Question

Question

Factor out the GCF
minus, 10, x, to the power 5 , minus, 15, x, cubed, plus, 20, x, squared−10x
5
−15x
3
+20x
2

Answer
Attempt 1 out of 2
Multiple Choice Answers
5, x, squared, left parenthesis, 2, x, cubed, plus, 3, x, plus, 4, right parenthesis5x
2
(2x
3
+3x+4)
5, x, squared, left parenthesis, minus, 2, x, cubed, minus, 3, x, plus, 4, right parenthesis5x
2
(−2x
3
−3x+4)
5, x, left parenthesis, minus, 2, x, cubed, minus, 3, x, plus, 4, right parenthesis5x(−2x
3
−3x+4)
minus, 5, x, squared, left parenthesis, minus, 2, x, cubed, minus, 3, x, plus, 4, right parenthesis−5x
2
(−2x
3
−3x+4)
Submit Answer

Answer 1

To factor out the greatest common factor (GCF) from the expression \( -10x^5 - 15x^3 + 20x^2 \), we first determine the GCF of the coefficients and the variable parts.

1. Coefficients: The coefficients are -10, -15, and 20. The GCF of these numbers is 5.
2. Variable part: The variable with the smallest exponent is \(x^2\) (from \(20x^2\)). Therefore, the GCF for the variable part is \(x^2\).

Combining these two, the GCF of the entire expression is \(5x^2\).

Next, we factor out \(5x^2\) from each term:

\[ -10x^5 ÷ 5x^2 = -2x^3 \]

\[ -15x^3 ÷ 5x^2 = -3x \]

\[ 20x^2 ÷ 5x^2 = 4 \]

Putting these factored results together, we have:

\[ -10x^5 - 15x^3 + 20x^2 = 5x^2(-2x^3 - 3x + 4) \]

Now looking at the answer choices provided, the correct answer is:

Option: \(5x^2(-2x^3 - 3x + 4)\)