Question

factor completely.
$4d^2 - 7d + 3$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(4\times3 = 12\) and add up to \(-7\). The numbers are \(-4\) and \(-3\) since \((-4)\times(-3)=12\) and \(-4 + (-3)=-7\).

Step2: Rewrite the middle term

Rewrite \(-7d\) as \(-4d-3d\) in the expression \(4d^{2}-7d + 3\):
\(4d^{2}-4d-3d + 3\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((4d^{2}-4d)+(-3d + 3)\)
Factor out the greatest common factor from each group:
\(4d(d - 1)-3(d - 1)\)

Step4: Factor out the common binomial

Factor out \((d - 1)\) from both terms:
\((4d - 3)(d - 1)\)

Answer:

\((4d - 3)(d - 1)\)