Class 10 Mathematics - Chapter Polynomials NCERT Solutions | Give examples of polynomials p(x), g(x),
Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0
we know that
(i) Deg P(x) = deg g (x)
The degree of dividend or quotient can be equal, only if the divisor is a constant (degree 0)
Then, let p(x) = 3x2 – 6x + 5
Let g(x) = 3
Therefore, q(x) = x2 – 2x +1 and r(x) = 2
(ii) Deg q(x) = deg r(x)
Let p(x) = x2 + 1
Let g(x) = x
Therefore, q(x) = x + 1 and r(x) = 0
Here, we can see the degree of quotient is equal to the degree of remainder.
Hence, division algorithm is satisfied here.
(iii) deg r(x) = 0
The degree of remainder is zero, only if the remainder left after division algorithm is Constant.
Let p(x) = x2 + 1
Let g(x) = x
Therefore, q(x)= x and r(x) = 1
Here we can see the degree of remainder is zero.
Hence division algorithm is satisfied here.
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