Question

Find the degree of the polynomial $2x{y}^3+(5xy+3x{y}^2)y+5.$

• A. $3$
• B. $4$
• C. $5$
• D. None of the above

Answer 1

The correct option is B $4$

$\underset{–}{\text{Need to Find:}}$
Degree of the polynomial $2x{y}^3+(5xy+3x{y}^2)y+5$

As the given polynomial is not in standard form, we'll simplify it and express it in standard form first.

$2x{y}^3+(5xy+3x{y}^2)y+5$
Opening the bracket

$=2x{y}^3+5xy\cdot y+3x{y}^2\cdot y+5$

$=2x{y}^3+5x{y}^2+3x{y}^3+5$ $[\because a^m\cdot a^n=a^{m+n}]$
Now, combining the like terms

$=(2x{y}^3+3x{y}^3)+5x{y}^2+5$

$=5x{y}^3+5x{y}^2+5$

Degree of each term of the above simplified polynomial is listed in below table,
As per the above table, simplified polynomial, $\underset{–}{5x{y}^3+5x{y}^2+5}$ is in standard form. Term $\underset{–}{5x{y}^3}$ has the highest degree i.e. $\underset{–}{4}.$

As a result, degree of the given polynomial is $\underset{–}{4}.$

Therefore, option (b.) is the correct choice.