Question

When a polynomial is divided by x+2, the quotient and remainder are 2x-1 and 3 respectively. Find the polynomial. *

Answer 1

Answer:

We know, p(x)=[g(x)×q(x)]+r(x) [Division algorithm for polynomials]

p(x)=(2x−1)(7x  

2

+x+5)+4

p(x)=14x  

3

+2x  

2

+10x−7x  

2

−x−5+4

p(x)=14x  

3

−5x  

2

+9x−1

∴$ the dividend p(x)=14x  

3

−5x  

2

+9x−1

Step-by-step explanation:

We know, p(x)=[g(x)×q(x)]+r(x) [Division algorithm for polynomials]

p(x)=(2x−1)(7x  

2

+x+5)+4

p(x)=14x  

3

+2x  

2

+10x−7x  

2

−x−5+4

p(x)=14x  

3

−5x  

2

+9x−1

∴$ the dividend p(x)=14x  

3

−5x  

2

+9x−1