Question

$(25x^5-15x^4)÷5x^3$

• A. $x(5x+3)$
• B. $(5x-3)$
• C. $x(5x-3)$
• D. None

Answer 1

The correct option is C $x(5x-3)$

We divide the given polynomial $25x^5-15x^4$ by the monomial $5x^3$ as shown below:

$\frac{25x^5-15x^4}{5x^3}=\frac{25x^5}{5x^3}-\frac{15x^4}{5x^3}=\left(\frac{5\times 5\times x^5}{5x^3}\right)-\left(\frac{3\times 5\times x^4}{5x^3}\right)=\left(\frac{5\times x^5\times x^{-3}}{1}\right)-\left(\frac{3\times x^4\times x^{-3}}{1}\right)$

$=(5\times x^{(5-3)})-(3\times x^{(4-3)})(\because a^x+a^y=a^{x+y})=5x^2-3x=x(5x-3)$

Hence, $\frac{25x^5-15x^4}{5x^3}=x(5x-3)$.