Question

Factor out the greatest common factor (GCF) of each polynomial.
Numbers
3x + b GCF:
choose your answer...
Variables x°-x'+x
GCF:
choose your answer...
く
Expressions
2x2-10x
GCF:
choose your answer...
Factor Out:
3x+ 6=
Answer
Factor Out:
-9
x3-x2+x=
Answer
Factor Out:
2x2 - 10x=| Answer
"Answer,
: 3(x+2)
:: 2xx- 5)
x(x*-x+1)

Answer 1

Let's factor out the greatest common factor (GCF) for each of the given polynomials step by step.

1. **For the polynomial \(3x + b\)**:
- The GCF of \(3x\) and \(b\) is **1** (assuming \(b\) is not a multiple of \(3x\)). Therefore:
- **GCF:** \(1\)

2. **For the polynomial \(x^3 - x^2 + x\)**:
- Each term (\(x^3\), \(-x^2\), and \(x\)) has a common factor of \(x\).
- Factor out \(x\):
- \(x(x^2 - x + 1)\)
- **GCF:** \(x\)
- Answer: \(x(x^2 - x + 1)\)

3. **For the expression \(2x^2 - 10x\)**:
- The coefficients \(2\) and \(-10\) have a GCF of \(2\), and both terms also share a factor of \(x\).
- GCF is \(2x\).
- Factor out \(2x\):
- \(2x(x - 5)\)
- **GCF:** \(2x\)
- Answer: \(2x(x - 5)\)

4. **For the expression \(3x + 6\)**:
- The GCF of \(3x\) and \(6\) is \(3\).
- Factor out \(3\):
- \(3(x + 2)\)
- **GCF:** \(3\)
- Answer: \(3(x + 2)\)

5. **For the expression \(-9(x^3 - x^2 + x)\)**:
- The GCF is \(-9\). We factor out \(-9\):
- \(-9((x^3 - x^2 + x)/-9)\)
- When we factor out \(-9\), we are left with \(x^3 - x^2 + x\).
- Therefore, it remains \( -9(x(x^2 - x + 1))\)
- **GCF:** \(-9\)
- Answer: \(-9(x(x^2 - x + 1))\)

Thus the consolidated results are:
- \(3x + b\): GCF = 1
- \(x^3 - x^2 + x\): GCF = \(x\), Factored Form: \(x(x^2 - x + 1)\)
- \(2x^2 - 10x\): GCF = \(2x\), Factored Form: \(2x(x - 5)\)
- \(3x + 6\): GCF = \(3\), Factored Form: \(3(x + 2)\)
- \(-9(x^3 - x^2 + x)\): GCF = \(-9\), Factored Form: \(-9(x(x^2 - x + 1))\)