What you’ll learn
Factor GCF from algebraic expressions.
Key idea
Every original term must be divided by the same extracted monomial, retaining its sign.
Require greatest common monomial outside; equivalent expansion or a remaining common inner factor does not complete the task.
Worked example
Enter the exact value or ordered values in the format requested below.
Factor 6x²+16x by its greatest common monomial completely. Enter factored expression, not expansion or an incomplete factor.
- Coefficient gcd(6,16)=2; both terms share x, so maximal common monomial is 2x.
- Divide both terms by 2x: 3x and 8; 2x(3x+8) expands to 6x²+16x with no shared inner factor.
Answer: 2x(3x+8)
Quick Check
Evaluate a worked attempt at factor gcf from algebraic expressions, identify the first invalid step, and provide the correction.
Factor 14x²-10x: Step 1 chooses greatest monomial 2x. Step 2 writes 2x(7x-10), leaving the original linear coefficient inside. Locate the first invalid step and repair the product.