Question

1. $15n^{2}-27n-6$
2. $5x^{2}-18x+9$
3. $4n^{2}-15n-25$
4. $4x^{2}-35x+49$
5. $4n^{2}-17n+4$
6. $6x^{2}+7x-49$
7. $6x^{2}+37x+6$
8. $-6a^{2}-25a-25$
9. $6n^{2}+5n-6$
10. $16b^{2}+60b-100$

Explanation:

Step1: Factor $15n^2-27n-6$

First factor out GCF 3: $3(5n^2-9n-2)$. Then factor quadratic: $3(5n+1)(n-2)$

Step2: Factor $5x^2-18x+9$

Find pair: $-15,-3$. Split and factor: $(5x-3)(x-3)$

Step3: Factor $4n^2-15n-25$

Find pair: $-20,5$. Split and factor: $(4n+5)(n-5)$

Step4: Factor $4x^2-35x+49$

Find pair: $-28,-7$. Split and factor: $(4x-7)(x-7)$

Step5: Factor $4n^2-17n+4$

Find pair: $-16,-1$. Split and factor: $(4n-1)(n-4)$

Step6: Factor $6x^2+7x-49$

Find pair: $21,-14$. Split and factor: $(3x+7)(2x-7)$

Step7: Factor $6x^2+37x+6$

Find pair: $36,1$. Split and factor: $(6x+1)(x+6)$

Step8: Factor $-6a^2-25a-25$

Factor out -1: $-(6a^2+25a+25)$. Factor quadratic: $-(2a+5)(3a+5)$

Step9: Factor $6n^2+5n-6$

Find pair: $9,-4$. Split and factor: $(3n-2)(2n+3)$

Step10: Factor $16b^2+60b-100$

First factor GCF 4: $4(4b^2+15b-25)$. Factor quadratic: $4(4b-5)(b+5)$

Answer:

1. $3(5n+1)(n-2)$
2. $(5x-3)(x-3)$
3. $(4n+5)(n-5)$
4. $(4x-7)(x-7)$
5. $(4n-1)(n-4)$
6. $(3x+7)(2x-7)$
7. $(6x+1)(x+6)$
8. $-(2a+5)(3a+5)$
9. $(3n-2)(2n+3)$
10. $4(4b-5)(b+5)$