 4
Let l(n) be the second derivative of -n**7/42 - n**6/12 - n**5/12 - 77*n**2 + 24*n. Let z(q) be the first derivative of l(q). Suppose z(u) = 0. What is u?
-1, 0
Let g(y) be the second derivative of -60*y**2 - 35*y + 0 - 2/3*y**3 + 1/3*y**4. Suppose g(b) = 0. What is b?
-5, 6
Factor 408*x**2 + 10265763*x - 10271766*x + 932 + 253 - 7*x**3 + 497.
-(x - 29)**2*(7*x - 2)
Let h = 35 - 38. Let l be h/(2*3/(-40)). Determine s, given that 4*s**3 - l*s**3 + 15*s**2 - 18*s + 13*s**3 = 0.
0, 2, 3
Let h(g) be the second derivative of -g**7/56 - g**6/10 + 3*g**5/10 + 21*g**4/8 + 9*g**3/8 - 81*g**2/4 - 155*g. Let h(v) = 0. What is v?
-3, -2, 1, 3
Let o(f) be the first derivative of -2*f**3/21 + 8*f**2 + 610*f/7 - 5455. Factor o(m).
-2*(m - 61)*(m + 5)/7
Let d(y) = 3*y**3 + 4*y**2 + y - 4. Let u(r) = 4*r**3 + 4*r**2 - 5. Let x be 25/(-25) + (-9)/3*1. Let b(n) = x*u(n) + 5*d(n). Solve b(z) = 0 for z.
-1, 0, 5
Let n be (-3 + (-75)/(-36))/((-3597)/872). Solve 34/9*y**2 - n*y**5 - 4/3*y + 0 + 14/9*y**4 - 34/9*y**3 = 0.
0, 1, 2, 3
Let a(j) = -8*j**2 + 188*j + 77. Let k(q) = 2*q**2 - 46*q - 20. Let w(b) = -8*a(b) - 34*k(b). Factor w(z).
-4*(z - 16)*(z + 1)
Let z(m) = m**3 - 3*m**2 - 19*m - 17. Let f be z(-11). Let c = f - -10518/7. Determine y so that -y**2 - 12/7*y + 3/7*y**3 - c + 2/7*y**4 = 0.
-2, -1, -1/2, 2
Let r be 225 - ((6 - 4)*1 - -3). Let n = 244 - r. Factor n*q**3 + 6*q**2 + 0 + 15/2*q**4 + 0*q - 75/2*q**5.
-3*q**2*(q - 1)*(5*q + 2)**2/2
Let m be -6 + ((-106)/(-6) + 6 - -15) + 2/3. Factor -4/3*v**2 + 0 + m*v.
-4*v*(v - 25)/3
Let c be (-44)/(-20) - 7/35. Suppose -133*l**2 - 6*l + 133*l**c - 4 + 2*l**3 = 0. What is l?
-1, 2
Suppose -2 + 274 = 2*w. Factor -58*q - 36*q**4 + 2*q - 4*q**5 - 20 - 104*q**3 - w*q**2 - 28*q.
-4*(q + 1)**4*(q + 5)
Let d(b) be the first derivative of 9/2*b**2 - 3/8*b**4 - 4*b - 48 - 7/6*b**3. Suppose d(l) = 0. What is l?
-4, 2/3, 1
Let w(o) be the second derivative of 8/25*o**5 + 1/75*o**6 + 80*o**2 - 64/3*o**3 - 106*o + 4/5*o**4 + 0. Factor w(z).
2*(z - 2)**2*(z + 10)**2/5
Let s(f) be the second derivative of -f**7/42 + 17*f**6/30 - 67*f**5/20 - 53*f**4/12 + 122*f**3/3 - 70*f**2 - 488*f. Solve s(l) = 0.
-2, 1, 7, 10
Let w = 1713 + -1712. Suppose -49*t - w = -99. Find g, given that -6/5*g + 0 + 3/5*g**t = 0.
0, 2
Let i = -574453 - -574456. Solve -47/3*n**2 - 176*n - 1/3*n**i + 192 = 0 for n.
-24, 1
Solve -24*d**2 - 2/11*d**4 + 56/11*d**3 - 1792/11*d - 2048/11 = 0.
-2, 16
Factor -2*v**2 - 126*v - 145 + 1 - 34 - 76 + 10.
-2*(v + 2)*(v + 61)
Suppose -11*m - 2*k - 16 = -3*m, 4*k = -3*m - 32. Factor 8/9*g**2 + 40/9*g**3 + 0 + m*g + 2*g**4.
2*g**2*(g + 2)*(9*g + 2)/9
Let y(j) be the third derivative of j**6/40 - 7*j**5/10 - 325*j**4/8 + 169*j**3 + 12*j**2 + 152. Let y(r) = 0. Calculate r.
-13, 1, 26
Factor 44*q - 3 - 484/3*q**2.
-(22*q - 3)**2/3
Let q(p) be the third derivative of p**5/60 + 33*p**4/8 + 135*p**3 + 2471*p**2. Factor q(z).
(z + 9)*(z + 90)
Let a(z) = z**3 - 14*z**2 - 34*z - 19. Let o be 8*(-6)/(-72)*3. Let t(b) = -b**2 - b. Let l(k) = o*a(k) + 6*t(k). Solve l(y) = 0 for y.
-1, 19
Let j = 1487861 - 1487831. Solve -5/3*s**3 + j*s + 0 + 85/3*s**2 = 0 for s.
-1, 0, 18
Let a = 102040 + -814847/8. Let d = -184 + a. Determine m so that 0 + 0*m**2 + 1/8*m - d*m**3 = 0.
-1, 0, 1
Let i be (20*(-300)/125)/(-16). Factor -4/7*y**i + 0*y + 8/7*y**4 - 4/7*y**5 + 0*y**2 + 0.
-4*y**3*(y - 1)**2/7
Let a(s) be the first derivative of 9 + 0*s**3 + 0*s**2 - 10*s - 1/15*s**5 + 0*s**6 + 0*s**4 + 2/63*s**7. Let l(p) be the first derivative of a(p). Factor l(v).
4*v**3*(v - 1)*(v + 1)/3
Find y, given that -1 + 340*y + 7 - 973*y - 6 + 3*y**2 = 0.
0, 211
Let p(f) be the third derivative of f**8/168 - 4*f**7/105 + f**6/60 + f**5/5 + 227*f**2. Factor p(y).
2*y**2*(y - 3)*(y - 2)*(y + 1)
Let f = 204 + -108. Let g = f + -91. Find s, given that 1/2*s**4 - 3/4*s**g - 1/4*s + s**3 - 1/2*s**2 + 0 = 0.
-1, -1/3, 0, 1
Let p(q) be the first derivative of -193 + 35/8*q**3 - 75/16*q**2 - 33/32*q**4 + 3/40*q**5 + 0*q. Let p(y) = 0. What is y?
0, 1, 5
Let m = 179286/5 - 35857. Let 2*s**2 - 1/5*s - 2 + m*s**3 = 0. Calculate s.
-10, -1, 1
Let l = -822235 + 7400167/9. Factor -2/9*p**2 - 10/3*p - l.
-2*(p + 2)*(p + 13)/9
Let u be ((-13948)/(-264) + -7)*8/20. Solve -35/2 - u*n - 5/6*n**2 = 0.
-21, -1
Let k = 224 + -155. Let m be (-2*(-4)/(-6))/((-14)/21). Find b such that -54*b**5 - 17*b**2 + k*b**5 + 55*b**4 + 25*b**3 + m*b**2 = 0.
-3, -1, 0, 1/3
Let p(o) be the third derivative of o**5/45 - 7*o**4/18 - 152*o**3/3 - 2*o**2 + 11931*o. Factor p(u).
4*(u - 19)*(u + 12)/3
Suppose 16*c = -5*c + 3864. Factor -211*g - 4*g**2 + 267*g - c*g.
-4*g*(g + 32)
Let n = -7826 + 7856. Let r(v) be the first derivative of -1/8*v**3 - 3/2*v**2 - n + 0*v. Factor r(i).
-3*i*(i + 8)/8
Let p be 7 - 51/(-17) - 5. Let v(h) be the third derivative of 0*h - 1/480*h**6 - 1/12*h**4 - 7/240*h**p + 0 + 2/3*h**3 - 2*h**2. Factor v(u).
-(u - 1)*(u + 4)**2/4
Let m(n) = 10*n**3 - 50*n**2 + 36*n + 46. Let j(q) = -39*q**3 + 199*q**2 - 146*q - 183. Let x(l) = -2*j(l) - 9*m(l). What is u in x(u) = 0?
-2/3, 2, 3
Suppose 3*b + 1654 - 1642 = 2*a, 0 = b + a - 6. Let m(x) be the second derivative of b*x**2 + 1/39*x**3 + 11*x + 0 - 1/78*x**4. Let m(h) = 0. What is h?
0, 1
Suppose 2*m - 1192 = -2*z + 3*m, -2980 = -5*z - m. Let g be z/11 + 8/44*-1. Factor 8*i**4 - 134*i + 12*i**3 + 64*i - 4*i**5 - 16*i**2 + g*i.
-4*i*(i - 2)**2*(i + 1)**2
Let r(l) be the first derivative of l**7/168 - l**5/8 + 5*l**4/12 - l**3 + 22*l + 5. Let x(y) be the third derivative of r(y). Determine m, given that x(m) = 0.
-2, 1
Let d(r) be the second derivative of -r**7/4620 + r**6/1980 + r**5/110 - 29*r**3/2 + r**2/2 - 4*r. Let f(i) be the second derivative of d(i). Solve f(z) = 0.
-2, 0, 3
Let o(v) = -16*v**3 - 621*v**2 - 1337*v - 667. Let x(g) = 11*g**3 + 413*g**2 + 892*g + 445. Let z(q) = -9*o(q) - 13*x(q). Determine k so that z(k) = 0.
-218, -1
Let p(i) be the third derivative of 5/18*i**5 + 0*i**4 + 0 + 29*i**2 + 1/18*i**6 + 0*i + 0*i**3 + 1/315*i**7. Factor p(u).
2*u**2*(u + 5)**2/3
Let y = 157133/125700 + -2/31425. Suppose 7/4 - 23/8*s + y*s**2 - 1/8*s**3 = 0. Calculate s.
1, 2, 7
Let m(z) = z**3 + 2*z**2 + 5*z + 16. Let h be m(-2). Factor 95 + h*u**2 + 16*u - 151 - 104 - 88*u - 2*u**2.
4*(u - 20)*(u + 2)
Let g(r) be the third derivative of 1/120*r**5 - 1/36*r**4 + 0 - 1/1080*r**6 + 7/3*r**3 + 0*r + 3*r**2. Let d(q) be the first derivative of g(q). Factor d(x).
-(x - 2)*(x - 1)/3
Suppose -c = -1 - 0, -5*t = -2*c - 19108. Let i be 2*(t/4)/7. Factor 2*q**5 + 2*q**2 - 269*q - q**4 - 6*q**3 - q**4 + i*q.
2*q*(q - 2)*(q - 1)*(q + 1)**2
Let v(u) be the second derivative of u**4/21 + 14*u**3/3 + 1188*u**2/7 - 161*u - 13. Factor v(a).
4*(a + 22)*(a + 27)/7
Let c = 65 - 63. Suppose 3*d + a = c*d + 261, -5*a = 3*d - 789. What is p in -328 - 42*p**2 - 294*p - 7*p**3 + 5*p**3 + d - 616 = 0?
-7
Let t(i) be the first derivative of -1/16*i**4 + 166 + 13/12*i**3 - 3/2*i**2 + 0*i. Suppose t(m) = 0. Calculate m.
0, 1, 12
Let f(t) be the first derivative of 28/5*t + 3*t**2 + 2/15*t**3 + 24. Suppose f(d) = 0. Calculate d.
-14, -1
Let k(p) = 24914*p - 373707. Let f be k(15). Suppose -10/9*s**4 + 10/3*s**2 + 2/9 + 23/9*s - 1/9*s**f = 0. What is s?
-1, -1/10, 2
Let p(r) be the third derivative of -r**6/180 + 2*r**5/9 - 19*r**4/36 - 2*r**2 - 181*r + 5. Solve p(x) = 0 for x.
0, 1, 19
Let z = 40 - 36. Suppose 25 = g - 5*b, g + 3*b + 3 = -z. Find o, given that o**4 + 191*o**g - 190*o**5 + 7*o**2 + 9*o**3 + 2*o + 0*o + 4*o**4 = 0.
-2, -1, 0
Suppose -365 - 204 = -268*w + 293 + 210. Factor 1/4*c**5 - 1/2*c**w + 0 + 1/2*c**2 - c**3 + 3/4*c.
c*(c - 3)*(c - 1)*(c + 1)**2/4
Factor 1376/5*j - 392/5 + 6/5*j**3 - 602/5*j**2.
2*(j - 98)*(j - 2)*(3*j - 1)/5
Let y = -10 + 14. Let v(o) = 37*o**2 + 79*o + 127. Let i(z) = -17*z**2 - 39*z - 62. Let l(k) = y*v(k) + 9*i(k). Factor l(u).
-5*(u + 2)*(u + 5)
Let w(u) be the first derivative of 1/2*u**2 + 3/4*u**4 - 6*u + 10/3*u**3 - 91. Determine d, given that w(d) = 0.
-3, -1, 2/3
Let p(q) be the first derivative of 5*q**4/2 - 995*q**3/6 + 1715*q**2/2 + 460*q + 5807. Determine r, given that p(r) = 0.
-1/4, 4, 46
Let i be (-126)/(-336) - 3/(-6). Let g(a) be the first derivative of -i*a**2 - 1/12*a**3 + 1 - 3/2*a. Factor g(u)