Question

Select all the factors of 20x2 + 4x - 24.

4

x - 1

5x + 1

3

5x + 6

x + 6

5x - 6

5x - 1

x + 1

x - 6

Answer 1

To factor the expression \( 20x^2 + 4x - 24 \), let's start by factoring out the greatest common factor (GCF):

1. The GCF of the coefficients \( 20, 4, \) and \( -24 \) is \( 4 \).
2. Factoring out \( 4 \) gives us:

\[
20x^2 + 4x - 24 = 4(5x^2 + x - 6)
\]

Next, we need to factor the quadratic \( 5x^2 + x - 6 \).

Now, we look for two numbers that multiply to \( 5 \times -6 = -30 \) and add to \( 1 \). The numbers \( 6 \) and \( -5 \) work since:

- \( 6 \times -5 = -30 \)
- \( 6 + (-5) = 1 \)

Using these, we can rewrite the expression:

\[
5x^2 + 6x - 5x - 6
\]

Now, we group the terms:

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

Factoring by grouping, we get:

\[
x(5x + 6) - 1(5x + 6)
\]

This can be further factored as:

\[
(5x + 6)(x - 1)
\]

Putting everything together, we have:

\[
20x^2 + 4x - 24 = 4(5x + 6)(x - 1)
\]

The factors of the entire expression \( 20x^2 + 4x - 24 \) are thus:

1. \( 4 \)
2. \( 5x + 6 \)
3. \( x - 1 \)

Now, let's see if any of the given choices match these factors. The options were:

- 4
- \( x - 1 \)
- \( 5x + 1 \)
- 3
- \( 5x + 6 \)
- \( x + 6 \)
- \( 5x - 6 \)
- \( 5x - 1 \)
- \( x + 1 \)
- \( x - 6 \)

The factors of \( 20x^2 + 4x - 24 \) from the options provided are:

- **4**
- **\( x - 1 \)**
- **\( 5x + 6 \)**

Therefore, the selected factors of \( 20x^2 + 4x - 24 \) are:

- **4**
- **\( x - 1 \)**
- **\( 5x + 6 \)**