Question

HCF of x2 – 3x + 2 and x2 – 5x +4 is (x – k) then find the value of k
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Answer 1

Step-by-step explanation:

Step-by-step explanation:x2−3x+2=x2−2x−x+2

Step-by-step explanation:x2−3x+2=x2−2x−x+2x(x−2)−1(x−2)=(x−2)(x−1)

Step-by-step explanation:x2−3x+2=x2−2x−x+2x(x−2)−1(x−2)=(x−2)(x−1)Now

Step-by-step explanation:x2−3x+2=x2−2x−x+2x(x−2)−1(x−2)=(x−2)(x−1)Nowx2−4x+3=x2−3x−x+3

Step-by-step explanation:x2−3x+2=x2−2x−x+2x(x−2)−1(x−2)=(x−2)(x−1)Nowx2−4x+3=x2−3x−x+3x(x−3)−1(x−3)=(x−3)(x−1)

Step-by-step explanation:x2−3x+2=x2−2x−x+2x(x−2)−1(x−2)=(x−2)(x−1)Nowx2−4x+3=x2−3x−x+3x(x−3)−1(x−3)=(x−3)(x−1)Thus, the only common factor is (x-1)

Answer 2

Answer:

$\huge{\boxed{\rm{\red{k=1}}}}$

Step-by-step explanation:

Given expressions are :-

x²-3x+2 and x²-5x+4

now,

x²-3x+2 can be written as

=>x²-x-2x+2

=>x(x-1)-2(x-1)

=>(x-1)(x-2)

x²-3x+2=(x-1)(x-2).....(1)

and x²-5x+4 can be written as

=>x²-5x+4

=>x²-x-4x+4

=>x(x-1)-4(x-4)

=>(x-1)(x-4)

x²-5x+4=(x-1)(x-4)......(2)

from (1/&(2)

x²-3x+2=(x-1)(x-2)

x²-5x+4=(x-1)(x-4)

HCF =(x-1)

according to the given problem

HCF =(x-k)

therefore, (x-k)=(x-1)

On comparing both sides

k=1

The value of k is 1

Used concept:-

The HCF of the two or more expressions is the least common factor of every expression.