Answer :
To factor the expression [tex]\(20x^4 + 45x^5\)[/tex] completely, we can follow these steps:
1. Identify Common Factors:
Look for the greatest common factor (GCF) of the terms in the expression. The terms are [tex]\(20x^4\)[/tex] and [tex]\(45x^5\)[/tex].
- The numerical GCF of 20 and 45 is 5.
- The variable factor involves [tex]\(x^4\)[/tex] and [tex]\(x^5\)[/tex]. The smallest power of [tex]\(x\)[/tex] is [tex]\(x^4\)[/tex], so [tex]\(x^4\)[/tex] is the variable part of the GCF.
Therefore, the GCF of the expression is [tex]\(5x^4\)[/tex].
2. Factor Out the GCF:
Divide each term by the GCF [tex]\(5x^4\)[/tex] and factor it out:
- [tex]\(20x^4 \div 5x^4 = 4\)[/tex]
- [tex]\(45x^5 \div 5x^4 = 9x\)[/tex]
So when you factor out [tex]\(5x^4\)[/tex], the expression becomes:
[tex]\[
5x^4(4 + 9x)
\][/tex]
3. Verify Simplification:
The expression inside the parentheses is [tex]\(4 + 9x\)[/tex]. Check if this can be simplified further or if it has any common factors, which in this case, it does not.
So, the completely factored form of the expression is:
[tex]\[
5x^4(9x + 4)
\][/tex]
1. Identify Common Factors:
Look for the greatest common factor (GCF) of the terms in the expression. The terms are [tex]\(20x^4\)[/tex] and [tex]\(45x^5\)[/tex].
- The numerical GCF of 20 and 45 is 5.
- The variable factor involves [tex]\(x^4\)[/tex] and [tex]\(x^5\)[/tex]. The smallest power of [tex]\(x\)[/tex] is [tex]\(x^4\)[/tex], so [tex]\(x^4\)[/tex] is the variable part of the GCF.
Therefore, the GCF of the expression is [tex]\(5x^4\)[/tex].
2. Factor Out the GCF:
Divide each term by the GCF [tex]\(5x^4\)[/tex] and factor it out:
- [tex]\(20x^4 \div 5x^4 = 4\)[/tex]
- [tex]\(45x^5 \div 5x^4 = 9x\)[/tex]
So when you factor out [tex]\(5x^4\)[/tex], the expression becomes:
[tex]\[
5x^4(4 + 9x)
\][/tex]
3. Verify Simplification:
The expression inside the parentheses is [tex]\(4 + 9x\)[/tex]. Check if this can be simplified further or if it has any common factors, which in this case, it does not.
So, the completely factored form of the expression is:
[tex]\[
5x^4(9x + 4)
\][/tex]
