What is the HCF of the polynomials (x–2)(x2 +x–2) and (x–1)(x2 –3x+2)?
Answers
Answer:
(x–2)(x2 +x–2)
(x-2)(x2+2x - x -2)
(x-2)[ x(x+2) -1(x+2)]
(x-2)(x+2)(x-1)
(x–1)(x2 –3x+2)
(x–1)(x2 -2x -x +2)
(x–1)[x(x-2) -1(x-2)]
(x–1)(x-2)(x–1)
HCF :- (x–1)(x-2)
=> x2 -2x -x +2
=> x2 -3x +2
Given : polynomials (x–2)(x² +x–2) and (x–1)(x² –3x+2)
To Find : HCF
Solution:
HCF - Highest common Factor
(x–2)(x² +x–2)
= (x–2)(x² +2x-x–2)
= (x–2)(x(x +2) -1(x+2))
= (x - 2)(x + 2)(x-1)
(x–1)(x² –3x+2)
= (x–1)(x² –2x -x +2)
= (x–1)(x(x –2) -1(x -2))
=(x–1)(x - 2)(x - 1)
(x - 2) & (x - 1) are common Factors
HCF = (x - 2)(x - 1)
=x² - 3x + 2
x² - 3x + 2 is the HCF of polynomials (x–2)(x² +x–2) and (x–1)(x² –3x+2)
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