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Factor the polynomial [tex]$12c^9 + 28c^7$[/tex].

1. Find the GCF of [tex]$12c^9$[/tex] and [tex]$28c^7$[/tex].
[tex]\[
\text{GCF} = 4c^7
\][/tex]

2. Write each term as a product, where one factor is the GCF.
[tex]\[
12c^9 = 4c^7(3c^2), \quad 28c^7 = 4c^7(7)
\][/tex]

3. Use the distributive property.

What is the resulting expression?

A. [tex]$4(3c^9 + 7c^7)$[/tex]
B. [tex]$4c^7(3c^2 + 7)$[/tex]
C. [tex]$4c^7(3c^9 + 7c^7)$[/tex]
D. [tex]$4c^7(12c^9 + 28c^7)$[/tex]

Sagot :

GinnyAnsweridn
To factor the polynomial [tex]\( 12 c^9 + 28 c^7 \)[/tex], let's follow the steps one by one:

1. Find the Greatest Common Factor (GCF):
- For the coefficients 12 and 28, the GCF is 4.
- For the variable parts [tex]\( c^9 \)[/tex] and [tex]\( c^7 \)[/tex], the GCF is [tex]\( c^7 \)[/tex] since it's the smallest power of [tex]\( c \)[/tex] common to both terms.

Therefore, the GCF of [tex]\( 12 c^9 \)[/tex] and [tex]\( 28 c^7 \)[/tex] is [tex]\( 4 c^7 \)[/tex].

[tex]\[ \text{GCF} = 4 c^7 \][/tex]

2. Write each term as a product, where one factor is the GCF:
- For [tex]\( 12 c^9 \)[/tex]:
[tex]\[ 12 c^9 = (4 c^7) \cdot 3 c^2 \][/tex]
- For [tex]\( 28 c^7 \)[/tex]:
[tex]\[ 28 c^7 = (4 c^7) \cdot 7 \][/tex]

So, we can rewrite the polynomial as:
[tex]\[ 12 c^9 + 28 c^7 = 4 c^7 (3 c^2) + 4 c^7 (7) \][/tex]

3. Use the distributive property:
Factor out the common term [tex]\( 4 c^7 \)[/tex]:

[tex]\[ 12 c^9 + 28 c^7 = 4 c^7 (3 c^2 + 7) \][/tex]

The correct resulting expression is:
[tex]\[ 4 c^7 (3 c^2 + 7) \][/tex]

So, the correct answer is:
[tex]\[ 4 c^7 \left( 3 c^2 + 7 \right) \][/tex]
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