Ontbinden in factoren (2)

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

1. \(48a^{10}+24a^{7}p+3a^{4}p^2\)
2. \(-4x^{16}+49x^{2}\)
3. \(-16x^{6}-8x^{5}-x^{4}\)
4. \(-48x^{7}+168x^{6}-147x^{5}\)
5. \(25x^{4}-49x^{2}\)
6. \(-2s^{4}+72s^{2}\)
7. \(-147x^{13}-252x^{9}-108x^{5}\)
8. \(-6b^{4}+48b^{3}-96b^{2}\)
9. \(5b^{4}+10b^{3}+5b^{2}\)
10. \(-294y^{9}-84y^{7}-6y^{5}\)
11. \(-128s^{4}+224s^{3}-98s^{2}\)
12. \(48p^{13}+72p^{9}q+27p^{5}q^2\)

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

Verbetersleutel

1. \(48a^{10}+24a^{7}p+3a^{4}p^2=3a^{4}(16a^{6}+8a^3p+p^2)=3a^{4}(4a^3+p)^2\)
2. \(-4x^{16}+49x^{2}=-x^{2}(4x^{14}-49)=-x^{2}(2x^7+7)(2x^7-7)\)
3. \(-16x^{6}-8x^{5}-x^{4}=-x^{4}(16x^{2}+8x+1)=-x^{4}(4x+1)^2\)
4. \(-48x^{7}+168x^{6}-147x^{5}=-3x^{5}(16x^{2}-56x+49)=-3x^{5}(4x-7)^2\)
5. \(25x^{4}-49x^{2}=x^{2}(25x^{2}-49)=x^{2}(5x+7)(5x-7)\)
6. \(-2s^{4}+72s^{2}=-2s^{2}(s^2-36)=-2s^{2}(s-6)(s+6)\)
7. \(-147x^{13}-252x^{9}-108x^{5}=-3x^{5}(49x^{8}+84x^4+36)=-3x^{5}(7x^4+6)^2\)
8. \(-6b^{4}+48b^{3}-96b^{2}=-6b^{2}(b^2-8b+16)=-6b^{2}(b-4)^2\)
9. \(5b^{4}+10b^{3}+5b^{2}=5b^{2}(b^2+2b+1)=5b^{2}(b+1)^2\)
10. \(-294y^{9}-84y^{7}-6y^{5}=-6y^{5}(49y^{4}+14y^2+1)=-6y^{5}(7y^2+1)^2\)
11. \(-128s^{4}+224s^{3}-98s^{2}=-2s^{2}(64s^{2}-112s+49)=-2s^{2}(8s-7)^2\)
12. \(48p^{13}+72p^{9}q+27p^{5}q^2=3p^{5}(16p^{8}+24p^4q+9q^2)=3p^{5}(4p^4+3q)^2\)