| Statement - I: If p(x) and g(x) are two polynomials with \[g(x)\ne 0,\] then we can find polynomials q(x) and r(x) such that \[p(x)=g(x)\times q(x)+r(x),\] where degree of r(x) is greater than degree of g(x). |
| Statement - II: When \[4{{x}^{5}}+3{{x}^{3}}+2{{x}^{2}}+8\] is divided by \[4{{x}^{2}}+2x+1,\] then degree of remainder is 1. |
A) Both Statement - I and Statement - II are true.
B) Statement - I is true but Statement - II is false.
C) Statement - I is false but Statement - II is true.
D) Both Statement - I and Statement - II are false.
Correct Answer: C
Solution :
Statement - I is false because if p(x) and g(x) are two polynomials with \[g(x)\ne 0,\]. then we can find polynomials q(x) and r(x) such that \[p(x)=g(x)\times q(x)+r(x)\] where \[r(x)=0\] or degree of \[r(x)\,\,<\] degree of g(x). Statement - II is false as when \[4{{x}^{5}}+3{{x}^{3}}+2{{x}^{2}}+8\] is divided by \[4{{x}^{2}}+2x+1,\]the remainder is \[-\frac{5x}{4}+\frac{31}{4}\]which is a polynomial of degree 1.
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