How do you factor using GCF?

Understand the Problem

The question is asking for the process of factoring an expression by using the greatest common factor (GCF). This involves finding the largest factor that divides all terms of the expression and using it to simplify or factor the expression further.

Answer

The factored form of $ 12x^2 + 8x $ is $ 4x(3x + 2) $.

Steps to Solve

Identify the expression
First, write down the expression you want to factor. For example, consider the expression ( 12x^2 + 8x ).
Find the GCF of the coefficients
Look at the coefficients (the numbers in front of the variables) in the expression. Here, the coefficients are 12 and 8. The GCF of 12 and 8 is 4.
Identify the GCF of the variables
Next, look for the variables. In this case, both terms have ( x ) in them. The GCF for the variables is ( x ) since the lowest power of ( x ) present in both terms is ( x^1 ).
Combine the GCF
Now combine both parts of the GCF. The GCF for the expression ( 12x^2 + 8x ) is ( 4x ).
Factor out the GCF
Rewrite the original expression by factoring out the GCF. This means you can express ( 12x^2 + 8x ) as: $$ 12x^2 + 8x = 4x(3x + 2) $$
Check your work
Finally, ensure that when you distribute ( 4x ) back into ( (3x + 2) ), you return to the original expression: $$ 4x(3x + 2) = 12x^2 + 8x $$

The factored form of the expression ( 12x^2 + 8x ) is ( 4x(3x + 2) ).

More Information

Factoring by using the greatest common factor (GCF) is an essential skill in algebra. It helps to simplify expressions before solving equations or performing further operations. Factoring can also reveal the roots of equations when set to zero.

Tips

Forgetting to find the GCF of the variable terms. Always check for the lowest power present in each term.
Not distributing back to the original expression to verify the factorization. It's essential to double-check your work by expanding the factored expression.

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