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Answer :
Sure! Let's factorize the expression [tex]\(27x^3 - 21x^2 + 15x^4\)[/tex] step-by-step:
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients: 27, 21, and 15. The greatest common factor of these numbers is 3.
- Look at the variables: each term contains at least [tex]\(x^2\)[/tex]. So, the GCF of the variable part is [tex]\(x^2\)[/tex].
2. Factor out the GCF:
- We first factor out [tex]\(3x^2\)[/tex] from the expression:
[tex]\[
27x^3 - 21x^2 + 15x^4 = 3x^2(9x - 7 + 5x^2)
\][/tex]
3. Reorder the terms inside the parenthesis:
- Rearrange the terms inside the parentheses in standard form (highest power of x to lowest) to make it easier to read:
[tex]\[
3x^2(5x^2 + 9x - 7)
\][/tex]
So, the factorized form of the expression is [tex]\(3x^2(5x^2 + 9x - 7)\)[/tex]. This is your answer!
1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients: 27, 21, and 15. The greatest common factor of these numbers is 3.
- Look at the variables: each term contains at least [tex]\(x^2\)[/tex]. So, the GCF of the variable part is [tex]\(x^2\)[/tex].
2. Factor out the GCF:
- We first factor out [tex]\(3x^2\)[/tex] from the expression:
[tex]\[
27x^3 - 21x^2 + 15x^4 = 3x^2(9x - 7 + 5x^2)
\][/tex]
3. Reorder the terms inside the parenthesis:
- Rearrange the terms inside the parentheses in standard form (highest power of x to lowest) to make it easier to read:
[tex]\[
3x^2(5x^2 + 9x - 7)
\][/tex]
So, the factorized form of the expression is [tex]\(3x^2(5x^2 + 9x - 7)\)[/tex]. This is your answer!
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