Can someone help me factor this problem?
Generally I wouldn't have a problem doing it, but today we're supposed to factor problems without knowing what exactly to do, (Trinomial squares, difference of squares, magic diamond, etc), and it's really stumping me.
For exampled I'm stuck on this one,
p^5 + 3p^3 + p^2 + 3
p^5 + p^2 + 3 (p^3+1)
p^2 (p^3+1) + 3(p^3+1)
(p^2+3)(p^3+1)
Of course, I can help you factor the expression p^5 + 3p^3 + p^2 + 3. Factoring can be approached using various methods depending on the form of the expression. In this case, we can factor it by grouping.
To factor by grouping, we group terms in pairs and search for a common factor that can be factored out. Let's break down the problem step by step:
Step 1: Group the terms by pairs:
p^5 + 3p^3 + p^2 + 3
Step 2: Look for a common factor within each pair of terms:
For the first pair (p^5 + 3p^3), the common factor is p^3.
For the second pair (p^2 + 3), there is no common factor.
Step 3: Factor out the common factor from each pair:
p^3(p^2 + 3) + (p^2 + 3)
Step 4: Notice that (p^2 + 3) appears in both terms. We can factor that out as well:
(p^3 + 1)(p^2 + 3)
And now, we have factored the expression p^5 + 3p^3 + p^2 + 3 into (p^3 + 1)(p^2 + 3).
To check if the factoring is correct, you can expand the factored expression using the distributive property to see if you get back to the original expression.
I hope this explanation helps you understand how to factor this particular expression. If you have any more questions, feel free to ask!