Factor

Question

8x2+16x−10completely. Which of the following expressions is a factor?

You will need to show your work to get full credit on this problem. You can either show it on the sketch pad to the left, or attach your own document on the next screen.

x−10

2x+3

4x−1

2x+5

Answer 1

To factor the expression \( 8x^2 + 16x - 10 \) completely, we will start by factoring out the greatest common factor (GCF) from the expression.

1. Identify the GCF: The coefficients are 8, 16, and -10. The GCF of these numbers is 2.

2. Factor out the GCF: \[ 8x^2 + 16x - 10 = 2(4x^2 + 8x - 5) \]

3. Factor the quadratic \( 4x^2 + 8x - 5 \): Now, we will factor \( 4x^2 + 8x - 5 \) by finding two numbers that multiply to \( (4)(-5) = -20 \) and add to \( 8 \).

   The numbers that work are \( 10 \) and \( -2 \).

4. Re-write the middle term: \[ 4x^2 + 10x - 2x - 5 \]

5. Group the terms: \[ (4x^2 + 10x) + (-2x - 5) \]

6. Factor by grouping: \[ 2x(2x + 5) - 1(2x + 5) \] \[ = (2x + 5)(2x - 1) \]

7. Combine everything: So, we have \[ 8x^2 + 16x - 10 = 2(2x + 5)(2x - 1) \]

Now, we can determine if any of the provided options is a factor by checking each expression:

1. \( x - 10 \)
2. \( 2x + 3 \)
3. \( 4x - 1 \)
4. \( 2x + 5 \)

Since we factored the original expression into \( 2(2x + 5)(2x - 1) \), it's clear that:

• \( 2x + 5 \) is indeed a factor of \( 8x^2 + 16x - 10 \).

So the answer is:

\[ \text{The expression that is a factor is } 2x + 5. \]