Question

course
ap precalculus
segment
31 - factoring: sum o
due wed, oct 22, 2025
63
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in exercises 59 - 68, factor the trinomial.

1. ( 14 u ^ { 2 } - 33 u - 5 )

text math set matrix
answer

Explanation:

Step1: Multiply the coefficient of \(u^{2}\) and the constant term

For the trinomial \(14u^{2}-33u - 5\), \(a = 14\), \(b=-33\), \(c=-5\). Calculate \(a\times c=14\times(- 5)=-70\).

Step2: Find two numbers that multiply to \(a\times c\) and add up to \(b\)

We need two numbers \(m\) and \(n\) such that \(m\times n=-70\) and \(m + n=-33\). The numbers are \(-35\) and \(2\) since \((-35)\times2=-70\) and \(-35 + 2=-33\).

Step3: Rewrite the middle - term using the two numbers

Rewrite \(14u^{2}-33u - 5\) as \(14u^{2}-35u+2u - 5\).

Step4: Group the terms and factor by grouping

Group the terms: \((14u^{2}-35u)+(2u - 5)\).
Factor out the greatest common factor from each group: \(7u(2u - 5)+1(2u - 5)\).

Step5: Factor out the common binomial factor

Factor out \((2u - 5)\) to get \((7u + 1)(2u-5)\).

Answer:

\((7u + 1)(2u - 5)\)