Statement A (Assertion):The degree of the polynomial(x2 – 2)(x –3)(x + 4) is 3.Statement R( Reason) : A polynomial of degree 3 is called a cubicpolynomial.(a) Both assertion (A) and reason (R) are true and reason (R) is thecorrect explanation of assertion (A)(b) Both assertion (A) and reason (R) are true and reason (R) is not thecorrect explanation of assertion (A)(c) Assertion (A) is true but reason (R) is false.(d) Assertion (A) is false but reason (R) is true
Question
Statement A (Assertion):The degree of the polynomial(x2 – 2)(x –3)(x + 4) is 3.Statement R( Reason) : A polynomial of degree 3 is called a cubicpolynomial.(a) Both assertion (A) and reason (R) are true and reason (R) is thecorrect explanation of assertion (A)(b) Both assertion (A) and reason (R) are true and reason (R) is not thecorrect explanation of assertion (A)(c) Assertion (A) is true but reason (R) is false.(d) Assertion (A) is false but reason (R) is true
Solution
The degree of a polynomial is determined by the highest power of the variable in the polynomial.
In the polynomial (x^2 – 2)(x –3)(x + 4), when you multiply it out, the highest power of x that you get is 3 (because x^2 * x gives x^3). So, the degree of this polynomial is 3. That means Statement A (Assertion) is true.
Statement R (Reason) is also true. A polynomial of degree 3 is indeed called a cubic polynomial.
However, Statement R is not the correct explanation of Statement A. The fact that a polynomial of degree 3 is called a cubic polynomial doesn't explain why the degree of the polynomial (x
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