 3
Let k(r) = -r**3 - r**2 - r - 38. Let l be k(-7). Suppose -268*p = -l*p - 10. Factor 2/9*c**p - 2/9*c**4 + 2/9*c - 2/9*c**3 + 0.
-2*c*(c - 1)*(c + 1)**2/9
Let f = 470 + -62. Let a = f - 2848/7. Let 6/7*s**2 - 2/7*s**4 + a*s - 4/7*s**3 - 8/7 = 0. Calculate s.
-2, 1
Let f(h) be the third derivative of -h**8/728 - 32*h**7/1365 - 71*h**6/780 + 5*h**5/39 + 14*h**4/39 + 43*h**2 + 18. Let f(n) = 0. What is n?
-7, -4, -2/3, 0, 1
Solve -15*x**3 + 225319*x - 225319*x - 12*x**2 - 3*x**4 = 0.
-4, -1, 0
Let w = 29899 - 29893. Let o(g) be the third derivative of -1/165*g**5 + 0 + 1/1155*g**7 + 1/33*g**3 + 0*g**4 - 34*g**2 + 0*g**w + 0*g. What is s in o(s) = 0?
-1, 1
Find a such that 3185*a + 5*a**2 - 14791 + 8161 + 9810 = 0.
-636, -1
Suppose i - 194 + 173 = 0. Suppose 123*d - i = 116*d. Factor -12*p + 1/2*p**4 + 9/2 + 11*p**2 - 4*p**d.
(p - 3)**2*(p - 1)**2/2
Let w(k) = 14*k + 15*k - 28*k + 2. Let c be w(1). Solve -2*t**2 + 4 - 5 + 6 - c = 0 for t.
-1, 1
Solve 28*h + 0 + 6/5*h**5 - 78/5*h**2 + 14/5*h**4 - 42*h**3 = 0 for h.
-7, -1, 0, 2/3, 5
Let q(d) = -3*d**4 - 11*d**3 - 120*d**2 - 277*d - 180. Let u(a) = 2*a**4 + 6*a**3 + 61*a**2 + 138*a + 90. Let c(p) = 3*q(p) + 5*u(p). Solve c(y) = 0 for y.
-3, -1, 10
Let d = 76/71 - 461/497. Suppose 0 = -10*s - 0*s + 40. Factor 1/7 - 2/7*i + 2/7*i**3 - d*i**s + 0*i**2.
-(i - 1)**3*(i + 1)/7
Factor 35/2*a**2 - 1/6*a**4 + 0 + 23/6*a**3 + 27/2*a.
-a*(a - 27)*(a + 1)*(a + 3)/6
Determine c, given that 0 + 1/6*c**3 - 1/6*c + 1/2*c**2 - 1/2*c**4 = 0.
-1, 0, 1/3, 1
Find q, given that -72*q + 162*q**3 + 5*q**5 + 53*q + 75*q**2 - 3*q**4 - 131*q - 14*q**5 + 69*q**3 = 0.
-5, -1, 0, 2/3, 5
Let x = -249077 + 747247/3. Factor -1/3*k**2 - x - 8/3*k.
-(k + 4)**2/3
Determine p so that -320/7 - 60/7*p**2 + 264/7*p + 4/7*p**3 = 0.
2, 5, 8
Let n(b) = -6*b**4 - 22*b**3 + 6*b**2 + 18*b + 2. Suppose -7 = -26*a + 19*a. Let x(k) = k**5 + k - 1. Let c(p) = a*n(p) + 2*x(p). Let c(l) = 0. What is l?
-2, -1, 0, 1, 5
Let f**2 - 288 - 150263*f + 150350*f + 2*f**2 = 0. What is f?
-32, 3
Let y(b) = -b**3 + 657*b**2 - 101757*b - 102400. Let s(g) = g**3 - 651*g**2 + 101758*g + 102400. Let h(t) = 6*s(t) + 4*y(t). Factor h(u).
2*(u - 320)**2*(u + 1)
Let y(t) be the third derivative of t**5/300 + 52*t**4/15 + 21632*t**3/15 - 20*t**2 - 3*t. Let y(x) = 0. Calculate x.
-208
Suppose 50*n - 10 = -5*w + 48*n, 0 = 4*w - 5*n - 41. Let r(x) be the second derivative of -18*x + 0 + 1/2*x**3 + 3/4*x**2 + 1/8*x**w. Factor r(f).
3*(f + 1)**2/2
Let v(q) be the third derivative of -q**9/96768 - 23*q**8/40320 - q**7/1120 + 47*q**5/12 - 99*q**2. Let n(b) be the third derivative of v(b). Factor n(o).
-o*(o + 18)*(5*o + 2)/8
Let q(p) be the first derivative of -3/5*p**5 - 9/2*p**4 + 9*p**2 - 11 - 8*p**3 + 27*p. Factor q(u).
-3*(u - 1)*(u + 1)*(u + 3)**2
Let n(g) = -5*g**3 + 36*g**2 + 72*g + 49. Let w(i) = -22*i**3 + 143*i**2 + 287*i + 200. Let h(u) = -13*n(u) + 3*w(u). Find m, given that h(m) = 0.
-37, -1
Let s be (-5)/(-4) + 3/4. Suppose s*n - 3 = 1. Factor 9*o - 4*o + 17*o - 10*o**n - 4.
-2*(o - 2)*(5*o - 1)
Let w = -313 + 315. Determine i so that -8*i**4 + 53*i**3 + 43 + 192*i + 21 + 25*i**3 - 236*i**w = 0.
-1/4, 2, 4
Let m(f) = -15*f**3 - 152*f**2 - 65*f. Let l(p) = -2*p**3 - p. Let u(x) = 20*l(x) - 4*m(x). Factor u(w).
4*w*(w + 30)*(5*w + 2)
Let 4/3*k**4 + 8/3 - 6*k**2 + 2/3*k**3 - 8/3*k = 0. Calculate k.
-2, -1, 1/2, 2
Let a(w) = 2*w**4 - w**3 + 2*w - 1. Let i(k) = -13*k**4 + 3*k**3 + 22*k**2 + 12*k + 6. Let z(l) = -6*a(l) - i(l). Factor z(f).
f*(f - 4)*(f + 1)*(f + 6)
Suppose 151*n - 18559 + 7034 = -310*n. What is l in -20 - 10*l**2 + n*l + 5/4*l**3 = 0?
2, 4
Let t = -13993/2 + 69967/10. Factor 0 + t*q**4 + 0*q**2 + 13/5*q**3 + 0*q.
q**3*(q + 13)/5
Let k = 22 + -74. Let y = 54 + k. Determine d so that -2 + 2 - 7*d**y - 2*d + 9*d**2 = 0.
0, 1
Let k(v) be the third derivative of v**7/280 - 61*v**6/480 + 13*v**5/8 - 7*v**4 - 80*v**3/3 - 4072*v**2. Factor k(s).
(s - 8)**2*(s - 5)*(3*s + 2)/4
Let p(l) = -4*l**2 - 71*l - 1372. Suppose 62*s - 67*s + 30 = 0. Let m(f) = 23*f**2 + 427*f + 8231. Let i(u) = s*m(u) + 34*p(u). Factor i(x).
2*(x + 37)**2
Let q = -11945/24 - -3995/8. Let -35/3*f + 0 - q*f**2 = 0. What is f?
-7, 0
Suppose 0 = 3*x - 5*o + 34709 - 34779, -7*x - 2*o + 13 = 0. Determine w, given that -450*w - 781/2*w**3 - 1/2*w**x + 870*w**2 + 0 - 29*w**4 = 0.
-30, 0, 1
Let m(i) = -i**3 - i**2 + 1. Let u(y) = -44*y**2 - 72*y**2 - 39*y**3 - 23 - 12*y**2 - 104*y. Let s(h) = 3*m(h) + u(h). Factor s(d).
-(d + 2)*(6*d + 5)*(7*d + 2)
Let a(t) be the third derivative of t**8/30240 - t**7/504 - 2*t**6/135 - 61*t**5/60 - 109*t**2. Let z(j) be the third derivative of a(j). What is s in z(s) = 0?
-1, 16
Let m(n) = 15*n**2 - 2*n - 4. Let l be m(-2). Suppose -l + 78 + 7*c**2 + 8*c**2 + 0*c + 13*c - 64*c = 0. What is c?
2/5, 3
Let 63 + 713*c - 2*c**2 + 10 + 755*c - 1540*c - 1 + 2*c**3 = 0. What is c?
-6, 1, 6
Let l(s) = s**4 + s**3 - s**2 + 3*s. Let h(o) = 19*o + 6*o - o**2 + 3*o**3 + 3*o**4 - 16*o. Let y(n) = -2*h(n) + 7*l(n). Factor y(x).
x*(x - 1)**2*(x + 3)
Let r = -129 + 138. Find j, given that -8*j**4 - 6*j**3 + 2*j**3 - r*j**3 + 16*j**2 + j**3 + 12*j - 8 = 0.
-2, -1, 1/2, 1
Let b(g) be the second derivative of 35*g + 0*g**3 + g**4 + 1/10*g**6 - 3/4*g**5 + 0*g**2 + 0. Factor b(s).
3*s**2*(s - 4)*(s - 1)
Let r(w) be the third derivative of w**7/210 - 3*w**6/10 - 13*w**5/20 + 37*w**4/12 - 2465*w**2. Find p such that r(p) = 0.
-2, 0, 1, 37
Determine w so that -9/2 - 7/5*w - 1/10*w**2 = 0.
-9, -5
Let y(v) = v**3 + 5*v**2 + 2. Let a = 32 - 37. Let b be y(a). Determine z so that -3*z**3 + 8 - 60*z + 58*z**b + 12*z - 15*z**3 = 0.
2/9, 1, 2
Let g be (-64)/(-30)*(-80)/(-786). Let k = 2/393 + g. Factor -2/9*z**4 - k*z**3 + 0*z + 0*z**2 + 0.
-2*z**3*(z + 1)/9
Let 174*m + 192/5 + 411/5*m**2 + 12/5*m**3 = 0. What is m?
-32, -2, -1/4
Let y(b) be the second derivative of -19/20*b**5 + 9*b**2 + 65/12*b**4 - 6*b - 1/10*b**6 - 61/6*b**3 + 5. Factor y(s).
-(s - 1)**2*(s + 9)*(3*s - 2)
Let o(y) = -y**2 - 7*y + 30. Let c be o(6). Let v be 24/c*(1 + -1). Find x, given that 8 + 28*x - 16*x**3 + v - 5*x**2 - 15*x**2 = 0.
-2, -1/4, 1
Let g be (83055/3192 + -26)/(9/2). Let a(p) be the third derivative of 1/1140*p**6 - 12*p**2 + 0 + 0*p**5 - g*p**4 + 0*p**3 + 0*p. Factor a(f).
2*f*(f - 1)*(f + 1)/19
Let w(j) be the third derivative of 19/6*j**6 + 26/3*j**4 + 0 - 16/3*j**3 - 10/21*j**7 - 38/5*j**5 - 15*j**2 + 2*j. Let w(p) = 0. Calculate p.
2/5, 1, 2
Let j(u) be the first derivative of -u**4/2 - 18*u**3 + 154*u**2 - 384*u + 2327. Suppose j(z) = 0. Calculate z.
-32, 2, 3
Let q(v) be the second derivative of -v**8/2520 + v**7/315 - v**6/180 - 35*v**3/3 - 89*v. Let h(c) be the second derivative of q(c). Factor h(y).
-2*y**2*(y - 3)*(y - 1)/3
Find k, given that -5/2*k**2 + 1/2*k**4 - 2*k**3 - 18 + 18*k = 0.
-3, 2, 3
Let a(v) = -2*v + 80. Let d be a(40). Let s(j) be the first derivative of 3/5*j**5 + 0*j**4 + d*j**2 + 12*j - 5*j**3 - 16. Suppose s(o) = 0. Calculate o.
-2, -1, 1, 2
Let k(j) be the first derivative of -j**3/12 + 837*j**2/8 - 657. Factor k(y).
-y*(y - 837)/4
Factor -95*k**2 + 147*k - 11*k**3 - 30 - 9*k**3 - 2*k.
-5*(k - 1)*(k + 6)*(4*k - 1)
Let c = -15 - -57. Let l = -38 + c. Factor 89 - 3*i**l - 12*i**2 - 15*i**3 - 89.
-3*i**2*(i + 1)*(i + 4)
Let c be (((-140)/12)/7)/(0 + -1). Let m = c - 1/6. Factor 2*w + m*w**4 - 2*w**3 - 1/2 - w**2.
(w - 1)**2*(w + 1)*(3*w - 1)/2
Let l(s) = 170*s**3 - 10836*s**2 + 2926842*s - 16. Let z(d) = -32*d**3 + 2167*d**2 - 585368*d + 3. Let f(c) = 3*l(c) + 16*z(c). Factor f(n).
-2*n*(n - 541)**2
Let g = -2061 + 3584. Let m = -1518 + g. Find v, given that -1/5*v**2 + v**4 - 4/5 - 7/5*v**3 + 8/5*v - 1/5*v**m = 0.
-1, 1, 2
Let b(r) be the second derivative of -29 + 0*r**2 + r - 1/10*r**4 + 0*r**3. Suppose b(n) = 0. Calculate n.
0
Let r(i) = 0 + 25*i - 22*i**2 - 2 + 19*i**2. Let k(f) = 3*f**2 - 24*f + 3. Let w(c) = 2*k(c) + 3*r(c). Solve w(y) = 0 for y.
0, 9
Let s(u) = 5*u**2 + 31*u + 60. Let b(g) = 70*g**2 + 840 + 25*g + 238*g + 211*g - 39*g. Let a(l) = -4*b(l) + 55*s(l). Suppose a(o) = 0. Calculate o.
-4, -3
Let k(t) be the second derivative of 3*t**5/80 - 21*t**4/16 + 5*t**3/2 - 2127*t. Factor k(c).
3*c*(c - 20)*(c - 1)/4
Let f be (-136)/68*(-3)/(-1 - -4). Let a(l) 