Questions: Factor completely: 30x^4+45x.

Transcript text: Factor completely: $30 x^{4}+45 x$.

Solution

Solution Steps

To factor the given polynomial completely, we need to identify the greatest common factor (GCF) of the terms. The GCF is the largest factor that divides each term of the polynomial. Once we find the GCF, we can factor it out from the polynomial.

Step 1: Identify the Polynomial

We start with the polynomial $ 30x^4 + 45x $.

Step 2: Find the GCF

The coefficients of the terms are 30 and 45. The GCF of 30 and 45 is 15. The variable part has $ x^4 $ and $ x $, so the GCF in terms of $ x $ is $ x $. Therefore, the overall GCF is $ 15x $.

Step 3: Factor Out the GCF

We can factor out the GCF from the polynomial: \[ 30x^4 + 45x = 15x(2x^3 + 3) \]