Question

Divide f(y) by g(y) and find the quotient and remainder f (y) = y + 3y2 - 1 and g (y) = 1 + y​ please answer with explanation correctly please​

Answer 1

Answer:

quotient =3y-2

remainder=1

Step-by-step explanation:

f(y)=y+3y2-1

g(y)=1+y

or

u can find remainder by substituting y=-1

3y2+y- 1

3(-1)^2+(-1)-1

3-1-1

1

Answer 2

Given,

•  f(y) = y + 3y²-1
•  g(y) = 1 + y

We know that,

 

                    $\boxed{Dividend=Divisor \times quotient + remainder}$

Therefore,

   

              f(y) = g(y) × quotient + remainder

∵ remainder is always less than divisor

Similarily,

       f(y)>remainder of $f(y)\div g(y)$

∵f(y) is a quadratic polynomial

∴its remainder is always linear or constant

∴Let the remainder be ax+b

 Let quotient be Q

Therefore,

$f(y) = g(y) \times Q + (ay+b)$

$y+3y^2-1=(1+y)\times Q + (ay+b)$

Putting y = -1

-1 + (3(-1))^2 -1 = 0 - ay +b

    1 = -a +b

On comparing both sides,

we get,  

  a = 0 and b = 1

Therefore,

$\boxed{Remainder = 1}$

On putting value of remainder  

$y+3y^2-1= (1+y)\times Q + 1$

$\boxed{Q=3y-2}$

I had showed full method..

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