Question

the HCF of (a3-a2x) ,(a3-ax2)and(a4-ax3) is
​

Answer 1

$\textbf{Given:}$

$\text{ a^3-a^2x , a^3-ax^2 and a^4-ax^3 }$

$\textbf{To find:}$

$\text{H.C.F of the given polynomials}$

$\textbf{Solution:}$

$\text{First, we factorize the given polynomials}$

$a^3-a^2x=a^2(a-x)=\boxed{a}{\times}a{\times}\boxed{(a-x)}$

$a^3-ax^2=a(a^2-x^2)=\boxed{a}{\times}\boxed{(a-x)}{\times}(a+x)$

$a^4-ax^3=a(a^3-x^3)=\boxed{a}{\times}\boxed{(a-x)}{\times}(a^2+ax+x^2)$

$\text{Finding common factors from the above factorization}$

$\text{H.C.F}=a{\times}(a-x)$

$\text{H.C.F}=a(a-x)$

$\textbf{H.C.F}=a^2-ax$

$\textbf{Answer:}$

$\textbf{H.C.F is \bf\,a^2-ax }$