 - 9)*(i - 1)**2/2
Factor -8*i - 8 + 9/8*i**2.
(i - 8)*(9*i + 8)/8
Suppose 5*q = 73 + 7. Factor -q*y**3 + 2*y**4 + 162*y - 11*y**3 + 126*y**2 + 3*y**3 - 10*y**3.
2*y*(y - 9)**2*(y + 1)
Let k(j) be the third derivative of 196*j**3 - 175/2*j**4 - 29/8*j**6 + 176*j**2 + 47/2*j**5 + 0*j + 2/7*j**7 + 0 - 1/112*j**8. Determine g so that k(g) = 0.
2, 7
Suppose 2*m - 17 = 4*n - 53, -2*m = n + 1. Let j(b) = -b**3 + 6*b**2 + 7*b + 4. Let c be j(n). Factor -6*r**3 - 2*r**4 - c*r**2 - 6454*r + 6454*r.
-2*r**2*(r + 1)*(r + 2)
Let l = 1/106458 + 638735/1383954. Factor 0*g - l*g**3 + 0 + 4/13*g**2 + 2/13*g**5 + 0*g**4.
2*g**2*(g - 1)**2*(g + 2)/13
Suppose 2*l + 1 = 11. Let j be -1 + -2 + 25/l. Factor 6*c**3 - 7*c**4 + 14*c**4 + 6*c**j + 2*c - 5*c**4.
2*c*(c + 1)**3
Let z(n) = -n**3 + 7*n**2 - 8*n + 4. Let s be z(5). Let y = -5478 + 5481. Factor 11 - 38*h - 34*h + 11 - 6 - s*h**y + 60*h**2.
-2*(h - 2)**2*(7*h - 2)
Let w(c) be the first derivative of c**5/10 - 59*c**4/16 - 5*c**3/2 + 80. Let w(p) = 0. Calculate p.
-1/2, 0, 30
Determine k, given that 16/3*k + 14*k**3 - 16/3*k**4 + 2/3*k**5 + 0 - 44/3*k**2 = 0.
0, 1, 2, 4
Let k(v) = 2*v**2 - 181*v - 65653. Let b be k(232). Let -22/7*m**4 - 156/7*m**2 + 16/7 + 8*m + 106/7*m**b = 0. Calculate m.
-2/11, 1, 2
Suppose -5*u - 2*r + 6 = 0, -2*u - 5 - 10 = -5*r. Let k be 2/(-136) - 99/(-396). Factor -6/17*g**2 - 2/17*g**3 - k*g + u.
-2*g*(g + 1)*(g + 2)/17
Suppose -434/11*x - 2/11*x**2 + 0 = 0. Calculate x.
-217, 0
Solve 2*r**3 - 49402*r - 200117*r - 29485*r - 10*r**3 - 2990*r**2 + 69938 = 0 for r.
-187, 1/4
Let i(m) = 2*m**2 - 4*m + 1. Let x(l) = -3*l**5 - 33*l**4 - 21*l**3 + 97*l**2 + 172*l + 56. Let g(b) = -4*i(b) - x(b). Factor g(r).
3*(r - 2)*(r + 1)**3*(r + 10)
Suppose -250*s - 169*s**2 - 164*s**2 - 163*s**2 - 140 + 935 + 491*s**2 = 0. What is s?
-53, 3
Let k = 92 + -89. Solve -42*a - 5*a**2 - 16*a - 21 + k*a + 81 = 0.
-12, 1
Factor -1/5*f**3 + 12/5 - 12/5*f**2 + 1/5*f.
-(f - 1)*(f + 1)*(f + 12)/5
Determine q, given that 40*q**2 + 16905*q**3 - 13*q + q - 16925*q**3 - 20*q + 12*q**2 = 0.
0, 1, 8/5
Let w(k) = -3*k**2 + 11*k - 13. Suppose 14*h - 12*h - 6 = 5*z, h - 3*z = 4. Let x(s) = s**2 - s + 1. Let o(m) = h*w(m) - 10*x(m). Factor o(l).
-4*(l - 1)*(l + 4)
Suppose 2*i = -o - 172 - 193, -5*i - 5*o = 905. Let a be (-12)/54 - (2 + i/18). Factor 5*g**5 + 20*g**2 + 10*g**4 - 16*g**3 - 11*g**3 - a*g**3.
5*g**2*(g - 1)**2*(g + 4)
Suppose 370*p + 1447 = 2187. Let 94/11*s + 54/11*s**p - 60/11 - 4/11*s**3 = 0. Calculate s.
-2, 1/2, 15
Let d(j) be the third derivative of j**5/480 + 923*j**4/192 + 392*j**2. Factor d(x).
x*(x + 923)/8
Let i(h) = -3288*h**2 + 42484*h - 133388. Let n(d) = 469*d**2 - 6069*d + 19056. Let a(k) = 3*i(k) + 20*n(k). Let a(x) = 0. What is x?
69/11
Let w(d) be the second derivative of -d**4/20 - 75*d**3 - 84375*d**2/2 - 108*d - 6. Factor w(c).
-3*(c + 375)**2/5
Suppose 38 = 4*u + 2*l, -46 = -5*u - 3*l - l. Determine z so that 24*z + 1045*z**2 - 4 + 10 - 1033*z**2 + u + 2*z**3 = 0.
-2
Let -2/21*u**2 - 668/21*u - 55778/21 = 0. Calculate u.
-167
Let p be 224/144 + 4/9. Factor -26*i**3 - 4*i**4 - 15*i**p + 42*i**3 + 3*i**2.
-4*i**2*(i - 3)*(i - 1)
Suppose 5*i + 11*i = 52*i - 6*i. Let m(a) be the first derivative of 5*a**2 + 5*a**4 + i*a - a**5 - 25/3*a**3 + 18. What is r in m(r) = 0?
0, 1, 2
Let t(f) be the first derivative of 81*f**4/2 - 696*f**3 + 4480*f**2 - 12800*f + 148. Let t(u) = 0. Calculate u.
4, 40/9
Let s(t) be the first derivative of 570*t**3 - 1133*t**3 + 60*t**2 + 564*t**3 - 198. Solve s(d) = 0 for d.
-40, 0
Let s = 17928 + -71709/4. Let d(q) be the first derivative of -12*q - 17 - 27/2*q**2 - s*q**4 - 6*q**3. Determine b so that d(b) = 0.
-4, -1
Let c be 4*(290/60)/29. Let h = 111 + -329/3. Find j, given that 16/3 - c*j**2 - h*j = 0.
-4, 2
Let i(b) be the first derivative of -4/25*b**5 + 140 + 16/5*b - 2/5*b**4 + 4/5*b**3 + 16/5*b**2. Determine a, given that i(a) = 0.
-2, -1, 2
Let m(v) = -285*v**2 + 85955*v - 84980. Let j(a) = -5*a**2 + 1508*a - 1491. Let l(t) = 115*j(t) - 2*m(t). Let l(u) = 0. What is u?
1, 301
Let a(n) = 11*n**2 + 16*n - 6. Let g be a(1). Let t(u) be the second derivative of 1/40*u**5 + g*u - 1/60*u**6 + 11/12*u**3 + 0 + u**2 + 3/8*u**4. Factor t(k).
-(k - 4)*(k + 1)**3/2
Suppose -47*v - 104*v = -204*v + 212. Let t(h) be the first derivative of 3/20*h**v + 0*h - 1/5*h**3 + 1/10*h**2 - 18 - 1/25*h**5. Suppose t(d) = 0. What is d?
0, 1
Let v = -89 - -93. Let k(x) be the first derivative of -4*x - 24/5*x**5 + 28/3*x**3 - 5*x**v + 10*x**2 + 38. Solve k(n) = 0.
-1, 1/6, 1
Factor 6*y**2 + 42*y**2 - 477*y**4 - 4*y**3 + 243*y**4 + 144*y + 233*y**4 - 432.
-(y - 6)*(y - 2)*(y + 6)**2
Suppose 0 = 3*g - 13 + 7. Let t be g/7 - (54/(-7) + 6). Factor 843 - r**t - 3*r - 843.
-r*(r + 3)
Let u be (0 + 4/(-3))*234/(-52). Let z be ((-15)/u + -1)*84/(-147). Determine x so that -8/5*x + 8/5*x**3 + 4/5*x**z + 2/5 - 6/5*x**4 = 0.
-1, 1/3, 1
Let f = -17/14 + 2221/1806. Let a = 137/516 - f. Factor g - a - g**3 + 1/4*g**2.
-(g - 1)*(g + 1)*(4*g - 1)/4
Let n = 119127 - 357373/3. Determine z, given that -n*z - 10*z**2 + 0 = 0.
-4/15, 0
Suppose 0 = -26*m + 12*m + 1624. Factor m*z - 37*z**2 - 34*z - 47*z**2 + z**4 - 10*z**4 - 27 + 30*z**3 + 8*z**4.
-(z - 27)*(z - 1)**3
Let j = 617 + -930. Let s = j + 315. Let 2/3 + 1/3*q**s - q = 0. What is q?
1, 2
Suppose 0 = -4*n + 6*d + 7 - 51, -5*n + 23*d = 21*d. Determine w so that 16/7*w**2 + 4/7*w**5 + 0*w**3 + 0*w - 12/7*w**n + 0 = 0.
-1, 0, 2
Let n be 0/(-3 + (-5)/(-1)). Suppose -2*q + 10 - 4 = n. Suppose 2/3*u**q + 0*u - 2/3*u**2 + 0 = 0. Calculate u.
0, 1
Find o, given that -80/7*o - 76/7*o**2 + 78/7 - 2/7*o**4 + 80/7*o**3 = 0.
-1, 1, 39
Factor 35721 + 3*r**3 + 387*r**2 + 6297*r + 1737*r + 5007*r.
3*(r + 3)*(r + 63)**2
Let d be -1 + 1/(-3) + (-91)/(-21). Suppose d*n = 4*n - 4. Let -3*z + 4 - 5*z + 4*z**3 + n*z**3 - 4*z**4 = 0. What is z?
-1, 1
Determine z so that -812/3*z**2 + 48*z + 754/3*z**3 + 0 - 68/3*z**4 - 6*z**5 = 0.
-9, 0, 2/9, 1, 4
Let o(q) = 2*q**3 - 436*q**2 + 2224*q - 14. Let k(w) = -12*w**3 + 2181*w**2 - 11122*w + 77. Let d(l) = -4*k(l) - 22*o(l). Factor d(f).
4*f*(f - 5)*(f + 222)
Let m be 40/24*(390/(-50) + (2 - -7)). Determine g so that 9/2*g**2 + 1/4*g**4 - m*g**3 - 4*g + 5/4 = 0.
1, 5
Suppose -35*a + 22*a + 78 = 0. Suppose 0 = -8*q + a*q. Factor -2/13*x**5 + 4/13*x**3 + q + 0*x**2 + 0*x**4 - 2/13*x.
-2*x*(x - 1)**2*(x + 1)**2/13
Factor -168*w + 3*w**2 - 55*w**2 + 42*w**4 + 6*w**4 - 46*w**4 + 2*w**3 - 154 + 10.
2*(w - 6)*(w + 2)**2*(w + 3)
Let s(z) be the first derivative of -33*z**4/4 - 204*z**3 + 945*z**2/2 - 300*z - 3439. Determine d so that s(d) = 0.
-20, 5/11, 1
Let a(l) be the second derivative of l**5/30 - 5*l**4/6 - 11*l**3/3 - 53*l**2 - 17*l. Let q(m) be the first derivative of a(m). Determine n so that q(n) = 0.
-1, 11
Suppose 466*h - 470*h = -3*b + 35, 15 = -3*h. Let j(z) be the third derivative of -1/48*z**b + 5/6*z**3 - 5/32*z**4 - 9*z**2 + 0 + 0*z. Factor j(k).
-5*(k - 1)*(k + 4)/4
Let r(o) be the second derivative of o**5/40 + 5*o**4/12 + 9*o**3/4 + 9*o**2/2 - 1382*o - 2. Determine z so that r(z) = 0.
-6, -3, -1
Suppose 4*n - 6*d + 100 = -2*d, 0 = n - 3*d + 27. Let z = 30 + n. Factor -52*c**2 - z*c**4 - 34*c**2 + 25*c**2 - 50*c**3 - 51*c**2 - 32*c.
-2*c*(c + 4)**2*(3*c + 1)
Factor -27/4 - 13/4*x**2 + 1/4*x**3 + 39/4*x.
(x - 9)*(x - 3)*(x - 1)/4
Factor 145/2*d + 153/2 - 9/2*d**2 - 1/2*d**3.
-(d - 9)*(d + 1)*(d + 17)/2
Suppose -10*o + 8 = 218. Let t be -5 + o/(-6)*2. Factor 2/5 - 3*w + 13/5*w**t.
(w - 1)*(13*w - 2)/5
Let t(u) be the first derivative of 6*u**4 + 0*u - 172 + 20/3*u**3 + 4/5*u**5 - 24*u**2. Solve t(q) = 0 for q.
-4, -3, 0, 1
Let a(j) be the third derivative of j**5/75 + 104*j**4/5 + 6*j**2 + 338*j. Suppose a(g) = 0. What is g?
-624, 0
Let s = -5681 + 34087/6. Let h(y) be the first derivative of -17 + 1/18*y**6 - 1/5*y**5 + 1/3*y + s*y**4 - 1/2*y**2 + 2/9*y**3. Factor h(u).
(u - 1)**4*(u + 1)/3
Let q = -108 + 103. Let z be (12/(-6) - -47) + q. Factor 24 + 6*y**2 + z - 34*y**2 + 4*y**3 + 32*y.
4*(y - 4)**2*(y + 1)
Let b(c) = -c**3 + 5*c**2 + 11*c - 51. Let z be b(5). Factor -v**2 + 13*v**2 + 3*v**3 + v**3 + z*v**2 + 12*v.
4*v*(v + 1)*(v + 3)
Let p(h) be the third derivative of -h**6/2520 - h**5/84 - h**4/8 + 65*h*