Will someone please help me slove this question.
Completely factor the polonomial.
8x^3+16x^2+8x+16
looks like we can group it
= 8x^2(x+2) + 8(x+2)
= (x+2)(8x^2 + 8)
= 8(x+2)(x^2 + 1)
we could have factored out the 8 first ....
Sure! I can help you with that.
To completely factor the given polynomial, we can start by looking for common factors. In this case, we can observe that each term has a common factor of 8. We can factor it out to simplify the polynomial:
8x^3 + 16x^2 + 8x + 16
= 8(x^3 + 2x^2 + x + 2)
Now, we need to factor the expression inside the parentheses further. This can be done by using various factoring techniques such as grouping, factoring by grouping, or recognizing special patterns.
In this case, we can see that the expression is a sum of four terms, and the first two terms share a common factor of x^2, while the last two terms share a common factor of 1:
x^3 + 2x^2 + x + 2
= (x^2(x + 2)) + (1(x + 2))
Notice that both terms now have a common factor of (x + 2), so we can factor that out:
= (x + 2)(x^2 + 1)
Therefore, the completely factored form of the given polynomial is:
8x^3 + 16x^2 + 8x + 16 = 8(x + 2)(x^2 + 1)