To factor the expression [tex]\( 5p^3 - 10p^2 + 3p - 6 \)[/tex], let's break it down step-by-step.
1. Consider the polynomial [tex]\( 5p^3 - 10p^2 + 3p - 6 \)[/tex].
2. Look for a common factor in each term. In this polynomial, there isn't a greatest common factor that can be factored out directly from all terms.
3. Now, let's factor the polynomial by grouping the terms and applying other factorization methods. However, upon detailed factorization and splitting the terms, the expression can be rewritten in its factored form.
4. The completely factored form of the polynomial [tex]\( 5p^3 - 10p^2 + 3p - 6 \)[/tex] is:
[tex]\[
(p - 2)(5p^2 + 3)
\][/tex]
So, the factorization of the given polynomial [tex]\( 5p^3 - 10p^2 + 3p - 6 \)[/tex] is:
[tex]\[
(p - 2)(5p^2 + 3)
\][/tex]
