Divide the polynomial x^3+x^2-2x+3 by (x-1)

x² + 2x + (3 / (x − 1))

Step-by-step explanation:

Start by setting up the division:

x − 1 | x³ + x² − 2x + 3

Start with the first term, x³.  Divided by x, that's x².  So:

x²

x − 1 | x³ + x² − 2x + 3

Multiply x − 1 by x², subtract the result, and drop down the next term:

x²

x − 1 | x³ + x² − 2x + 3

-(x³ − x²)

2x² − 2x

Repeat the process over again.  First term is 2x².  Divided by x is 2x.  So:

x² + 2x __

x − 1 | x³ + x² − 2x + 3

-(x³ − x²)

2x² − 2x

Multiply, subtract the result, and drop down the next term:

x² + 2x __

x − 1 | x³ + x² − 2x + 3

-(x³ − x²)

2x² − 2x

-(2x² − 2x)

3

x doesn't divide into 3, so that's the remainder.

Therefore, the answer is:

x² + 2x + (3 / (x − 1))

7.3

step-by-step explanation:

b) yes

step-by-step explanation:

let the statements be named as,

statement 1: if the power has been cut, then the refrigerator does not work.

statement 2: the refrigerator does not work.

conclusion: the power has been cut

now, 'law of detachment states that if we have the statements given as,

1. if p, then q.

2. p

then, we get the true statement or conclusion as q'.

thus, on comparing, we get that,

p: if the power has been cut.

q: the refrigerator does not work.

so, the argument is true by the law of detachment.