Question

which constant term would mean that the expression is completely factored? $x^2 - 3x + $

Explanation:

Step1: Recall factoring quadratic rules

A quadratic $x^2+bx+c$ factors to $(x+m)(x+n)$ where $m+n=b$ and $m \times n=c$. For it to be completely factored (with integer coefficients, the standard for this type of problem), we need two integers that add to $-3$ (the coefficient of $x$).

Step2: Find valid integer pairs

Possible integer pairs that sum to $-3$:

• $m=-1, n=-2$: $(-1)+(-2)=-3$
• Calculate their product: $(-1) \times (-2)=2$

This gives a constant term where the quadratic factors to $(x-1)(x-2)$, which is completely factored.
(Note: Other non-integer constants could work, but integer constants are the standard expectation here.)

Answer:

$2$