Question

If the area of above rectangle is $7y^3+4y,$ then the degree of length's expression is. (Given, $3y$ is Breadth)

Answer 1

$\underset{–}{\text{Given:}}$
Area of the rectangle $=7y^3+4y$
Breadth of the rectangle $=3y$

$\underset{–}{\text{Need to Find:}}$
Degree of length's expression

As we know,
Area of rectangle $=$ Length $\times$ Breadth
$\Rightarrow$ $7y^3+4y=$ Length $\times 3y$

$\Rightarrow$ Length $=\frac{7y^3+4y}{3y}$

$\Rightarrow$ Length $=\frac{7}{3}{y}^{(3-1)}+\frac{4}{3}{y}^{(1-1)}$ $[\because \frac{a^m}{a^n}=a^{(m-n)}]$

$\Rightarrow$ Length $=\frac{7}{3}{y}^2+\frac{4}{3}{y}^0$

$\Rightarrow$ Length $=\frac{7}{3}{y}^2+\frac{4}{3}$ $[\because y^0=1]$

Now, as we know, the largest power of the variable is the degree of the polynomial. Here, the largest power of the variable $\underset{–}{y}$ is $\underset{–}{2}.$ Therefore, degree of the length's expression is $\underset{–}{2}.$