Advertisements
Advertisements
Question
Find the quotient and remainder of the following.
(8x3 – 1) ÷ (2x – 1)
Solution
∴ The quotient = 4x2 + 2x + 1
The remainder = 0
APPEARS IN
RELATED QUESTIONS
If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.
Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 15x3 − 20x2 + 13x − 12; g(x) = x2 − 2x + 2
Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm g(x) = 2x2 − x + 3, f(x) = 6x5 − x4 + 4x3 − 5x2 − x − 15
Obtain all zeros of f(x) = x3 + 13x2 + 32x + 20, if one of its zeros is −2.
Find all zeros of the polynomial f(x) = 2x4 − 2x3 − 7x2 + 3x + 6, if its two zeros are `-sqrt(3/2)` and `sqrt(3/2)`
What must be added to the polynomial f(x) = x4 + 2x3 − 2x2 + x − 1 so that the resulting polynomial is exactly divisible by x2 + 2x − 3 ?
Verify division algorithm for the polynomial `f(x)= (8 + 20x + x^2 – 6x^3) by g(x) =( 2 + 5x –3x^2).`
Can x2 – 1 be the quotient on division of x6 + 2x3 + x – 1 by a polynomial in x of degree 5?
If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)?
Find k so that x2 + 2x + k is a factor of 2x4 + x3 – 14 x2 + 5x + 6. Also find all the zeroes of the two polynomials.