Questions: Question 6 1 Point Factor Completely 18x^5-24x^4+30x^3 (A) 2x^3(9x^2-12x+15) (B) 6x^3(3x^2-4x+5) (C) 6x^2(3x^3-4x^2+5x) (D) 3x^2(6x^3-8x^2+10x)

Transcript text: Question 6 1 Point Factor Completely $18 x^{5}-24 x^{4}+30 x^{3}$ (A) \[ 2 x^{3}\left(9 x^{2}-12 x+15\right) \] (B) \[ 6 x^{3}\left(3 x^{2}-4 x+5\right) \] (c) \[ 6 x^{2}\left(3 x^{3}-4 x^{2}+5 x\right) \] (D) \[ 3 x^{2}\left(6 x^{3}-8 x^{2}+10 x\right) \] 1 Point Question 7

Solution

Solution Steps

To factor the polynomial $18x^5 - 24x^4 + 30x^3$ completely, we need to find the greatest common factor (GCF) of the coefficients and the variable terms. Then, we factor out the GCF from the polynomial.

Step 1: Identify the Greatest Common Factor (GCF)

To factor the polynomial $18x^5 - 24x^4 + 30x^3$ completely, we first identify the greatest common factor (GCF) of the coefficients and the variable terms.

The GCF of the coefficients $18$, $24$, and $30$ is $6$.

The GCF of the variable terms $x^5$, $x^4$, and $x^3$ is $x^3$.

Step 2: Factor Out the GCF

Next, we factor out the GCF $6x^3$ from each term in the polynomial:

\[ 18x^5 - 24x^4 + 30x^3 = 6x^3(3x^2) - 6x^3(4x) + 6x^3(5) \]

Step 3: Simplify the Expression Inside the Parentheses

Simplify the expression inside the parentheses:

\[ 6x^3(3x^2 - 4x + 5) \]