Question

factor $4n^2 - 17n - 15$\
$(4n - 5)(n - 3)$\
$(n - 5)(4n + 3)$\
$(n - 10)(6n + 1)$\
$(n - 5)(4n - 3)$

Explanation:

Step1: Expand the middle term

We need to factor \(4n^2 - 17n - 15\). First, find two numbers that multiply to \(4\times(-15)= - 60\) and add up to \(-17\). The numbers are \(-20\) and \(3\).
So, rewrite the middle term: \(4n^2-20n + 3n-15\)

Step2: Group the terms

Group the first two and the last two terms: \((4n^2 - 20n)+(3n - 15)\)

Step3: Factor out the GCF from each group

From the first group, factor out \(4n\): \(4n(n - 5)\)
From the second group, factor out \(3\): \(3(n - 5)\)

Step4: Factor out the common binomial factor

Now we have \(4n(n - 5)+3(n - 5)\), factor out \((n - 5)\): \((n - 5)(4n + 3)\)

Answer:

\((n - 5)(4n + 3)\) (corresponding to the option \((n - 5)(4n + 3)\))