Question

1. Find the remainder when x + 3x2 + 3x + 1 is divided by
iii) x​

Answer 1

$\huge\mathfrak\pink{Correct-question}$

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

GIVEN:-

Polynomial:- $p(x)=x+3x^2+3x+1$

Divisor:- $x+1$

TO FIND:-

REMAINDER

$\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {blue} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {} {answer}}}}}}}}}}}}}}}$

TO FIND THE REMAINDER ,LET'S USE REMAINDER THEOREM

SO REMAINDER THEOREM STATS THAT :-

If a polynomial f(x) is divided by x−a , the remainder is the constant f(a) , and f(x)=q(x)⋅(x−a)+f(a) , where q(x) is a polynomial with degree one less than the degree of f(x).

so x-a=x+1(divisor)

a=-1

now :-

$p(x)=x+3x^2+3x+1$

so p(-1) will be :-

$p(-1)=-1+3(-1)^2+3(-1)+1\\p(-1)=-1+3-3+1\\p(-1)=0$

SO THE REMAINDER IS 0

LEARN MORE AT:-

• https://brainly.in/question/41706183

Answer 2

Step-by-step explanation:

Given polynomial is f(x)=x3+3x 2+3x+1

It has to be divided by x+1.

Then x+1=0 or x=−1

Put the value x=−1, we get

f(−1)=(−1) 3 +3(−1)2+3(−1)+1

⇒f(−1)=−1+3−3+1

⇒f(−1)=0

So, the remainder is 0, then x+1 is divided polynomial x3 +3x2 +3x+1