Question

If the polynomial x^3 + 3x^2 + 3x + 1 is divided by 2x - 1, then the remainder is ​

Answer 1

AnswEr:-

Your Answer Is 27/8.

ExplanaTion:-

Here we can find it out by two methods:-

1) Long Division Method.

2) Factor Theorem.

[So long division method is already done in the attachment].

By Factor Theorem:-

Since we have to divide x³ + 3x² + 3x + 1 by 2x -1 to find out the remainder.

So firstly let us consider 2x - 1 be a factor of the given polynomial.

So let us find out the value of x by putting 2x -1 = 0.

↦ 2x - 1 = 0.

↦ 2x = 1.

↦ x = 1/2.

By putting the value of x in the given polynomial we get:-

↦ x³ + 3x² + 3x + 1

= (1/2)³ + 3(1/2)² + 3(1/2) + 1.

= 1/8 + 3(1/4) + 3/2 + 1.

= 1/8 + 3/4 + 3/2 + 1.

$\tt = \dfrac{1+6+12+8}{8}.$

[By Taking LCM].

= 27/8 = Remainder.

Therefore the remainder = 27/8.