Question

if x3+a3 is divided by x+a then the reminder is

Answer 1

Answer :

Remainder = 0

Note :

★ Remainder theorem : If a polynomial p(x) is divided by (x - c) , then the remainder obtained is given as R = p(c) .

★ Factor theorem :

If the remainder obtained on dividing a polynomial p(x) by (x - c) is zero , ie. if

R = p(c) = 0 , then (x - c) is a factor of the polynomial p(x) .

If (x - c) is a factor of the polynomial p(x) , then the remainder obtained on dividing the polynomial p(x) by (x - c) is zero ,

ie. R = p(c) = 0 .

Solution :

Here ,

The given polynomial is x³ + a³ .

Let the given polynomial be p(x) .

Thus ,

p(x) = x³ + a³

Here ,

The given polynomial p(x) is being divided by (x + a)

Thus ,

If x + a = 0 , then x = -a

Now ,

The the remainder obtained on dividing the given polynomial p(x) by (x + a) will be given as ;

=> R = p(-a)

=> R = (-a)³ + a³

=> R = -a³ + a³

=> R = 0

Hence , Remainder = 0 .

Answer 2

p(x) = x + a

→ x + a = 0

→ x = 0 - a

.°. x = -a

______________....

g(x) = x³ + a³

→ g(-a) = (-a)³ + a³

→ g(-a) = -a³ + a³

→ g(-a) = -a + a

As we know that,

(-) × (+) = -

→ g(-a) = 0

.°. The remainder is 0...