Let f(x) and g(x) be two polynomials (with real coefficients) having degree 3 and 4 respectively. What is the degree of f(x) g(x)a)12b)7c)4d)3Correct answer is option 'B'. Can you explain this answer?

Question

Answer

During product powers get added. so 3 and 4 makes up 7
eg.f(x)=x2 and g(x)=x3 so f(x)g(x) will be x5

Answer

Degree of a Polynomial
The degree of a polynomial is the highest power of the variable in the polynomial. In other words, it is the exponent of the term with the highest power.

Given Information
We are given two polynomials, f(x) and g(x), with degrees 3 and 4 respectively.

Multiplying Polynomials
To find the degree of the product of two polynomials, we need to multiply the polynomials and determine the highest power of the variable in the resulting expression.

Degree of f(x)g(x)
The degree of the product f(x)g(x) is the sum of the degrees of the individual polynomials.

In this case, the degree of f(x)g(x) = degree of f(x) + degree of g(x) = 3 + 4 = 7.

Hence, the degree of f(x)g(x) is 7.

Answer
Therefore, the correct answer is option B) 7.

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