Question

10) In the division of one
Polynomial by another, if the
divisor, quotient and
remainder are respectively (x-
2). (3x+1) and 3. Find the
dividend​

Answer 1

Answer:

We know that the division algorithm states that:

Dividend=Divisor×Quotient+Remainder

It is given that the divisor is x

2

+3x+5, the quotient is 2x

2

+x+2 and the remainder is 3. And let the dividend be p(x). Therefore, using division algorithm we have:

p(x)=[(x

2

+3x+5)(2x

2

+x+1)]+3

=[x

2

(2x

2

+x+1)+3x(2x

2

+x+1)+5(2x

2

+x+1)]+3

=2x

4

+x

3

+x

2

+6x

3

+3x

2

+3x+10x

2

+5x+5+3

=2x

4

+7x

3

+14x

2

+8x+8

Hence, the dividend p(x) is 2x

4

+7x

3

+14x

2

+8x+8.

Step-by-step explanation:

hope it helps you

Answer 2

Answer:

(x-2)*(3x-1)+3

3x²-x-6x+2+3

3x²-7x+3