Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
30u5–45u3
First, we identify the greatest common factor (GCF) of the terms in the given polynomial, which is 15u3 (there are two factors of 15 and one factor of u3 in both terms).
We can then rewrite the polynomial as:
30u5 - 45u3 = 15u3 * (2u2 - 3)
Therefore, the factored form of the polynomial is 15u3(2u2 - 3).
To factor out the greatest common factor, start by finding the largest number that divides evenly into both terms. In this case, the largest number that divides evenly into both 30 and 45 is 15.
Next, look at the variables. The variable "u" is common to both terms. To find the highest power of "u" that divides into both terms, you need to look at the lowest power of "u" in each term.
In the first term, 30u^5, the lowest power of "u" is u^5.
In the second term, -45u^3, the lowest power of "u" is u^3.
To factor out the greatest common factor, you can write it as 15u^3.
So, factoring out the greatest common factor of 30u^5 - 45u^3 gives:
15u^3(2u^2 - 3)