Answer :
Sure, let's factor the expression [tex]\(9x^8 + 6x^7 + 33x^5\)[/tex] by pulling out the greatest common factor (GCF).
1. Identify the GCF of the coefficients:
- The terms in the expression are [tex]\(9x^8\)[/tex], [tex]\(6x^7\)[/tex], and [tex]\(33x^5\)[/tex].
- The coefficients are 9, 6, and 33.
- The GCF of 9, 6, and 33 is 3, since 3 is the largest number that divides all of them.
2. Identify the GCF of the variables:
- The variable parts are [tex]\(x^8\)[/tex], [tex]\(x^7\)[/tex], and [tex]\(x^5\)[/tex].
- Since [tex]\(x^5\)[/tex] is the smallest power of [tex]\(x\)[/tex] in all terms, it is the GCF for the variable part.
3. Combine the GCFs:
- Combine the GCF of the coefficients (3) with the GCF of the variables ([tex]\(x^5\)[/tex]).
- The overall GCF is [tex]\(3x^5\)[/tex].
4. Factor out the GCF from the expression:
- Divide each term of the expression by the GCF [tex]\(3x^5\)[/tex]:
[tex]\[
\begin{align*}
\frac{9x^8}{3x^5} &= 3x^3, \\
\frac{6x^7}{3x^5} &= 2x^2, \\
\frac{33x^5}{3x^5} &= 11.
\end{align*}
\][/tex]
5. Write the factored expression:
- The expression [tex]\(9x^8 + 6x^7 + 33x^5\)[/tex] can be factored as:
[tex]\[
3x^5(3x^3 + 2x^2 + 11).
\][/tex]
That’s the fully factored expression!
1. Identify the GCF of the coefficients:
- The terms in the expression are [tex]\(9x^8\)[/tex], [tex]\(6x^7\)[/tex], and [tex]\(33x^5\)[/tex].
- The coefficients are 9, 6, and 33.
- The GCF of 9, 6, and 33 is 3, since 3 is the largest number that divides all of them.
2. Identify the GCF of the variables:
- The variable parts are [tex]\(x^8\)[/tex], [tex]\(x^7\)[/tex], and [tex]\(x^5\)[/tex].
- Since [tex]\(x^5\)[/tex] is the smallest power of [tex]\(x\)[/tex] in all terms, it is the GCF for the variable part.
3. Combine the GCFs:
- Combine the GCF of the coefficients (3) with the GCF of the variables ([tex]\(x^5\)[/tex]).
- The overall GCF is [tex]\(3x^5\)[/tex].
4. Factor out the GCF from the expression:
- Divide each term of the expression by the GCF [tex]\(3x^5\)[/tex]:
[tex]\[
\begin{align*}
\frac{9x^8}{3x^5} &= 3x^3, \\
\frac{6x^7}{3x^5} &= 2x^2, \\
\frac{33x^5}{3x^5} &= 11.
\end{align*}
\][/tex]
5. Write the factored expression:
- The expression [tex]\(9x^8 + 6x^7 + 33x^5\)[/tex] can be factored as:
[tex]\[
3x^5(3x^3 + 2x^2 + 11).
\][/tex]
That’s the fully factored expression!
