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Answer :
Let's factor the expression [tex]\(9x^3 + 45x^2\)[/tex] step-by-step.
1. Identify the Greatest Common Factor (GCF):
- Look at both terms: [tex]\(9x^3\)[/tex] and [tex]\(45x^2\)[/tex].
- The coefficients are 9 and 45. The greatest common factor of 9 and 45 is 9.
- Also, each term has a factor of [tex]\(x^2\)[/tex].
2. Factor out the GCF:
- The GCF identified is [tex]\(9x^2\)[/tex].
3. Write the expression in factored form:
- When you factor out [tex]\(9x^2\)[/tex] from [tex]\(9x^3\)[/tex], you get [tex]\(x\)[/tex] because [tex]\(9x^3 \div 9x^2 = x\)[/tex].
- When you factor out [tex]\(9x^2\)[/tex] from [tex]\(45x^2\)[/tex], you get 5 because [tex]\(45x^2 \div 9x^2 = 5\)[/tex].
4. Combine these into a single expression:
- The expression becomes [tex]\(9x^2(x + 5)\)[/tex].
So, the factored form of [tex]\(9x^3 + 45x^2\)[/tex] is [tex]\(9x^2(x + 5)\)[/tex].
1. Identify the Greatest Common Factor (GCF):
- Look at both terms: [tex]\(9x^3\)[/tex] and [tex]\(45x^2\)[/tex].
- The coefficients are 9 and 45. The greatest common factor of 9 and 45 is 9.
- Also, each term has a factor of [tex]\(x^2\)[/tex].
2. Factor out the GCF:
- The GCF identified is [tex]\(9x^2\)[/tex].
3. Write the expression in factored form:
- When you factor out [tex]\(9x^2\)[/tex] from [tex]\(9x^3\)[/tex], you get [tex]\(x\)[/tex] because [tex]\(9x^3 \div 9x^2 = x\)[/tex].
- When you factor out [tex]\(9x^2\)[/tex] from [tex]\(45x^2\)[/tex], you get 5 because [tex]\(45x^2 \div 9x^2 = 5\)[/tex].
4. Combine these into a single expression:
- The expression becomes [tex]\(9x^2(x + 5)\)[/tex].
So, the factored form of [tex]\(9x^3 + 45x^2\)[/tex] is [tex]\(9x^2(x + 5)\)[/tex].
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