Question

$3x^{2}+\boldsymbol{?}x - 4$
this quadratic expression in standard form has an unknown $b$-value.
if we know the expression can be factored, list two possibilities for the unknown value.
possible values

Explanation:

Step1: Recall factoring form

A quadratic $ax^2+bx+c$ factors to $(mx+n)(px+q)$, where $mp=a$, $nq=c$, $b=mq+np$.
Here $a=3$, $c=-4$, so $mp=3$, $nq=-4$.

Step2: Test factor pairs for $a,c$

First pair: $m=3,p=1$; $n=4,q=-1$.
Calculate $b$: $b=(3)(-1)+(4)(1)=-3+4=1$.

Step3: Test second factor pair

Second pair: $m=3,p=1$; $n=-2,q=2$.
Calculate $b$: $b=(3)(2)+(-2)(1)=6-2=4$.
(Alternative pair: $m=1,p=3$; $n=1,q=-4$ gives $b=(1)(-4)+(1)(3)=-1$, also valid)

Answer:

1, -1 (or 4, -4; any two valid values)