Factor out the GCF

Question

20, x, to the power 5 , plus, 10, x, to the power 4 , minus, 15, x, cubed20x
5
+10x
4
−15x
3

Answer
Attempt 1 out of 2
Multiple Choice Answers
5, x, left parenthesis, 4, x, to the power 5 , plus, 2, x, to the power 4 , minus, 3, x, cubed, right parenthesis5x(4x
5
+2x
4
−3x
3
)
5, x, cubed, left parenthesis, 4, x, squared, plus, 2, x, minus, 3, right parenthesis5x
3
(4x
2
+2x−3)
5, left parenthesis, 4, x, to the power 5 , plus, 2, x, to the power 4 , minus, 3, x, cubed, right parenthesis5(4x
5
+2x
4
−3x
3
)
5, x, cubed, left parenthesis, 4, x, squared, plus, 10, x, minus, 15, right parenthesis5x
3
(4x
2
+10x−15)

Answer 1

To factor out the greatest common factor (GCF) from the expression \(20x^5 + 10x^4 - 15x^3\), we first need to identify the coefficients and the lowest power of \(x\) in each term.

1. The coefficients are 20, 10, and -15. The GCF of 20, 10, and -15 is 5.
2. The powers of \(x\) are \(x^5\), \(x^4\), and \(x^3\). The lowest power is \(x^3\).

Combining these, the GCF of the expression is \(5x^3\).

Now we factor out \(5x^3\) from the expression:

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

Thus, the factored expression is:

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

So, the correct answer is:

5, x, cubed, left parenthesis, 4, x, squared, plus, 2, x, minus, 3, right parenthesis or in symbols, \(5x^3(4x^2 + 2x - 3)\).