Question

Factor x2 − 2x + 3.

(x − 3)(x − 1)
(x + 3)(x + 1)
(x − 3)(x + 1)
Prime

Answer 1

When trying to factor
`x^(2) -2x+3`, you are asking for three questions that help you get the factors, that, when multiplied through FOIL - First, Outside, Inside, Last, give you
`x^(2) -2x+3`.

1) What pair of numbers multiply together to get 3? (The "L" part of FOIL)

2) What pair of numbers times x multiply together to get 1
`x^(2)` (The "F" part)

3) What pair of numbers that multiply to 3 also add to -2? (The "OI" part).

Let's answer them one-by-one. Three has only three and one that multiply to three. There's only one pair that multiplies to one, one and one. When adding, three and one (can't use any other pair from question 1), we get four. (If we were using -3 and -1, they would add to -4).

So the answer to question 3 is None, and this polynomial is PRIME because we can't answer all three questions with a pair of numbers.

Answer 2

The correct answer is: Prime.

Explanation:

We are given a quadratic expression in terms of variable ''x'' as:

`x^2-2x+3`

Now we are asked to factorize the given polynomial expression of possible.

1)

(x − 3)(x − 1)

On expanding this expression we get:

`(x-3)(x-1) =x^2-3x-x+3\\\\\\(x-3)(x-1) =x^2-4x+3`

which is not equal to the given expression.

Hence, option: 1 is incorrect.

2)

(x + 3)(x + 1)

`(x+3)(x+1)=x^2+3x+x+3\\\\\\(x+3)(x+1)=x^2+4x+3`

which is not equal to the given expression.

Hence, option: 2 is incorrect.

3)

(x − 3)(x + 1)

`(x-3)(x+1)=x^2-3x+x-3\\\\\\(x-3)(x+1)=x^2-2x-3`

Hence, again this is not the required expression.

Hence , option: 3 is incorrect.

Hence, the answer is:

Prime.