Answer :
To factor the given expression [tex]\(45x^5 - 9x^4\)[/tex], follow these steps:
1. Identify Common Factors:
First, look for common factors in the terms of the expression. In this case, both terms, [tex]\(45x^5\)[/tex] and [tex]\(9x^4\)[/tex], have a common factor of [tex]\(9x^4\)[/tex].
2. Factor Out the Common Factor:
Extract the greatest common factor (GCF) from the expression. Here, the GCF is [tex]\(9x^4\)[/tex], so factor it out:
[tex]\[
45x^5 - 9x^4 = 9x^4(5x - 1)
\][/tex]
3. Check Your Work:
Multiply back to ensure the factorization is correct:
[tex]\[
9x^4(5x - 1) = 9x^4 \cdot 5x - 9x^4 \cdot 1 = 45x^5 - 9x^4
\][/tex]
The original expression is obtained, confirming that the factorization is accurate.
The factored expression is [tex]\(9x^4(5x - 1)\)[/tex].
1. Identify Common Factors:
First, look for common factors in the terms of the expression. In this case, both terms, [tex]\(45x^5\)[/tex] and [tex]\(9x^4\)[/tex], have a common factor of [tex]\(9x^4\)[/tex].
2. Factor Out the Common Factor:
Extract the greatest common factor (GCF) from the expression. Here, the GCF is [tex]\(9x^4\)[/tex], so factor it out:
[tex]\[
45x^5 - 9x^4 = 9x^4(5x - 1)
\][/tex]
3. Check Your Work:
Multiply back to ensure the factorization is correct:
[tex]\[
9x^4(5x - 1) = 9x^4 \cdot 5x - 9x^4 \cdot 1 = 45x^5 - 9x^4
\][/tex]
The original expression is obtained, confirming that the factorization is accurate.
The factored expression is [tex]\(9x^4(5x - 1)\)[/tex].
