Question

Drag each tile to the correct box.
Factor each expression completely by factoring out the largest common whole number possible.

Then, order the expressions from least to greatest whole number that was factored out of each expression.
122+42x
3x+29-2x
4x+16x+24
24x+48-3x

Answer 1

To factor each expression completely by factoring out the largest common whole number, we will analyze each expression one by one.

1. **Expression: \(122 + 42x\)**
- The GCF of \(122\) and \(42\) is \(2\).
- Factored form: \(2(61 + 21x)\)

2. **Expression: \(3x + 29 - 2x\)**
- Combine like terms: \(3x - 2x + 29 = x + 29\)
- The GCF is \(1\) (since there's no whole number greater than \(1\) that divides both terms).
- Factored form: \(1(x + 29)\)

3. **Expression: \(4x + 16x + 24\)**
- Combine like terms: \(4x + 16x = 20x\)
- The GCF of \(20x\) and \(24\) is \(4\).
- Factored form: \(4(5x + 6)\)

4. **Expression: \(24x + 48 - 3x\)**
- Combine like terms: \(24x - 3x + 48 = 21x + 48\)
- The GCF of \(21\) and \(48\) is \(3\).
- Factored form: \(3(7x + 16)\)

Now we will summarize the GCFs we found:

1. \(122 + 42x\) → GCF = \(2\)
2. \(3x + 29 - 2x\) → GCF = \(1\)
3. \(4x + 16x + 24\) → GCF = \(4\)
4. \(24x + 48 - 3x\) → GCF = \(3\)

Now, let's order the expressions from least to greatest based on the whole number factored out:

1. \(3x + 29 - 2x\) → GCF = \(1\)
2. \(24x + 48 - 3x\) → GCF = \(3\)
3. \(4x + 16x + 24\) → GCF = \(4\)
4. \(122 + 42x\) → GCF = \(2\)

Ordering them gives us:

1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

So the boxed order is:

- **Least to greatest common whole number factored out:**
- \(1\) (from \(3x + 29 - 2x\))
- \(2\) (from \(122 + 42x\))
- \(3\) (from \(24x + 48 - 3x\))
- \(4\) (from \(4x + 16x + 24\))