part ii - assorted factoring completely problems\nfactor each of the following polynomials as completely as…

part ii - assorted factoring completely problems\nfactor each of the following polynomials as completely as possible. show each step. (each of these will require that you factor more than once.)\n10. ( 3 x^{4}-75 x^{2} )\n11. ( x^{4}+6 x^{2}-7 )\n12. ( x^{3}-x^{2}-9 x+9 )\n13. ( 54-6 x^{4} )\n14. ( 4 x^{2}+20 x+24 )\n15. ( x^{4}+21 x^{2}-100 )\n16. ( 2 x^{3}-x^{2}-2 x+1 )\n17. ( 20-45 x^{2} )\n18. ( 4 x^{3}-12 x^{2}-40 x )\n19. ( y^{4}-8 y^{2}+16 )\n20. ( x^{5}-81 x )\n21. ( x^{3}+2 x^{2}-4 x-8 )

part ii - assorted factoring completely problems\nfactor each of the following polynomials as completely as possible. show each step. (each of these will require that you factor more than once.)\n10. ( 3 x^{4}-75 x^{2} )\n11. ( x^{4}+6 x^{2}-7 )\n12. ( x^{3}-x^{2}-9 x+9 )\n13. ( 54-6 x^{4} )\n14. ( 4 x^{2}+20 x+24 )\n15. ( x^{4}+21 x^{2}-100 )\n16. ( 2 x^{3}-x^{2}-2 x+1 )\n17. ( 20-45 x^{2} )\n18. ( 4 x^{3}-12 x^{2}-40 x )\n19. ( y^{4}-8 y^{2}+16 )\n20. ( x^{5}-81 x )\n21. ( x^{3}+2 x^{2}-4 x-8 )

Answer

Explanation:

Step1: Factor out the greatest common factor (GCF)

For (3x^{4}-75x^{2}), the GCF of (3x^{4}) and (75x^{2}) is (3x^{2}). [3x^{4}-75x^{2}=3x^{2}(x^{2} - 25)]

Step2: Use the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b))

Here (a=x) and (b = 5) since (x^{2}-25=x^{2}-5^{2}) [3x^{2}(x^{2}-25)=3x^{2}(x + 5)(x - 5)]

Answer:

(3x^{2}(x + 5)(x - 5))