Question

Show that (x-1) is a factor of 2x^3 - 3x^2 + 7x-6

Answer 1

$\Large{\underline{\underline{\bf{Solution:-}}}}$

$⟹x - 1 = 0 \\ \\ ⟹x = 1$

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${\bold{\underline{\underline{Putting\: value \: of \: x \: in \: polynomial:-}}}}$

$⟹2 {x}^{3} - 3 {x}^{2} + 7x - 6 = 0 \\ \\ ⟹{2(1)}^{3} - 3 {(1)}^{2} + 7(1) - 6 = 0 \\ \\ ⟹2 - 3 + 7 - 6 = 0 \\ \\⟹ 2 - 3 + 1 = 0 \\ \\⟹ - 1 + 1 = 0 \\ \\ ⟹0 = 0$

$\bold{\underline{\underline{\bf{Hence, \: x-1 \: is \: a \: factor \: of \: 2x^3-3x^2+7x-6}}}}$

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$\Large{\underline{\underline{\bf{Thanks}}}}$

Answer 2

SoluTion:

Given Polynomial :

• p(x) = 2x³ - 3x² + 7x - 6

We have to prove that -

• (x-1) is a factor of given polynomial.

Now equate (x - 1) to zero.

→ (x - 1) = 0

→ x = 1

Put x = 1 in given Polynomial.

→ 2(1)³ - 3(1)² + 7(1) - 6

→ 2 - 3 + 7 - 6

→ -1 + 1

→ 0

Hence, (x - 1) is a factor of given Polynomial p(x).