Question

if deg p(x)=m and deg q(x)=n then the value of deg (p(x)-q(x)) is:-

Answer 1

Answer:

Step-by-step explanation:

if m > n , then deg( p(x) - q(x) ) = m

if m < n , then deg( p(x) - q(x) ) = n

Answer 2

Answer:

• "m" if (m > n)
• "m" if (m > n)"n" if (n > m)

Step-by-step explanation:

Given,

• deg p(x)=m
• deg p(x)=mdeg q(x)=n

To Find: The value of deg (p(x)-q(x))

Explanation:

• To solve this question, first we need to have a clear understanding of "Degree" of a Funtion or Polynomial.
• The Degree of a function is simply, the most number of solutions that a function could have, i.e., the most number of times a function will cross the x-axis. Sometimes the degree can be 0, which means, the equation does not have any solutions or any instances of the graph crossing the x-axis and this is quite normal.
• The Degree of a function is simply, the most number of solutions that a function could have, i.e., the most number of times a function will cross the x-axis. Sometimes the degree can be 0, which means, the equation does not have any solutions or any instances of the graph crossing the x-axis and this is quite normal.And, the Degree of polynomials in one variable is the highest power of the variable in the algebraic expression.

For example, if a polynomial function

$f(x) = 4{x}^{4} + {x}^{2} + 3x + 7$

Here, the Degree of f(x) will be 4 as 4 is the highest power of the variable.

• Using this above concept in our question, the [degree of p(x) = m] means the highest power of the variable in the algebraic expression of p(x) is m, i.e.,

${ x}^{m}$

with whatever coefficient maybe.

• Similarly, [degree of q(x) = n] means the highest power of the variable in the algebraic expression of q(x) is n, i.e.,

${x}^{n}$

again with whatever coefficient it maybe.

• Now if (m > n), then [p(x) - q(x)] will have both the variables

${ x}^{m} \: and \: { x}^{n}$

with their concerned coefficients and in the resulting algebraic expression,

${ x}^{m}$

will still remain the variable with highest power.

• Hence, [deg (p(x)-q(x)) = m] since (m > n)
• Similarly, if [deg (p(x)-q(x)) = n] since (n > m)

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