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Answer :
Sure! Let's factor each of the given polynomials using their Greatest Common Factor (GCF). When we factor using the GCF, we look for the largest factor that can divide each term in the polynomial evenly.
11) [tex]\( 20 - 35n^2 - 20n^3 \)[/tex]
Find the GCF of [tex]\( 20, -35n^2, \)[/tex] and [tex]\( -20n^3 \)[/tex]. The GCF is 5. Factoring 5 out, we get:
[tex]\[ 5(4 - 7n^2 - 4n^3) \][/tex]
Rearrange terms:
[tex]\[ -5(4n^3 + 7n^2 - 4) \][/tex]
12) [tex]\( 9x^6 - 63x^3 - 90x^2 \)[/tex]
The GCF of [tex]\( 9x^6, -63x^3, \)[/tex] and [tex]\( -90x^2 \)[/tex] is [tex]\( 9x^2 \)[/tex].
[tex]\[ 9x^2(x^4 - 7x - 10) \][/tex]
13) [tex]\( -3k^3 + 15k^2 - 6k \)[/tex]
The GCF of [tex]\( -3k^3, 15k^2, \)[/tex] and [tex]\( -6k \)[/tex] is [tex]\(-3k\)[/tex].
[tex]\[ -3k(k^2 - 5k + 2) \][/tex]
14) [tex]\( 50p^3 + 50p^2 - 20 \)[/tex]
The GCF here is 10.
[tex]\[ 10(5p^3 + 5p^2 - 2) \][/tex]
15) [tex]\( 32n^3 + 28n - 20 \)[/tex]
Here, the GCF is 4.
[tex]\[ 4(8n^3 + 7n - 5) \][/tex]
16) [tex]\( -90x^5 + 100x + 60 \)[/tex]
The GCF is 10.
[tex]\[ -10(9x^5 - 10x - 6) \][/tex]
17) [tex]\( 3m^2 + 9m + 27 \)[/tex]
The GCF is 3.
[tex]\[ 3(m^2 + 3m + 9) \][/tex]
18) [tex]\( 12r^2 + 4r - 12 \)[/tex]
The GCF is 4.
[tex]\[ 4(3r^2 + r - 3) \][/tex]
19) [tex]\( 64 + 40x^2 + 72x \)[/tex]
The GCF is 8.
[tex]\[ 8(5x^2 + 9x + 8) \][/tex]
20) [tex]\( -18n^2 + 15n - 15 \)[/tex]
The GCF is 3.
[tex]\[ -3(6n^2 - 5n + 5) \][/tex]
These are the factored forms of each polynomial using their greatest common factors. If you work through them step-by-step, you'll understand how each term contributes to the factorization process!
11) [tex]\( 20 - 35n^2 - 20n^3 \)[/tex]
Find the GCF of [tex]\( 20, -35n^2, \)[/tex] and [tex]\( -20n^3 \)[/tex]. The GCF is 5. Factoring 5 out, we get:
[tex]\[ 5(4 - 7n^2 - 4n^3) \][/tex]
Rearrange terms:
[tex]\[ -5(4n^3 + 7n^2 - 4) \][/tex]
12) [tex]\( 9x^6 - 63x^3 - 90x^2 \)[/tex]
The GCF of [tex]\( 9x^6, -63x^3, \)[/tex] and [tex]\( -90x^2 \)[/tex] is [tex]\( 9x^2 \)[/tex].
[tex]\[ 9x^2(x^4 - 7x - 10) \][/tex]
13) [tex]\( -3k^3 + 15k^2 - 6k \)[/tex]
The GCF of [tex]\( -3k^3, 15k^2, \)[/tex] and [tex]\( -6k \)[/tex] is [tex]\(-3k\)[/tex].
[tex]\[ -3k(k^2 - 5k + 2) \][/tex]
14) [tex]\( 50p^3 + 50p^2 - 20 \)[/tex]
The GCF here is 10.
[tex]\[ 10(5p^3 + 5p^2 - 2) \][/tex]
15) [tex]\( 32n^3 + 28n - 20 \)[/tex]
Here, the GCF is 4.
[tex]\[ 4(8n^3 + 7n - 5) \][/tex]
16) [tex]\( -90x^5 + 100x + 60 \)[/tex]
The GCF is 10.
[tex]\[ -10(9x^5 - 10x - 6) \][/tex]
17) [tex]\( 3m^2 + 9m + 27 \)[/tex]
The GCF is 3.
[tex]\[ 3(m^2 + 3m + 9) \][/tex]
18) [tex]\( 12r^2 + 4r - 12 \)[/tex]
The GCF is 4.
[tex]\[ 4(3r^2 + r - 3) \][/tex]
19) [tex]\( 64 + 40x^2 + 72x \)[/tex]
The GCF is 8.
[tex]\[ 8(5x^2 + 9x + 8) \][/tex]
20) [tex]\( -18n^2 + 15n - 15 \)[/tex]
The GCF is 3.
[tex]\[ -3(6n^2 - 5n + 5) \][/tex]
These are the factored forms of each polynomial using their greatest common factors. If you work through them step-by-step, you'll understand how each term contributes to the factorization process!
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