Question

factor.
4v² + 42v - 46
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Explanation:

Step1: Factor out GCF

The greatest common factor (GCF) of \(4v^2\), \(42v\), and \(-46\) is 2. Factor out 2:
\(2(2v^2 + 21v - 23)\)

Step2: Factor quadratic

Factor \(2v^2 + 21v - 23\). Find two numbers \(a\) and \(b\) such that \(a \times b = 2 \times (-23) = -46\) and \(a + b = 21\). The numbers are 23 and -2.
Rewrite the middle term:
\(2v^2 + 23v - 2v - 23\)

Group and factor:
\(v(2v + 23) - 1(2v + 23) = (2v + 23)(v - 1)\)

Combine with the GCF:
\(2(2v + 23)(v - 1)\)

Answer:

\(2(2v + 23)(v - 1)\)