Question

What should be subtracted from 12x^3 − 2x^3 + x + 7 so that ( 3x +1 ) is its factor? Also  find quotient.​

Answer 1

Answer:

Step-by-step explanation:

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

⇒p(x)−r(x)=g(x)×q(x)

It is clear the RHS of the above equation is divisible by g(x). i.e., the divisor.

∴ LHS is also divisible by the divisor.

Therefore, if we subtract remainder r(x) from dividend p(x), then it will be exactly divisible by the divisor g(x)]

Let us divide, 6x  

4

+13x  

3

+13x  

2

+30x+20 by 3x  

2

+2x+5

we get, quotient q(x)=2x  

2

+3x−1 remainder r(x)=17x+25

∴ If we subtract 17x+25 from 6x  

4

+13x  

3

+13x  

2

+30x+20, it will be exactly divisible by (3x  

2

+2x+5).

Answer 2

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

⇒p(x)−r(x)=g(x)×q(x)

It is clear the RHS of the above equation is divisible by g(x). i.e., the divisor.

∴ LHS is also divisible by the divisor.

Therefore, if we subtract remainder r(x) from dividend p(x), then it will be exactly divisible by the divisor g(x)]

Let us divide, 6x  

4

+13x  

3

+13x  

2

+30x+20 by 3x  

2

+2x+5

we get, quotient q(x)=2x  

2

+3x−1 remainder r(x)=17x+25

∴ If we subtract 17x+25 from 6x  

4

+13x  

3

+13x  

2

+30x+20, it will be exactly divisible by (3x  

2

+2x+5).