Answer:
The degree of [tex]f(x)\times g(x)[/tex] is 3.
Explanation:
Given:
[tex]f(x) = 3x^{2}\\g(x) = 4x +1[/tex]
To find the degree of [tex]f(x)\times g(x)[/tex]
First we will find [tex]f(x)\times g(x)[/tex]
Therefore,
[tex]f(x)\times g(x) = (3x^{2})\times (4x + 1)[/tex]
now applying distributive property that is [tex]A\times (B + C) = A\times B + A\times C[/tex] we get
[tex]f(x)\times g(x) = (3x^{2})\times (4x + 1)[/tex]
[tex]f(x)\times g(x) = 3x^{2}\times 4x + 3x^{2}\times 1)[/tex]
[tex]f(x)\times g(x) = 12x^{3} + 3x^{2}[/tex]
Degree is define as highest Power raised to the variable.
Therefore,in this polynomial highest power is three hence the degree is also 3.
The degree of [tex]f(x)\times g(x)[/tex] is 3.
