How to factor $4p^2 - 15p - 25$ step by step

Key takeaway: This is a standard trinomial factoring problem. The goal is to rewrite the expression as a product of two binomials, then verify by expansion.

Step 1: Look for two numbers

We want to factor

$4p^2-15p-25$

Find two numbers that multiply to $4\cdot (-25)=-100$ and add to $-15$.

Those numbers are $-20$ and $5$.

Step 2: Split the middle term

$4p^2-20p+5p-25$

Step 3: Group and factor

$4p(p-5)+5(p-5)$

Step 4: Factor out the common binomial

$\boxed{(4p+5)(p-5)}$

Quick check

$(4p+5)(p-5)=4p^2-20p+5p-25=4p^2-15p-25$

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Pitfalls the pros know 👇 A common mistake is to pair the factors as $(4p-5)(p+5)$. That expansion gives the wrong middle term. Always check the product and the sum before you commit.

What if the problem changes? If the coefficient of $p^2$ were different, the same idea still works: multiply the leading coefficient and constant term first, then search for two numbers with the correct sum. If the trinomial does not factor nicely over integers, you would need the quadratic formula instead.

Tags: trinomial factoring, FOIL check, difference of binomials