Question

Factor out the GCF and write your answer in factored form.

10cd^4e^3 - 16c^2d^6e^3 +4c^5d^2e^4

please show how you get the answer!!

Answer 1

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.

`(10cd^4e^3)/(2cd^2e^3) = 5d^2\\\\(-16c^2d^6e^3)/(2cd^2e^3) = -8cd^4\\\\(4c^5d^2e^4)/(2cd^2e^3) = 2c^4e\\\\`

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.