Question

check the whether x-1 is a factor of P(x)=x3-2x2+2x-1​

Answer 1

Given:-

• f ( x ) = x - 1

• P (x) = x³ - 2x² + 2x - 1

To Find:-

• Check whether f ( x ) is a factor of p ( x ) or not.

Now,

→ f ( x ) = x - 1

→ x - 1 = 0

→ x = 1

Putting the value of x in P ( x )

→ P(x) = x³ - 2x² + 2x - 1

→ P(1) = (1)³ - 2(1)² + 2(1) - 1

→ 1 - 2 + 2 - 1 = 0

→ -1 + 2 - 1 = 0

→ 1 - 1 = 0

→ 0 = 0

Therefore, f(x) is a factor of p(x).

Answer 2

Step-by-step explanation:

Given :

• the whether x - 1 is a factor

To Find :

• P(x) = x³ -2x² + 2x - 1

Solution :

Concept :

The Solve by Factoring process will require four major steps:

• Move all terms to one side of the equation, usually the left, using addition or subtraction.

• Factor the equation completely.

• Set each factor equal to zero, and solve.

• List each solution from Step 3 as a solution to the original equation.

__________________________

According to the Question :

• the whether x - 1 is a factor

$: \sf \implies \: \: \: \: \: x - 1 \\ \\ : \sf \implies \: \: \: \: \:x = 1$

We Have to find ,

$: \sf \implies \: \: \: \: \: p(1) =x^{3} - 2 {x}^{2} + 2x - 1$

• Substitute all values :

$: \sf \implies \: \: \: \: \: p(1) = 1^{3} - 2 \times {1}^{2} + 2 \times 1 - 1 \\ \\ \\ : \sf \implies \: \: \: \: \: p(1) = 1 - 2 \times 1 + 2 - 1 \\ \\ \\ : \sf \implies \: \: \: \: \: p(1) = 1 - 2 + 1 \\ \\ \\ : \sf \implies \: \: \: \: \: p(1) = 0$