Question

factor: (greatest coefficient first. if coefficients are the same, least valued constant first.)
$4x^2 - 15x - 25$
$= a (bx + c) (dx + e)$
$= \boxed{} (\boxed{} x + \boxed{}) (\boxed{} x + \boxed{})$

Explanation:

Step1: Find factors of \(4\times(-25)\)

We need two numbers that multiply to \(4\times(-25)= - 100\) and add up to \(-15\). The numbers are \(-20\) and \(5\) since \(-20\times5=-100\) and \(-20 + 5=-15\).

Step2: Rewrite the middle term

Rewrite \(-15x\) as \(-20x+5x\) in the quadratic expression: \(4x^{2}-20x + 5x-25\).

Step3: Group and factor

Group the first two terms and the last two terms: \((4x^{2}-20x)+(5x - 25)\). Factor out the GCF from each group: \(4x(x - 5)+5(x - 5)\). Now factor out \((x - 5)\): \((4x + 5)(x - 5)\). Here \(a = 1\), \(b = 4\), \(c = 5\), \(d = 1\), \(e=-5\).

Answer:

\(1\) \((4x + 5)(x - 5)\) (So filling the boxes: first box \(1\), second box \(4\), third box \(5\), fourth box \(1\), fifth box \(-5\))