Question

. When a polynomial p(x) is divided by the
polynomial x2 + 2x + 3, then the remainder is 4
and quotient is x – 3. Then p(x) is equal to
(a) x3 – x2 + 3x + 5 (b) x3 – x2 – 3x – 5
(C) x3 + x2 + 3x + 5 (d) x3 + x2 + 3x - 5​

Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

Answer:

make me BRAINLIEST

Step-by-step explanation:

use this formula

dividend = divisor x quotient x remainder