Algebraic Division Bronze

Question 1 of 25

1. Question

\(\text{Show that }{x}^{3}+15{x}^{2}+84x+196\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+7\right)\text{ as a factor, using long division }\)

\(1{x}^{2}+8x+16\text{ remainder }0\)
\(1{x}^{2}+8x+28\text{ remainder }0\)
\(1{x}^{2}+14x+16\text{ remainder }0\)
\(1{x}^{2}+8x+18\text{ remainder }0\)

Question 2 of 25

2. Question

\(\text{Show that }{x}^{3}+15{x}^{2}+60x+72\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+3\right)\text{ as a factor, using long division }\)

\(1{x}^{2}+14x+48\text{ remainder }0\)
\(1{x}^{2}+12x+24\text{ remainder }0\)
\(1{x}^{2}+16x+18\text{ remainder }0\)
\(1{x}^{2}+6x+48\text{ remainder }0\)

Question 3 of 25

3. Question

\(\text{Show that }{x}^{3}+21{x}^{2}+119x+147\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+7\right)\text{ as a factor, using long division }\)

\(1{x}^{2}+10x+21\text{ remainder }0\)
\(1{x}^{2}+6x+49\text{ remainder }0\)
\(1{x}^{2}+14x+21\text{ remainder }0\)
\(1{x}^{2}+14x+27\text{ remainder }0\)

Question 4 of 25

4. Question

\(\text{Show that }{x}^{3}+27{x}^{2}+170x+72\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+9\right)\text{ as a factor, using long division }\)

\(1{x}^{2}+9x+8\text{ remainder }0\)
\(1{x}^{2}+18x+8\text{ remainder }0\)
\(1{x}^{2}+16x+9\text{ remainder }0\)
\(1{x}^{2}+2x+72\text{ remainder }0\)

Question 5 of 25

5. Question

\(\text{Show that }{x}^{3}-2{x}^{2}-32\phantom{\rule{0ex}{0ex}}\text{ has }\left(x-4\right)\text{ as a factor, using long division }\)

\(1{x}^{2}-1x-2\text{ remainder }0\)
\(1{x}^{2}+2x+8\text{ remainder }0\)
\(1{x}^{2}-8x-2\text{ remainder }0\)
\(1{x}^{2}-4x-4\text{ remainder }0\)

Question 6 of 25

6. Question

\(\text{Show that }{x}^{3}-{x}^{2}-9x+9\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+3\right)\text{ as a factor, using long division }\)

\(1{x}^{2}-1x-2\text{ remainder }0\)
\(1{x}^{2}-4x+3\text{ remainder }0\)
\(1{x}^{2}+2x-6\text{ remainder }0\)
\(1{x}^{2}+6x-2\text{ remainder }0\)

Question 7 of 25

7. Question

\(\text{Show that }{x}^{3}-3{x}^{2}+x+1\phantom{\rule{0ex}{0ex}}\text{ has }\left(x-1\right)\text{ as a factor, using long division }\)

\(1{x}^{2}+0x-1\text{ remainder }0\)
\(1{x}^{2}-2x-1\text{ remainder }0\)
\(1{x}^{2}-3x-1\text{ remainder }0\)
\(1{x}^{2}+2x+1\text{ remainder }0\)

Question 8 of 25

8. Question

\(\text{Show that }{x}^{3}-5{x}^{2}+18x-36\phantom{\rule{0ex}{0ex}}\text{ has }\left(x-3\right)\text{ as a factor, using long division }\)

\(1{x}^{2}-5x+4\text{ remainder }0\)
\(1{x}^{2}-2x+12\text{ remainder }0\)
\(1{x}^{2}-8x+3\text{ remainder }0\)
\(1{x}^{2}-6x+4\text{ remainder }0\)

Question 9 of 25

9. Question

\(\text{Show that }6{x}^{3}-39{x}^{2}-126x-81\phantom{\rule{0ex}{0ex}}\text{ has }\left(2x+3\right)\text{ as a factor, using long division }\)

\(3{x}^{2}-13x+12\text{ remainder }0\)
\(3{x}^{2}-24x-27\text{ remainder }0\)
\(2{x}^{2}+12x+24\text{ remainder }0\)
\({x}^{2}-6x-12\text{ remainder }0\)

Question 10 of 25

10. Question

\(\text{Show that }6{x}^{3}+39{x}^{2}-36x-54\phantom{\rule{0ex}{0ex}}\text{ has }\left(2x-3\right)\text{ as a factor, using long division }\)

\(6{x}^{2}+2x-8\text{ remainder }0\)
\(3{x}^{2}+24x+18\text{ remainder }0\)
\(2{x}^{2}-8x-24\text{ remainder }0\)
\({x}^{2}-6x-8\text{ remainder }0\)

Question 11 of 25

11. Question

\(\text{Show that }3{x}^{3}+13{x}^{2}-5x-3\phantom{\rule{0ex}{0ex}}\text{ has }\left(3x+1\right)\text{ as a factor, using long division }\)

\(1{x}^{2}-1x-6\text{ remainder }0\)
\({x}^{2}+4x-3\text{ remainder }0\)
\({x}^{2}-6x+2\text{ remainder }0\)
\(3{x}^{2}+6x-18\text{ remainder }0\)

Question 12 of 25

12. Question

\(\text{Show that }16{x}^{3}+60{x}^{2}+32x-12\phantom{\rule{0ex}{0ex}}\text{ has }\left(4x-1\right)\text{ as a factor, using long division }\)

\(12{x}^{2}-6x-6\text{ remainder }0\)
\(4{x}^{2}+16x+12\text{ remainder }0\)
\(4{x}^{2}-8x-24\text{ remainder }0\)
\(3{x}^{2}-18x-6\text{ remainder }0\)

Question 13 of 25

13. Question

\(\text{Show that }{x}^{4}+9{x}^{3}+30{x}^{2}+42x+18\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+3\right)\text{ as a factor, using long division }\)

\(1{x}^{3}+6{x}^{2}+12x+8\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+12x+6\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+12x+16\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+27x+4\text{ remainder }0\)

Question 14 of 25

14. Question

\(\text{Show that }{x}^{4}+15{x}^{3}+63{x}^{2}+93x+36\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+3\right)\text{ as a factor, using long division }\)

\(1{x}^{3}+11{x}^{2}+40x+48\text{ remainder }0\)
\(1{x}^{3}+12{x}^{2}+27x+12\text{ remainder }0\)
\(1{x}^{3}+12{x}^{2}+48x+9\text{ remainder }0\)
\(1{x}^{3}+9{x}^{2}+27x+16\text{ remainder }0\)

Question 15 of 25

15. Question

\(\text{Show that }{x}^{4}+7{x}^{3}+54{x}^{2}+51x+3\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+1\right)\text{ as a factor, using long division }\)

\(1{x}^{3}+9{x}^{2}+26x+24\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+48x+3\text{ remainder }0\)
\(1{x}^{3}+9{x}^{2}+3x+8\text{ remainder }0\)
\(1{x}^{3}+3{x}^{2}+12x+12\text{ remainder }0\)

Question 16 of 25

16. Question

\(\text{Show that }{x}^{4}+8{x}^{3}+24{x}^{2}+28x+8\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+2\right)\text{ as a factor, using long division }\)

\(1{x}^{3}+6{x}^{2}+12x+8\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+12x+4\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+12x+14\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+12x+7\text{ remainder }0\)

Question 17 of 25

17. Question

\(\text{Show that }{x}^{4}-7{x}^{3}+12{x}^{2}+4x-16\phantom{\rule{0ex}{0ex}}\text{ has }\left(x-4\right)\text{ as a factor, using long division }\)

\(1{x}^{3}-3{x}^{2}+4\text{ remainder }0\)
\(1{x}^{3}+3{x}^{2}+12x+8\text{ remainder }0\)
\(1{x}^{3}-12{x}^{2}+12x-2\text{ remainder }0\)
\(1{x}^{3}-6{x}^{2}+3x+8\text{ remainder }0\)

Question 18 of 25

18. Question

\(\text{Show that }{x}^{4}-{x}^{3}-6{x}^{2}+4x+8\phantom{\rule{0ex}{0ex}}\text{ has }\left(x+2\right)\text{ as a factor, using long division }\)

\(1{x}^{3}-3{x}^{2}+4\text{ remainder }0\)
\(1{x}^{3}+3{x}^{2}+12x+4\text{ remainder }0\)
\(1{x}^{3}-6{x}^{2}+3x-4\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+12x-2\text{ remainder }0\)

Question 19 of 25

19. Question

\(\text{Show that }{x}^{4}-15{x}^{2}+10x+24\phantom{\rule{0ex}{0ex}}\text{ has }\left(x-2\right)\text{ as a factor, using long division }\)

\(1{x}^{3}+2{x}^{2}-11x-12\text{ remainder }0\)
\(1{x}^{3}+12{x}^{2}+27x-2\text{ remainder }0\)
\(1{x}^{3}+3{x}^{2}+48x+6\text{ remainder }0\)
\(1{x}^{3}-9{x}^{2}+12x+4\text{ remainder }0\)

Question 20 of 25

20. Question

\(\text{Show that }{x}^{4}-4{x}^{3}-{x}^{2}+16x-12\phantom{\rule{0ex}{0ex}}\text{ has }\left(x-1\right)\text{ as a factor, using long division }\)

\(1{x}^{3}-3{x}^{2}-4x+12\text{ remainder }0\)
\(1{x}^{3}+6{x}^{2}+12x+3\text{ remainder }0\)
\(1{x}^{3}-6{x}^{2}+3x-6\text{ remainder }0\)
\(1{x}^{3}-9{x}^{2}+12x+2\text{ remainder }0\)

Question 21 of 25

21. Question

\(\text{Show that }8{x}^{4}+12{x}^{3}-54{x}^{2}-27x+81\phantom{\rule{0ex}{0ex}}\text{ has }\left(2x-3\right)\text{ as a factor, using long division }\)

\(4{x}^{3}+12{x}^{2}-9x-27\text{ remainder }0\)
\(2{x}^{3}-18{x}^{2}+54x-36\text{ remainder }0\)
\(2{x}^{3}-18{x}^{2}+54x+36\text{ remainder }0\)
\({x}^{3}+9{x}^{2}+27x-9\text{ remainder }0\)

Question 22 of 25

22. Question

\(\text{Show that }8{x}^{4}-8{x}^{3}-54{x}^{2}+54\phantom{\rule{0ex}{0ex}}\text{ has }\left(2x+3\right)\text{ as a factor, using long division }\)

\(4{x}^{3}-10{x}^{2}-12x+18\text{ remainder }0\)
\(2{x}^{3}+18{x}^{2}+54x+24\text{ remainder }0\)
\(2{x}^{3}+18{x}^{2}+24x-36\text{ remainder }0\)
\(2{x}^{3}-12{x}^{2}+54x+36\text{ remainder }0\)

Question 23 of 25

23. Question

\(\text{Show that }8{x}^{4}-4{x}^{3}-92{x}^{2}+184x-96\phantom{\rule{0ex}{0ex}}\text{ has }\left(2x-3\right)\text{ as a factor, using long division }\)

\(4{x}^{3}+4{x}^{2}-40x+32\text{ remainder }0\)
\(2{x}^{3}-24{x}^{2}+96x+24\text{ remainder }0\)
\({x}^{3}+12{x}^{2}+12x+12\text{ remainder }0\)
\(2{x}^{3}-12{x}^{2}+54x-64\text{ remainder }0\)

Question 24 of 25

24. Question

\(\text{Show that }8{x}^{4}-8{x}^{3}-34{x}^{2}+18x+36\phantom{\rule{0ex}{0ex}}\text{ has }\left(2x-3\right)\text{ as a factor, using long division }\)

\(4{x}^{3}+2{x}^{2}-14x-12\text{ remainder }0\)
\(2{x}^{3}-18{x}^{2}+24x+4\text{ remainder }0\)
\(2{x}^{3}+18{x}^{2}+24x+24\text{ remainder }0\)
\({x}^{3}-6{x}^{2}+27x-6\text{ remainder }0\)

Question 25 of 25

25. Question

\(\text{Show that }8{x}^{4}-30{x}^{2}+10x+12\phantom{\rule{0ex}{0ex}}\text{ has }\left(2x-2\right)\text{ as a factor, using long division }\)

\(4{x}^{3}+4{x}^{2}-11x-6\text{ remainder }0\)
\(2{x}^{3}-18{x}^{2}+24x+8\text{ remainder }0\)
\(2{x}^{3}-12{x}^{2}+24x-12\text{ remainder }0\)
\({x}^{3}+6{x}^{2}+3x+6\text{ remainder }0\)

AQA A level

Get video help

Quiz Summary

Information

Results