Question

find remainder when 3x^2+x-1 is divided by x+1​

Answer 1

Given :-

Quadratic expression : 3x² + x - 1

Required to find :-

Remainder when it is divided by ( x + 1 )

Condition mentioned :-

• No condition

Method used :-

• Remainder theorem

Solution :-

Given information :-

Quadratic expression :- 3x² + x - 1

we need to find the remainder when it is divided by ( x + 1 )

Let's consider the polynomial as ;

p ( x ) = 3x² + x - 1

when p ( x ) is divided by ( x + 1 ) it leaves remainder

So,

Let ;

=> x + 1 = 0

=> x = - 1

substitute this value in place of x in p ( x )

p ( - 1 ) = 3 ( - 1 )² + ( - 1 ) - 1

p ( - 1 ) = 3 ( 1 ) - 1 - 1

p ( - 1 ) = 3 - 2

p ( - 1 ) = 1

Therefore ,

When ( x + 1 ) divided p ( x ) it leaves remainder as 1

Verification :-

Now, let's perform long division to know whether our answer is correct or wrong

$\rm x + 1 \big)3 {x}^{2} + x - 1 \big(3x - 2 \\ \: \: \: \: \: \: \: \: \: \: \rm \: \: 3 {x}^{2} +3x \\ \: \: \: \: \: \: \: \: \: \: \rm \underline{( - )( - ) \: \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm - 2x - 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm - 2x - 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \underline{( + ) \: ( + ) \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 \: \: \: \: }$

Hence verified !

Answer 2

$\huge\sf\pink{Answer}$

☞ Remainder is equal to 1

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ 3x²+x-1 ÷ x+1

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ The remainder?

$\rule{110}1$

$\huge\sf\purple{Steps}$

So here we simply have to equate the divisor with Zeros and then substitute the value found in the dividend. Then we would get a final number and that would be our Remainder

Calculating

➝ $\sf x+1 = 0$

➝ $\sf\red{ x = -1}$

Substituting the value of x in the dividend,

»» $\sf 3(-1)^2 + (-1) -1$

»» $\sf 3(1) - 1 -1$

»» $\sf 3 - 2$

»» $\sf\orange{Remainder = 1}$

$\rule{170}3$