Question

Find the remainder when x^3 + 3x^2 + 3x + 1 is divided by 5 + 2x​

Answer 1

Answer:

-27/8

Step-by-step explanation:

p(x)=x^3 + 3x^2 + 3x + 1=x³+3x²+3x+1

g(x)=5 + 2x​=2x​+5

∴2x+5=0 or x= (-5/2)

Let us use the Remainder theorem to obtain the remainder when p(x) is divided by g(x)

p(x)=x³+3x²+3x+1

p(-5/2)=(-5/2)³+3(-5/2)²+3(-5/2)+1

=(-125/8)+3(25/4)-(15/2)+1

=(-125/8)+(75/4)-(15/2)+1

Taking LCM as 8, we get

p(-5/2)=(-125+150-60+8)/8

= -27/8

∴ -27/8 is the remainder