In division algorithm i.e Dividend = Divisior X Quotient +Remainder, if the divisor is a linear polynomial i.e degree is I, what will be the value of the remainder? (Koi h?)
Answers
Answer:
Assume polynomial p ( x ) in which degree of quotient q ( x ) is equal to the degree of r ( x ) , then put the values of p ( x ) , g ( x ) , q ( x ) and r ( x ) in the division algorithm. If L.H.S is equal to R.H.S then the division algorithm is satisfied.
If L.H.S is equal to R.H.S, then the division algorithm is satisfied.
Use the below given statement of Division algorithm to solve this question
Division algorithm
Dividend = Divisor × Quotient + Remainder
According to division algorithm, if p(x) and g(x) are two polynomials with g(x)≠0, then we can find polynomial q(x) and r(x) such that
p(x)=g(x)×q(x)+r(x)
Where r(x)=0 or degree of r(x)< degree of g(x)
Put the given values in the above equation and simplify it, get the value of g(x).
deg q(x)= deg r(x)
Let us assume the division of
x^{3}+x \text { by } x^{2} \\ p(x)=x^{3}+x \\ g(x)=x^{2} \\ q(x)=x, r(x)=x
Clearly, degree of
p(x) and q(x) is same i.e. 1.
Checking for division algorithm
p(x) =g(x) \times q(x)+r(x) \\ x^{3}+x =\left(x^{2} \times x\right)+x \\ x^{3}+x =x^{3}+x
Thus, the division algorithm is satisfied.
Step-by-step explanation:
hana me huo yarr...✌️
Answer:
Assume polynomial p ( x ) in which degree of quotient q ( x ) is equal to the degree of r ( x ) , then put the values of p ( x ) , g ( x ) , q ( x ) and r ( x ) in the division algorithm. If L.H.S is equal to R.H.S then the division algorithm is satisfied.
If L.H.S is equal to R.H.S, then the division algorithm is satisfied.
Use the below given statement of Division algorithm to solve this question
Division algorithm
Dividend = Divisor × Quotient + Remainder
According to division algorithm, if p(x) and g(x) are two polynomials with g(x)≠0, then we can find polynomial q(x) and r(x) such that
p(x)=g(x)×q(x)+r(x)
Where r(x)=0 or degree of r(x)< degree of g(x)
Put the given values in the above equation and simplify it, get the value of g(x).
deg q(x)= deg r(x)
Let us assume the division of
x^{3}+x \text { by } x^{2} \\ p(x)=x^{3}+x \\ g(x)=x^{2} \\ q(x)=x, r(x)=x
Clearly, degree of
p(x) and q(x) is same i.e. 1.
Checking for division algorithm
p(x) =g(x) \times q(x)+r(x) \\ x^{3}+x =\left(x^{2} \times x\right)+x \\ x^{3}+x =x^{3}+x
Thus, the division algorithm is satisfied.
Step-by-step explanation:
u boy or girls?