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Answer :
Alright! Let's go through the problem together and simplify the expression [tex]\(6c^2 + 27c - 15\)[/tex].
1. Identify the Polynomial:
The expression we have is [tex]\(6c^2 + 27c - 15\)[/tex]. This is a quadratic polynomial, which means it is in the form of [tex]\(ax^2 + bx + c\)[/tex].
2. Look for Common Factors:
Before factoring, we can check if there is a common factor in all the terms. The coefficients are 6, 27, and -15.
3. Factor out the Greatest Common Factor (GCF):
The greatest common factor of 6, 27, and -15 is 3. Let's factor 3 out:
[tex]\[
6c^2 + 27c - 15 = 3(2c^2 + 9c - 5)
\][/tex]
4. Simplified Form:
After factoring out the GCF, the expression becomes [tex]\(3(2c^2 + 9c - 5)\)[/tex].
This is the simplified form. We’ve factored out the common factor, making the expression easier to work with if you're using it in further calculations or need to solve equations involving it. Let me know if you have any more questions!
1. Identify the Polynomial:
The expression we have is [tex]\(6c^2 + 27c - 15\)[/tex]. This is a quadratic polynomial, which means it is in the form of [tex]\(ax^2 + bx + c\)[/tex].
2. Look for Common Factors:
Before factoring, we can check if there is a common factor in all the terms. The coefficients are 6, 27, and -15.
3. Factor out the Greatest Common Factor (GCF):
The greatest common factor of 6, 27, and -15 is 3. Let's factor 3 out:
[tex]\[
6c^2 + 27c - 15 = 3(2c^2 + 9c - 5)
\][/tex]
4. Simplified Form:
After factoring out the GCF, the expression becomes [tex]\(3(2c^2 + 9c - 5)\)[/tex].
This is the simplified form. We’ve factored out the common factor, making the expression easier to work with if you're using it in further calculations or need to solve equations involving it. Let me know if you have any more questions!
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