Question

The remainder obtained when x⁵-x⁴+3x³+4x²-3x-3 divide by x²+1.​

Answer 1

Step-by-step explanation:



TOPICS

Number Systems

Polynomials

Coordinate Geo.

Linear Equation

Euclid's Geo.

Lines & Angles

Triangles

Quadrilaterals

Area of Triangles

Circles

Constructions

Heron's Formula

Surface Area & Vol.

Statistics

Probability

Exercise - 2.4

PreviousHomeNext

Polynomials

Question-1 :- Determine which of the following polynomials has (x + 1) a factor :

(i) x³ + x² + x + 1,    (ii) x⁴ + x³ + x² + x + 1,    (iii) x⁴ + 3x³ + 3x² + x + 1,    (iv) x³ - x² - (2 + √2)x + √2.

Solution :-

(i) x³ + x² + x + 1

Let x + 1 is a factor of given polynomial.

Now, x + 1 = 0

x = -1

p(-1) = (-1)³ + (-1)² + (-1) + 1

= -1 + 1 - 1 + 1

= 2 - 2 = 0

Therefore, It is confirmed that x + 1 is a factor of x³ + x² + x + 1.

(ii) x⁴ + x³ + x² + x + 1

Let x + 1 is a factor of given polynomial.

Now, x + 1 = 0

x = -1

p(-1) = (-1)⁴ + (-1)³ + (-1)² + (-1) + 1

= 1 - 1 + 1 - 1 + 1

= 3 - 2 = 1

Therefore, x + 1 is not a factor of x⁴ + x³ + x² + x + 1.

Answer 2

Answer:

answer is x³-x²+2x+5.

r = -5x-8