Answer :
Sure, let's factor out the greatest common factor from the given polynomial [tex]\( 3x^3 + 7x^2 + 27x \)[/tex]. Here is the step-by-step solution:
1. Identify the terms in the polynomial:
[tex]\[ 3x^3, \quad 7x^2, \quad 27x \][/tex]
2. Determine the greatest common factor (GCF) of the terms:
- Identify the common factors in each term:
- [tex]\( 3x^3 \)[/tex] has factors: [tex]\( 3 \times x \times x \times x \)[/tex]
- [tex]\( 7x^2 \)[/tex] has factors: [tex]\( 7 \times x \times x \)[/tex]
- [tex]\( 27x \)[/tex] has factors: [tex]\( 27 \times x \)[/tex]
- The common factor across all terms is [tex]\( x \)[/tex] since each term has at least one [tex]\(x\)[/tex].
3. Factor out the GCF (which is [tex]\( x \)[/tex]):
[tex]\[ 3x^3 + 7x^2 + 27x = x(3x^2) + x(7x) + x(27) \][/tex]
4. Rewrite the polynomial with the GCF factored out:
[tex]\[ 3x^3 + 7x^2 + 27x = x(3x^2 + 7x + 27) \][/tex]
Thus, the factored form of the polynomial [tex]\( 3x^3 + 7x^2 + 27x \)[/tex] is:
[tex]\[ x(3x^2 + 7x + 27) \][/tex]
So, we have successfully factored out the greatest common factor from the given polynomial.
1. Identify the terms in the polynomial:
[tex]\[ 3x^3, \quad 7x^2, \quad 27x \][/tex]
2. Determine the greatest common factor (GCF) of the terms:
- Identify the common factors in each term:
- [tex]\( 3x^3 \)[/tex] has factors: [tex]\( 3 \times x \times x \times x \)[/tex]
- [tex]\( 7x^2 \)[/tex] has factors: [tex]\( 7 \times x \times x \)[/tex]
- [tex]\( 27x \)[/tex] has factors: [tex]\( 27 \times x \)[/tex]
- The common factor across all terms is [tex]\( x \)[/tex] since each term has at least one [tex]\(x\)[/tex].
3. Factor out the GCF (which is [tex]\( x \)[/tex]):
[tex]\[ 3x^3 + 7x^2 + 27x = x(3x^2) + x(7x) + x(27) \][/tex]
4. Rewrite the polynomial with the GCF factored out:
[tex]\[ 3x^3 + 7x^2 + 27x = x(3x^2 + 7x + 27) \][/tex]
Thus, the factored form of the polynomial [tex]\( 3x^3 + 7x^2 + 27x \)[/tex] is:
[tex]\[ x(3x^2 + 7x + 27) \][/tex]
So, we have successfully factored out the greatest common factor from the given polynomial.
Answer:
x(3x²+7x+27)
Step-by-step explanation:
To factor out the greatest common factor (GCF) from the expression [tex]3x^3 + 7x^2 + 27x[/tex] , follow these steps:
1. Identify the GCF of the terms:
The terms are [tex]3x^3 , 7x^2 , \:and \: 27x .[/tex]
- The coefficients are 3, 7, and 27. The GCF of these coefficients is 1 since 3, 7, and 27 have no common factors other than 1.
- The variable part involves x with the smallest power being x (as x is present in all terms).
Therefore, the GCF is x .
2. Factor out the GCF:
Factor x out from each term:
[tex]3x^3 + 7x^2 + 27x = x(3x^2 + 7x + 27)[/tex]
