Ontbinden in factoren (2)

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

1. \(3x^{5}-48x^{4}+192x^{3}\)
2. \(27s^{8}+72s^{5}+48s^{2}\)
3. \(-2a^{7}+8a^{5}\)
4. \(6a^{7}+84a^{6}+294a^{5}\)
5. \(45p^{17}-80p^{5}\)
6. \(-54x^{6}+288x^{5}-384x^{4}\)
7. \(-80q^{5}+280q^{4}-245q^{3}\)
8. \(2q^{7}-18q^{5}\)
9. \(p^{7}-64p^{5}\)
10. \(-12a^{4}+147a^{2}\)
11. \(294x^{7}-168x^{6}+24x^{5}\)
12. \(-75x^{6}-240x^{5}-192x^{4}\)

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

Verbetersleutel

1. \(3x^{5}-48x^{4}+192x^{3}=3x^{3}(x^2-16x+64)=3x^{3}(x-8)^2\)
2. \(27s^{8}+72s^{5}+48s^{2}=3s^{2}(9s^{6}+24s^3+16)=3s^{2}(3s^3+4)^2\)
3. \(-2a^{7}+8a^{5}=-2a^{5}(a^2-4)=-2a^{5}(a-2)(a+2)\)
4. \(6a^{7}+84a^{6}+294a^{5}=6a^{5}(a^2+14a+49)=6a^{5}(a+7)^2\)
5. \(45p^{17}-80p^{5}=5p^{5}(9p^{12}-16)=5p^{5}(3p^6+4)(3p^6-4)\)
6. \(-54x^{6}+288x^{5}-384x^{4}=-6x^{4}(9x^{2}-48x+64)=-6x^{4}(3x-8)^2\)
7. \(-80q^{5}+280q^{4}-245q^{3}=-5q^{3}(16q^{2}-56q+49)=-5q^{3}(4q-7)^2\)
8. \(2q^{7}-18q^{5}=2q^{5}(q^2-9)=2q^{5}(q-3)(q+3)\)
9. \(p^{7}-64p^{5}=p^{5}(p^2-64)=p^{5}(p+8)(p-8)\)
10. \(-12a^{4}+147a^{2}=-3a^{2}(4a^{2}-49)=-3a^{2}(2a+7)(2a-7)\)
11. \(294x^{7}-168x^{6}+24x^{5}=6x^{5}(49x^{2}-28x+4)=6x^{5}(7x-2)^2\)
12. \(-75x^{6}-240x^{5}-192x^{4}=-3x^{4}(25x^{2}+80x+64)=-3x^{4}(5x+8)^2\)