Question

examine whether x²-3x+2 has the factor x-2​

Answer 1

• x - 2 = 0
• => x = 2
• then ,
• p(x) = x² - 3x + 2 = 0
• (2)² - 3(2) + 2 = 0
• 4 - 6 + 2 = 0
• 6-6 = 0
• 0 = 0
• LHS = RHS
• Hence , x - 2 is a factor of x²-3x+2

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Answer 2

Consider the given polynomial,

x

2

−x+1 is a factor of x

3

−3x

2

+3x−2 when Remainder is zero.

As shown in the figure.

Quotient is x−2.

Remainder is 0.

Hence, x

2

−x+1 is a factor of x

3

−3x

2

+3x−2