Question

factor $20x^2 - 11x - 4$
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Explanation:

Step1: Find two numbers

We need two numbers \(a\) and \(b\) such that \(a\times b = 20\times(- 4)=-80\) and \(a + b=-11\). After checking, we find that \(a = -16\) and \(b = 5\) since \((-16)\times5=-80\) and \(-16 + 5=-11\).

Step2: Rewrite the middle term

Rewrite \(-11x\) as \(-16x+5x\) in the quadratic expression:
\(20x^{2}-16x + 5x-4\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((20x^{2}-16x)+(5x - 4)\)
Factor out the greatest common factor from each group:
\(4x(5x - 4)+1(5x - 4)\)

Step4: Factor out the common binomial

Factor out the common binomial \((5x - 4)\):
\((4x + 1)(5x-4)\)

Answer:

\((4x + 1)(5x - 4)\)