t p(z) = z**2 - 472*z + 48841. Let n(h) = 6*o(h) - 17*p(h). Suppose n(a) = 0. Calculate a.
221
Find n such that -1/11*n**3 + 2021/11*n - 1011/11 - 1009/11*n**2 = 0.
-1011, 1
Let j(w) be the third derivative of 2*w**7/35 - 23*w**6/15 + 16*w**5 - 75*w**4 + 250*w**3/3 + 276*w**2 - 3. Find g such that j(g) = 0.
1/3, 5
Let n be (-3002)/57 - (8 + -62). Solve -2/3*p**4 - 2/3*p + 2*p**2 - n + 2/3*p**3 = 0.
-1, 1, 2
Let p(n) be the first derivative of 49 + 0*n + 12/5*n**5 + 2/3*n**6 - 16*n**2 - 2*n**4 - 16*n**3. Suppose p(y) = 0. What is y?
-2, -1, 0, 2
Suppose -3*p + 79 = 5*c, c = 172*p - 169*p - 67. What is l in 83*l**3 - p*l**2 + 4*l**4 - 13*l**2 - 51*l**3 = 0?
-9, 0, 1
Suppose 819 = 373*p - 334*p. Solve -16 - p*i**2 - 11/2*i**3 - 32*i - 1/2*i**4 = 0.
-4, -2, -1
Let h(f) = 3*f**2 - 5*f - 8. Let v be h(-4). Suppose -3*t + v = 7*t. Find x, given that -3 - 2*x + t*x + 9 - 2*x**2 = 0.
-1, 3
Let v(k) = k**5 - k**4 - 2*k**3 - 7*k**2. Let l(t) = -20*t**5 + 80*t**4 - 80*t**3 + 126*t**2. Let i(r) = 2*l(r) + 36*v(r). Factor i(y).
-4*y**3*(y - 29)*(y - 2)
Suppose 5*m + 26*g - 45 = 31*g, 4*m - 30 = 3*g. Let a(y) be the first derivative of -2*y**m + 0*y + 8 - 3/8*y**4 + 0*y**2. Find i, given that a(i) = 0.
-4, 0
Let p(z) be the first derivative of 3*z**4/4 - 3*z**3 - 147*z**2/2 - 135*z + 1285. Factor p(j).
3*(j - 9)*(j + 1)*(j + 5)
Factor -1/4*j**3 + 1/4*j - 5/2*j**2 + 5/2.
-(j - 1)*(j + 1)*(j + 10)/4
Let y(g) be the third derivative of -17/96*g**4 + 1/240*g**5 + 0 - 2*g + 2/3*g**3 + 3*g**2. Factor y(z).
(z - 16)*(z - 1)/4
Let s(v) be the second derivative of -v**5/270 + 17*v**4/108 + 2*v**3/3 + 171*v**2/2 + v + 73. Let a(u) be the first derivative of s(u). Factor a(q).
-2*(q - 18)*(q + 1)/9
Let k(w) = 29*w**2 + 2*w + 1. Let l be k(2). Let z(s) = s**3 - 60*s**2 - 120*s - 88. Let o be z(62). Factor 7 + f**3 + 34*f**2 + f**3 + l + o*f.
2*(f + 1)*(f + 8)**2
Let 2016/13 - 2/13*u**2 + 1004/13*u = 0. What is u?
-2, 504
Suppose -10302*l - 142 = -10373*l. Factor -1/5*x**4 - 11/5*x**3 + 13/5*x**l - 12/5 + 11/5*x.
-(x - 1)**2*(x + 1)*(x + 12)/5
Let a(s) be the first derivative of -s**4/8 - 51*s**3/2 - 113*s**2 - 150*s + 5224. Factor a(m).
-(m + 1)*(m + 2)*(m + 150)/2
Let k(y) be the third derivative of -y**7/1260 + 19*y**6/720 + 7*y**5/120 - 19*y**4/144 - 5*y**3/9 - 311*y**2. Factor k(g).
-(g - 20)*(g - 1)*(g + 1)**2/6
Let i be -1*(9/(-3) + 3). Let n = i + 12. Factor n*m + 3 - 28*m**2 - 12*m**2 + 13 + 12*m**2.
-4*(m - 1)*(7*m + 4)
Let b(r) = 2*r**5 - 56*r**4 + 332*r**3 + 847*r**2 + 436*r. Let h(n) = -n**5 + 28*n**4 - 166*n**3 - 424*n**2 - 217*n. Let q(w) = 4*b(w) + 7*h(w). Factor q(z).
z*(z - 15)**2*(z + 1)**2
Solve -773*x - 535*x - 262 - 10840*x**2 + 4589*x**2 + 5213*x**2 + 8*x**3 = 0 for x.
-1, -1/4, 131
Let w(b) be the third derivative of -2/3*b**3 + 0*b + 13 + 1/360*b**5 + 4*b**2 + 23/144*b**4. Factor w(r).
(r - 1)*(r + 24)/6
What is o in -4*o**3 + 12/5*o**4 - 2 - 1/5*o**5 - 2/5*o**2 + 21/5*o = 0?
-1, 1, 10
Let c(x) be the second derivative of -x**4/20 + 32*x**3/5 + 603*x**2/10 + 14*x + 4. Factor c(j).
-3*(j - 67)*(j + 3)/5
Let q(d) = -8*d**2 + 132*d + 326. Let g(x) = 105*x**2 - 1715*x - 4250. Let k(l) = -3*g(l) - 40*q(l). Factor k(u).
5*(u - 29)*(u + 2)
Let p(r) = -43*r**2 - 51*r**2 - 45*r**2 + 138*r**2 + 20*r - r**3 + 3. Let u be p(-5). Solve -2/3*g**u + 10/3*g**2 + 2 - 14/3*g = 0 for g.
1, 3
Find q such that -51/10*q**3 - 59/10*q**2 - 13/10*q**4 + 4*q - 1/10*q**5 + 42/5 = 0.
-7, -3, -2, 1
Factor 0*c**2 - 780/11*c**3 + 0 + 0*c - 378/11*c**4 + 6/11*c**5.
6*c**3*(c - 65)*(c + 2)/11
Let x(g) = -g**4 + 6*g**3 - 13*g**2 + 12*g + 2. Suppose 18*n = 7*n + 11. Let l(b) = -b**4 + 2*b**3 + b + 1. Let c(s) = n*x(s) - 2*l(s). Solve c(p) = 0.
-5, 0, 1, 2
Let t(f) be the second derivative of -5*f**7/42 + 539*f**6/6 - 536*f**5 + 2675*f**4/3 - 4787*f. Determine r so that t(r) = 0.
0, 2, 535
Let c(a) be the second derivative of a**8/1344 - a**7/42 + a**6/4 - 50*a**4/3 - 165*a. Let i(s) be the third derivative of c(s). What is q in i(q) = 0?
0, 6
Let g(c) = -6*c + 26. Let i be (-2 - -1 - -8) + (9 - 12). Let s be g(i). Find b, given that 137*b**2 - 140*b**s + 0*b**3 - b**3 = 0.
-3, 0
Let l(h) be the third derivative of 2*h**7/105 - 38*h**6/15 + 143*h**5/5 - 105*h**4 + 6576*h**2. Factor l(k).
4*k*(k - 70)*(k - 3)**2
Let a(v) be the third derivative of -6*v**2 - 5/72*v**4 - 1/3*v**3 + 13/90*v**5 + 2/45*v**7 + 5/1008*v**8 + 0*v + 14 + 2/15*v**6. Find c, given that a(c) = 0.
-3, -1, 2/5
Suppose 16*v - 356 = -162*v. Let -15/7*c**4 - 72/7*c**v + 0 - 9*c**3 - 12/7*c = 0. What is c?
-2, -1/5, 0
Factor -2/7*v**2 + 258/7*v - 256/7.
-2*(v - 128)*(v - 1)/7
Let q = 34 + -59. Let l = q + 28. Factor -8*c**2 + 4*c**2 + 3*c - 7*c + l*c**2.
-c*(c + 4)
Let o(u) be the second derivative of -u**6/90 - 8*u**5/15 + 6*u**4 - 49*u**3/6 - 2*u + 45. Let n(x) be the second derivative of o(x). Solve n(d) = 0 for d.
-18, 2
Suppose 2324*h**2 + 15*h**4 - 1008 + 2172*h + 45*h**4 - 9069*h**3 + 9745*h**3 = 0. Calculate h.
-28/5, -3, 1/3
Let d = 6124 - 892. Determine i, given that 5232*i + 3*i**2 - d*i = 0.
0
Let h(s) be the second derivative of 0 - 3/7*s**2 - 1/35*s**6 - 42*s - 1/147*s**7 - 1/21*s**3 + 1/7*s**4 + 1/35*s**5. Solve h(b) = 0 for b.
-3, -1, 1
Let g(s) be the third derivative of -s**9/10584 + s**8/2940 - s**7/2940 + 10*s**3/3 + 39*s**2. Let c(j) be the first derivative of g(j). Factor c(h).
-2*h**3*(h - 1)**2/7
Let m(j) = -4*j**3 - 2*j**2 - j. Let z(l) = 13*l**3 - 27*l**2 - 17*l + 11. Let i(p) = 4*m(p) + z(p). Find d, given that i(d) = 0.
-11, -1, 1/3
Let w(b) be the third derivative of -1/36*b**4 + 0*b - 4/45*b**5 - 1/504*b**8 + 4/9*b**3 + 14*b**2 + 4/315*b**7 + 0 + 1/90*b**6. Find o, given that w(o) = 0.
-1, 1, 4
Let a(g) = g**2 + g - 8. Let i be a(-5). Factor 21*o**2 + 68*o - 26*o**2 + 113*o**2 + 28*o**3 - i.
4*(o + 1)*(o + 3)*(7*o - 1)
Suppose -8*c + 8*c + 118 = 59*c. Suppose 6/7*k + 27/7*k**5 + 0 + 3*k**4 - 3*k**c - 33/7*k**3 = 0. Calculate k.
-1, 0, 2/9, 1
Let c(b) = 2*b**4 - 68*b**3 - 65*b**2 + 128*b - 6. Let g(s) = -6*s**4 + 206*s**3 + 194*s**2 - 384*s + 20. Let a(t) = -10*c(t) - 3*g(t). Factor a(m).
-2*m*(m - 32)*(m - 1)*(m + 2)
Let j = 561 - 558. Factor 6*a**3 - 2*a**4 + 4*a**2 + 2*a**4 + j - 3*a + 3*a**4 - 10*a**2 - 3*a**5.
-3*(a - 1)**3*(a + 1)**2
Let w(c) = c**3 + 40*c**2 + 4*c + 157. Let l be w(-40). Let v be 1/(l*(4 - (1 - -4))). What is j in v*j - 1/3*j**2 + 0 = 0?
0, 1
Let k be (-43)/(-2)*(-4 - -6). Let i = k - 39. Factor i*z**3 + 4*z**2 + 6*z**3 + z - 7*z - 8*z**3.
2*z*(z - 1)*(z + 3)
Factor -1395/2*o**3 + 0 + 3*o**2 + 0*o.
-3*o**2*(465*o - 2)/2
Let s be (-2)/(-4) + 1/6. Let c be 9 + 2 + 144*(-84)/1344. Factor -s*q**c - 2 + 7/3*q.
-(q - 2)*(2*q - 3)/3
Let k be -2*(-1)/(-4)*(-6 + 2). Let z be (-8)/104*k - 23/(-65). Factor 0*m - 1/5*m**3 - z*m**2 + 0.
-m**2*(m + 1)/5
Let x(w) = -26*w - 1. Let q be x(-2). Let r = q + -47. Suppose -5*g**5 - 3*g**5 + 4*g**2 + 8*g**3 - g**r - 3*g**4 = 0. Calculate g.
-1, -1/2, 0, 1
Let r(b) be the first derivative of 3*b**5/5 - 33*b**4/2 + 177*b**3 - 924*b**2 + 2352*b + 3385. Factor r(n).
3*(n - 7)**2*(n - 4)**2
Let h(f) be the third derivative of -7*f**6/40 + 439*f**5/20 - 77*f**4/2 - 62*f**3 - 11*f**2 + 19. Suppose h(c) = 0. What is c?
-2/7, 1, 62
Let h = -16879/6 + 28133/10. Factor h*a**3 - 8/3 + 2/3*a**2 - 8/15*a.
2*(a - 2)*(a + 2)*(a + 5)/15
Let n(k) = 9*k**2 + k - 2. Let i be n(1). Suppose -3*w = 4*f - 145, -3*w = i*f - 3*f - 185. Solve -82*q + 2*q**2 + 38*q + f*q = 0.
0, 2
Let z(d) = -118*d**3 - 80*d**2 - 1443*d + 1524. Let t(n) = 39*n**3 + n**2 - 1. Let m(r) = 3*t(r) + z(r). Factor m(g).
-(g - 1)*(g + 39)**2
Let w(v) = -4*v**3 + 14*v**2 - 10*v. Let h(p) be the first derivative of -p**4/4 + p**3/3 - p**2 - 29. Let a(s) = 5*h(s) - w(s). Factor a(r).
-r**2*(r + 9)
Suppose -1283*v = 2147*v - 6860. Factor -2/3*y**4 + 22/3*y**v - 8*y - 24 + 4/3*y**3.
-2*(y - 3)**2*(y + 2)**2/3
Let s(c) = 144*c + 5*c**2 - 2 + 3*c**2 + c**3 - 130*c. Let p be s(-5). Let -1/3*a**2 - a**p - 1/3*a**4 + 2/3 + a = 0. Calculate a.
-2, -1, 1
Suppose 288*r**4 + 145 + 129 + 2543*r**3 + 5522*r**2 - 191*r**3 + 176 + 2940*r = 0. Calculate r.
-15/4, -1/3
Let r(y) = 3*y**3 + y**2 - 2*y. Let n(p) = -2*p**4 - 564*p**3 - 35914*p**2 + 73456*p - 36992. Let h(l) = -n(l) - 8*r(l). What is i in h(