How do you factor this polynomial?
y^6 + 3y^3 – 10
I personally would say x = y^3
then it is
x^2 + 3 x - 10
(x-5)(x+2)
now go back
(x^3-5)(x^3+2)
whoops
(x+5)(x-2)
(y^3+5)(y^3-2)
To factor the polynomial y^6 + 3y^3 – 10, we can use a technique called factoring by grouping. Here's how you can do it:
Step 1: Look for common factors, if any. In this case, there are no common factors among the terms.
Step 2: Identify a pair of terms that have a common factor. In this case, we can see that the first two terms y^6 and 3y^3 have y^3 as a common factor.
Step 3: Factor the common factor out of the pair of terms. For y^6 and 3y^3, we can factor out y^3:
y^6 + 3y^3 – 10
= y^3(y^3 + 3) – 10
Step 4: Now, look for another pair of terms to factor. In this case, we have y^3 + 3 and -10.
Step 5: Unfortunately, there are no common factors between y^3 + 3 and -10 that can be factored out.
Therefore, we have factored the polynomial as much as we can. The factored form of the polynomial y^6 + 3y^3 – 10 is:
y^3(y^3 + 3) – 10.