x + 4)
To find : divisor = g(x)
Dividend = Divisor × Quotient + Remainder
⇒ x3 - 3x2 + x +2 = g(x) × (x - 2) + (-2x + 4)
⇒ x3 - 3x2 + x + 2 + 2x - 4 = g(x)(x - 2)
⇒ x3 - 3x2 + 3x - 2 = g(x)(x - 2)
g(x) is the quotient when we divide (x3 - 3x2 + 3x - 2) by (x - 2)
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
RELATED QUESTIONS :
Obtain all other zeros of (x4 + 4x3 ‒ 2x2 ‒ 20x ‒15) if two of its zeros are √5 and – √5.RS Aggarwal - Mathematics
If two zeroes of the polynomial p(x) = 2x4 + 7x3 - 19x2- 14x + 30 are √2 and - √2 then find the other two zeroes.RS Aggarwal - Mathematics
Let p(x) = 2x4 - 3x3 - 5x2 + 9x - 3 and two of its zeros are √3 and -√3. Find the other two zeros.RS Aggarwal - Mathematics