Question

what is the remainder, when x^3+3x^2+4z+6 is divided by x +3?​

Answer 1

Correct Question :-

• What is the remainder, when x³+ 3x²+ 4x + 6 is divided by x + 3?

Answer :-

• Remainder = 0

Given :-

• Divisor = x + 3
• Dividend = x³+ 3x²+ 4x + 6

To Find :-

• Remainder = ?

Explanation :-

Let us first find the value of 'x' in divisor,

$\rm : \; \mapsto x+3 = 0$

$\rm : \; \mapsto x = 0-3$

$\green { \bf : \; \mapsto x = -3 \qquad \star}$

Now substituting the value of 'x' in dividend,

$\rm : \; \mapsto \; \; p(x) = x^3+3x^2+4x+6$

$\rm : \; \mapsto \; \; p(-3) = (-3)^3+3(-3)^2+4(-3)+6$

$\rm : \; \mapsto \; \; = (-3)+3(3)+(-12)+6$

$\rm : \; \mapsto \; \; = -3+9-12 +6$

$\rm : \; \mapsto \; \; = 9+6-3-12$

$\rm : \; \mapsto \; \; = 15-15$

$\blue { \underline { \boxed { \bf : \; \mapsto \; \; = 0 }}}$

Hence, the remainder when x³+ 3x²+ 4x + 6 is divided by x + 3 is 0.

Answer 2

Answer:

-6 is the remainder

Step-by-step explanation:

p(x) = x³ + 3x² + 4x + 6

g(x) = x+3

Using remainder theorem,

Zero of the divisor g(x) is:

g(x) = 0

=> x + 3 = 0

=> x = -3

Therefore,

Remainder = p(-3) = (-3)³ + 3×(-3)² + 4×-3 + 6

= -27 + 27 - 12 + 6 = -6