Question

find hcf of x2-3x+2 and x2-4x+3

Answer 1

 x^2-3x+2
=x^2+(-2-1)x +(-1)(-2)
=(x-2)(x-1)

 x^2-4x+3
=x^2+(-3-1)x +(-1)(-3)
=(x-3)(x-1)

the common factor in x2-3x+2 and x2-4x+3 is (x-1)

Answer 2

(x-1) is the HCF of $\bold{x^{2}-3 x+2 \text { and } x^{2}-4 x+3}$

HCF- “Highest Common Factor” Largest whole number that divides both numbers.Highest common factor of the provided numbers is the "greatest number" which "divides each of them" exactly. This HCF can be extended as polynomials and other "commutative rings" in the HCF.

$x^{2}-3 x+2$ ________(1)  

$x^{2}-4 x+3$ _________(2)

By factorization method,

$\begin{array}{l}{x^{2}-3 x+2=x^{2}-2 x-x+2 = x(x-2)-1(x-2)} \\ {x^{2}-3 x+2=(x-1)(x-2)}\end{array}$________(3)

By factorization method,

$\begin{array}{c}{x^{2}-4 x+3=x^{2}-3 x-x+3 =x(x-3)-1(x-3)} \\ {x^{2}-4 x+3=(x-1)(x-3)}\end{array}$ _________(4)

From eq (3) and (4) by taking the common term,

HCF of $x^{2}-3 x+2 \text { and } x^{2}-4 x+3=(x-1)$