Let's address the questions step-by-step.
### Question 3: Factoring [tex]\(20 - 4x^3\)[/tex]
To factor [tex]\(20 - 4x^3\)[/tex], we should look for the greatest common factor (GCF) of the terms in the expression.
1. Identify the terms: [tex]\(20\)[/tex] and [tex]\(-4x^3\)[/tex].
2. Determine the GCF of [tex]\(20\)[/tex] and [tex]\(-4\)[/tex]:
- [tex]\(20 = 2^2 \cdot 5\)[/tex]
- [tex]\(-4 = -2^2\)[/tex]
- The GCF is [tex]\(4\)[/tex].
3. Factor out [tex]\(4\)[/tex] from each term:
- [tex]\(20 \div 4 = 5\)[/tex]
- [tex]\(-4x^3 \div 4 = -x^3\)[/tex]
Therefore, we can write [tex]\(20 - 4x^3\)[/tex] as:
[tex]\[ 20 - 4x^3 = 4(5 - x^3) \][/tex]
From the provided multiple-choice options, the answer is:
[tex]\[ \boxed{4(5 - x^3)} \][/tex]
### Question 4: Factoring [tex]\(6x + 36\)[/tex]
To factor [tex]\(6x + 36\)[/tex], we should again look for the greatest common factor (GCF) of the terms in the expression.
1. Identify the terms: [tex]\(6x\)[/tex] and [tex]\(36\)[/tex].
2. Determine the GCF of [tex]\(6x\)[/tex] and [tex]\(36\)[/tex]:
- [tex]\(6x = 6 \cdot x\)[/tex]
- [tex]\(36 = 6 \cdot 6\)[/tex]
- The GCF is [tex]\(6\)[/tex].
3. Factor out [tex]\(6\)[/tex] from each term:
- [tex]\(6x \div 6 = x\)[/tex]
- [tex]\(36 \div 6 = 6\)[/tex]
Therefore, we can write [tex]\(6x + 36\)[/tex] as:
[tex]\[ 6x + 36 = 6(x + 6) \][/tex]
From the provided multiple-choice option, the answer is:
[tex]\[ \boxed{6(x + 36)} \][/tex]
However, note that there may be a typo in the option given, as the corrected factor form should be:
[tex]\[ 6(x + 6) \][/tex]
In conclusion:
- The correct answer to Question 3 is [tex]\(4(5 - x^3)\)[/tex].
- The correct answer to Question 4 should correct the error in the provided option and be [tex]\(6(x + 6)\)[/tex].
