Question

Find the H.C.F. of $p\left(x\right)=10(x-1{)}^4,q(x)=15(x-1{)}^6$ and $r\left(x\right)=20(x-1{)}^2$

• A. $3(x+1{)}^2$
• B. $3(x-2{)}^2$
• C. $5(x+1{)}^2$
• D. $5(x-1{)}^2$

Answer 1

The correct option is D $5(x-1{)}^2$

Here, $p\left(x\right)=10(x-1{)}^4=2\times 5(x-1{)}^4$
$q\left(x\right)=15(x-1{)}^6=3\times 5(x-1{)}^6$
and $r\left(x\right)=20(x-1{)}^2=2^2\times 5(x-1{)}^2$
Considering the lowest exponent of common numeric and algebraic factors, the H.C.F. of the given polynomials is $5(x-1{)}^2$