How do you factor the expression $15x^2 - 33x - 5$ ?

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Answer 1 · 2016-06-01T17:44:02

This equation does not have simple factor-able terms

$15*(-5)=75$ we need factors of $-75$ which sum to $-33$ .

$(-15)*(5)=75$ and $5-15=-10$ No

$(-3)*(25)=75$ and $25-3=22$ No

$(-1)*(75)=75$ and $75-1=74$ No

$(15)*(-5)=75$ and $-5+15=10$ No

$(3)*(-25)=75$ and $-25+3=-22$ No

$(1)*(-75)=75$ and $-75+1=-74$ No

This expression is NOT simple factor-able.

We can check Quadratic equation
$x_1, x_2 = (-b/{2a}) pm sqrt{b^2 - 4ac}/{2a}$

$x_1, x_2 = (-(-33)/{2*15}) pm sqrt{(-33)^2 - 4*15*(-5)}/{2*15}$

$x_1, x_2 = 33/{30} pm sqrt{1089 + 60/{30}$

$x_1, x_2 = 33/{30} pm sqrt{1149/{30}$

$x_1, x_2 =2.22989675, -0.02989675$

Clearly this equation does not have simple factor-able terms

How do you factor the expression 15x^2 - 33x - 5 15x^2 - 33x - 5?