Question

Determine wether (x-2) is a factor of (x³-3x²+4x-4) by factor theorem


pls answer fast its urgent​

Answer 1

Solution :

p(x) = x³-3x²+4x-4

g(x) = x - 2

Let's find the zero of x - 2

→ g(x) = 0

→ x - 2 = 0

→ x = 0 + 2

→ x = 2

The zero of (x-2) is 2.

→ p(x) = x³-3x²+4x-4

When x = 2

→ p(2) = (2)³-3(2)²+4(2)-4

→ p(2) = 8 - 3(4) + 8 - 4

→ p(2) = 8 - 12 + 8 - 4

→ p(2) = 16 - 16

→ p(2) = 0

$\therefore$ (x-2) is factor of the polynomial x³-3x²+4x-4

__________________________

About Factor Theorem :

★ If p(x) is a polynomial of degree n≥1 and a is any real number,then :

i) x - a is the factor of p(x),if p(a) = 0

ii)p(a) = 0,if x - a is a factor of p(x)

Answer 2

Given

Determine wether (x-2) is a factor of (x³-3x²+4x-4) by factor theorem

Solution

=> x - 2 = 0

=> x = 2

Putting the value of x

=> x³ - 3x² + 4x - 4

=> (2)³ - 3 × (2)² +4 × 2 - 4

=> 8 - 12 + 8 - 4

=> 16 - 12 - 4

=> 4 - 4 = 0

Hence, (x - 2) is a factor of of (x³ - 3x² + 4x - 4)