What is the remainder when \( x^3 - 2x^2 + 3x - 4 \) is divided by \( x - 1 \)?

What is the remainder when \( x^3 - 2x^2 + 3x - 4 \) is divided by \( x - 1 \)?

• A. 0
• B. -2
• C. 2
• D. 4

Answer: (B)

To find the remainder when \( x^3 - 2x^2 + 3x - 4 \) is divided by \( x - 1 \), you can apply the Remainder Theorem. This theorem states that the remainder of the division of a polynomial \( f(x) \) by \( x - k \) is simply \( f(k) \). Here, \( f(x) = x^3 - 2x^2 + 3x - 4 \) and we are dividing by \( x - 1 \), which means we should evaluate \( f(1) \). Calculating \( f(1) \): 1. Substitute \( 1 \) into the polynomial: \[ f(1) = (1)^3 - 2(1)^2 + 3(1) - 4 \] 2. Simplify each term: \[ = 1 - 2 + 3 - 4 \] 3. Combine the values: \[ = 1 - 2 = -1 \] \[ -1 + 3 = 2 \] \[

To find the remainder when ( x^3 - 2x^2 + 3x - 4 ) is divided by ( x - 1 ), you can apply the Remainder Theorem. This theorem states that the remainder of the division of a polynomial ( f(x) ) by ( x - k ) is simply ( f(k) ).

Here, ( f(x) = x^3 - 2x^2 + 3x - 4 ) and we are dividing by ( x - 1 ), which means we should evaluate ( f(1) ).

Calculating ( f(1) ):

1. Substitute ( 1 ) into the polynomial:

[

f(1) = (1)^3 - 2(1)^2 + 3(1) - 4

]

2. Simplify each term:

[

= 1 - 2 + 3 - 4

]

3. Combine the values:

[

= 1 - 2 = -1

]

[

-1 + 3 = 2

]

[