Factor Completely
8y^5+12y^3+4y
looks like a common factor of 4y
can you finish it?
So is it 4y(2y^4+3y^2+1) or 4y(y^2+1)(2y^2+1)
clearly
4y(y^2+1)(2y^2+1)
Always check your factored answer by expanding it again to make sure the original comes back
To factor the expression 8y^5 + 12y^3 + 4y completely, follow these steps:
Step 1: Look for the greatest common factor (GCF) among all the terms. In this case, the GCF is 4y. Factor out the GCF:
4y(2y^4 + 3y^2 + 1)
Step 2: Now, focus on the expression inside the parentheses: 2y^4 + 3y^2 + 1. Notice that this is a trinomial. There is no apparent GCF among the terms, so we need to find another way to factor it.
Step 3: Try factoring the trinomial by grouping. Group the terms in pairs:
(2y^4 + 3y^2) + 1
Step 4: Factor out the greatest common factor from the first group and second group separately:
y^2(2y^2 + 3) + 1
Step 5: Now, you can see that there is a common binomial factor, (2y^2 + 3), which can be factored further. However, the expression inside the parentheses cannot be factored any further with real numbers. So the factored form of 8y^5 + 12y^3 + 4y is:
4y(y^2(2y^2 + 3) + 1)