Answer: 2cd^2e^3( 5d^2 - 8cd^4 + 2c^4e )
The GCF is 2cd^2e^3
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Step-by-step explanation:
For now, we'll focus on the coefficients. These are the numbers to the left of the variable terms.
The coefficients are: 10, -16, 4
Find the prime factorization of each coefficient:
- 10 = 2*5
- 16 = 2*2*2*2
- 4 = 2*2
Notice that each prime factorization has exactly one copy of "2" and nothing else in common, which means the GCF of 10, 16, and 4 is 2. You can use a factor tree to help verify this.
Therefore, the final coefficient we'll factor out is 2.
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Now onto the variable terms.
The variable terms are: cd^4e^3 and c^2d^6e^3 and c^5d^2e^4
Focus on the c terms and they are: c, c^2, c^5
The GCF of the c terms will be the one with the smallest exponent. So that would be c.
The d terms are d^4, d^6, d^2. Circle d^2 since that involves the smallest exponent.
The e terms are e^3, e^3, e^4. The GCF of the e terms is e^3 because we circle the smallest exponent.
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Summary so far:
- The GCF of the coefficients is 2
- The GCF of the c terms is c
- The GCF of the d terms is d^2
- The GCF of the e terms is e^3
The GCF of each piece is glued together to get the overall GCF.
The overall GCF is 2cd^2e^3
What do we do with this GCF? We will divide each original term by the GCF to help us factor out the GCF.
Those results are then what's left in the parenthesis after factoring out the GCF.
So we have this final answer
2cd^2e^3( 5d^2 - 8cd^4 + 2c^4e )
The answer can be confirmed by distributing the outer term back through to each inner term.