Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(3b^{6}-42b^{5}+147b^{4}\)
2. \(147p^{7}+84p^{6}+12p^{5}\)
3. \(-48q^{7}+3q^{5}\)
4. \(150a^{14}+180a^{9}x+54a^{4}x^2\)
5. \(-45s^{8}+150s^{6}-125s^{4}\)
6. \(-45a^{13}+60a^{8}y-20a^{3}y^2\)
7. \(-5b^{7}+70b^{6}-245b^{5}\)
8. \(8b^{13}+8b^{9}x+2b^{5}x^2\)
9. \(50x^{4}-80x^{3}+32x^{2}\)
10. \(25p^{7}-90p^{6}+81p^{5}\)
11. \(-9s^{5}+4s^{3}\)
12. \(-2x^{5}+32x^{3}\)

---

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

Verbetersleutel

1. \(3b^{6}-42b^{5}+147b^{4}=3b^{4}(b^2-14b+49)=3b^{4}(b-7)^2\)
2. \(147p^{7}+84p^{6}+12p^{5}=3p^{5}(49p^{2}+28p+4)=3p^{5}(7p+2)^2\)
3. \(-48q^{7}+3q^{5}=-3q^{5}(16q^{2}-1)=-3q^{5}(4q+1)(4q-1)\)
4. \(150a^{14}+180a^{9}x+54a^{4}x^2=6a^{4}(25a^{10}+30a^5x+9x^2)=6a^{4}(5a^5+3x)^2\)
5. \(-45s^{8}+150s^{6}-125s^{4}=-5s^{4}(9s^{4}-30s^2+25)=-5s^{4}(3s^2-5)^2\)
6. \(-45a^{13}+60a^{8}y-20a^{3}y^2=-5a^{3}(9a^{10}-12a^5y+4y^2)=-5a^{3}(3a^5-2y)^2\)
7. \(-5b^{7}+70b^{6}-245b^{5}=-5b^{5}(b^2-14b+49)=-5b^{5}(b-7)^2\)
8. \(8b^{13}+8b^{9}x+2b^{5}x^2=2b^{5}(4b^{8}+4b^4x+x^2)=2b^{5}(2b^4+x)^2\)
9. \(50x^{4}-80x^{3}+32x^{2}=2x^{2}(25x^{2}-40x+16)=2x^{2}(5x-4)^2\)
10. \(25p^{7}-90p^{6}+81p^{5}=p^{5}(25p^{2}-90p+81)=p^{5}(5p-9)^2\)
11. \(-9s^{5}+4s^{3}=-s^{3}(9s^{2}-4)=-s^{3}(3s+2)(3s-2)\)
12. \(-2x^{5}+32x^{3}=-2x^{3}(x^2-16)=-2x^{3}(x+4)(x-4)\)