Question

which of the following correctly shows $x^2 - 3x + 2$ in factored form?\
\\(\bigcirc\\) $(x - 3)(x - 1)$\
\\(\bigcirc\\) $(x - 3)(x - 3)$\
\\(\bigcirc\\) $(x - 2)(x - 1)$\
\\(\bigcirc\\) $(x + 3)(x + 1)$

Explanation:

Step1: Recall factoring quadratic

To factor \(x^2 - 3x + 2\), we need two numbers that multiply to \(2\) and add to \(-3\).

Step2: Find the numbers

The numbers are \(-2\) and \(-1\) because \((-2)\times(-1)=2\) and \((-2)+(-1)=-3\).

Step3: Write factored form

So, \(x^2 - 3x + 2=(x - 2)(x - 1)\).

We can also check by expanding the options:

• For \((x - 3)(x - 1)=x^2 - 4x + 3\) (not correct).
• For \((x - 3)(x - 3)=x^2 - 6x + 9\) (not correct).
• For \((x - 2)(x - 1)=x^2 - 3x + 2\) (correct).
• For \((x + 3)(x + 1)=x^2 + 4x + 3\) (not correct).

Answer:

(x - 2)(x - 1) (corresponding to the option " (x - 2)(x - 1)")