Question

1. $45k^{2}+18k + 72$
2. $-6b^{6}+10b^{5}+6b^{4}$
3. $30n^{4}+6n^{3}+48n^{2}$
4. $35 + 50b+50b^{2}$

Explanation:

Problem 13: $45k^2 + 18k + 72$

Step1: Find GCF of coefficients

GCF(45,18,72) = 9

Step2: Factor out the GCF

$9(5k^2 + 2k + 8)$

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Problem 14: $-6b^6 + 10b^5 + 6b^4$

Step1: Find GCF of terms

GCF(-6,10,6) = 2; lowest $b$-power is $b^4$, so GCF = $2b^4$

Step2: Factor out the GCF

$2b^4(-3b^2 + 5b + 3)$

Step3: Factor out negative sign (optional)

$-2b^4(3b^2 - 5b - 3)$

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Problem 15: $30n^4 + 6n^3 + 48n^2$

Step1: Find GCF of terms

GCF(30,6,48) = 6; lowest $n$-power is $n^2$, so GCF = $6n^2$

Step2: Factor out the GCF

$6n^2(5n^2 + n + 8)$

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Problem 16: $35 + 50b + 50b^2$

Step1: Rewrite in standard form

$50b^2 + 50b + 35$

Step2: Find GCF of coefficients

GCF(50,50,35) = 5

Step3: Factor out the GCF

$5(10b^2 + 10b + 7)$

Answer:

1. $9(5k^2 + 2k + 8)$
2. $-2b^4(3b^2 - 5b - 3)$ or $2b^4(-3b^2 + 5b + 3)$
3. $6n^2(5n^2 + n + 8)$
4. $5(10b^2 + 10b + 7)$