Ontbinden in factoren (2)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

1. \(-147x^{10}-42x^{6}-3x^{2}\)
2. \(-54p^{5}+24p^{3}\)
3. \(32s^{7}+16s^{5}+2s^{3}\)
4. \(96q^{8}+48q^{6}s+6q^{4}s^2\)
5. \(-12a^{7}+27a^{5}\)
6. \(-8x^{6}-24x^{5}-18x^{4}\)
7. \(-80a^{8}+120a^{6}-45a^{4}\)
8. \(98a^{9}+168a^{7}y+72a^{5}y^2\)
9. \(y^{6}-8y^{5}+16y^{4}\)
10. \(5y^{4}-320y^{2}\)
11. \(-3a^{4}+192a^{2}\)
12. \(-320q^{15}+560q^{10}-245q^{5}\)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

Verbetersleutel

1. \(-147x^{10}-42x^{6}-3x^{2}=-3x^{2}(49x^{8}+14x^4+1)=-3x^{2}(7x^4+1)^2\)
2. \(-54p^{5}+24p^{3}=-6p^{3}(9p^{2}-4)=-6p^{3}(3p+2)(3p-2)\)
3. \(32s^{7}+16s^{5}+2s^{3}=2s^{3}(16s^{4}+8s^2+1)=2s^{3}(4s^2+1)^2\)
4. \(96q^{8}+48q^{6}s+6q^{4}s^2=6q^{4}(16q^{4}+8q^2s+s^2)=6q^{4}(4q^2+s)^2\)
5. \(-12a^{7}+27a^{5}=-3a^{5}(4a^{2}-9)=-3a^{5}(2a+3)(2a-3)\)
6. \(-8x^{6}-24x^{5}-18x^{4}=-2x^{4}(4x^{2}+12x+9)=-2x^{4}(2x+3)^2\)
7. \(-80a^{8}+120a^{6}-45a^{4}=-5a^{4}(16a^{4}-24a^2+9)=-5a^{4}(4a^2-3)^2\)
8. \(98a^{9}+168a^{7}y+72a^{5}y^2=2a^{5}(49a^{4}+84a^2y+36y^2)=2a^{5}(7a^2+6y)^2\)
9. \(y^{6}-8y^{5}+16y^{4}=y^{4}(y^2-8y+16)=y^{4}(y-4)^2\)
10. \(5y^{4}-320y^{2}=5y^{2}(y^2-64)=5y^{2}(y+8)(y-8)\)
11. \(-3a^{4}+192a^{2}=-3a^{2}(a^2-64)=-3a^{2}(a-8)(a+8)\)
12. \(-320q^{15}+560q^{10}-245q^{5}=-5q^{5}(64q^{10}-112q^5+49)=-5q^{5}(8q^5-7)^2\)