Find the quotient and remainder of the following. (8x3 – 1) ÷ (2x – 1)

Find the quotient and remainder of the following.

(8x³ – 1) ÷ (2x – 1)

Sum

∴ The quotient = 4x² + 2x + 1

The remainder = 0

shaalaa.com

Is there an error in this question or solution?

Chapter 3: Algebra - Exercise 3.7 [Page 111]

Chapter 3 Algebra
Exercise 3.7 | Q 1. (iii) | Page 111

Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are `sqrt(5/3)` and - `sqrt(5/3)`

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg q(x) = deg r(x)

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.

Find all the zeros of the polynomial x⁴ + x³ – 34x² – 4x + 120, if two of its zeros are 2 and –2.

If x³ + x² – ax + b is divisible by (x² – x), write the values of a and b.

State division algorithm for polynomials.

Find the quotient and remainder of the following.

(8y³ – 16y² + 16y – 15) ÷ (2y – 1)

Can x² – 1 be the quotient on division of x⁶ + 2x³ + x – 1 by a polynomial in x of degree 5?

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.

Given that `x - sqrt(5)` is a factor of the cubic polynomial `x^3 - 3sqrt(5)x^2 + 13x - 3sqrt(5)`, find all the zeroes of the polynomial.