**2*(t + 27)/4
Suppose -2*z = -14*z + 72. Let d be -50*15/((-45)/z). Factor 60*x + d + 4/5*x**3 + 12*x**2.
4*(x + 5)**3/5
Let x be 1708/294 - ((-856)/(-24) + -36). Factor 9/7*b**2 + x*b - 10/7.
(b + 5)*(9*b - 2)/7
Let t be (-20)/(-11) + (-36600)/(-5280). Factor -5/4*c**2 + 0 - t*c.
-5*c*(c + 7)/4
Suppose -8*n + 79 = 47. Suppose -3*k + 2*k**4 - 303*k**3 - k + n*k + 317*k**3 - 16*k**2 = 0. What is k?
-8, 0, 1
Let m(q) = -66*q**2 - 66*q + 51. Let v(y) be the first derivative of 5*y**3/3 + 5*y**2/2 - 4*y - 64. Let k(g) = 2*m(g) + 27*v(g). Solve k(n) = 0 for n.
-2, 1
Let n be (40 - 7429/184)/(-2 + (-17)/(-10)). Let f(s) be the first derivative of 25/4*s + 1/12*s**3 + n*s**2 - 35. Factor f(g).
(g + 5)**2/4
Let q be (32/50)/((-266)/(-35) - (-1368)/(-190)). Factor 18*b - q + 23/5*b**2.
(b + 4)*(23*b - 2)/5
Let b = -460586/13 - -35430. Determine k so that -18/13*k + b + 46/13*k**3 - 16/13*k**5 + 12/13*k**4 - 4/13*k**2 = 0.
-1, 1/4, 1/2, 2
Determine m, given that 12*m**4 + 3198*m - 9312*m**2 + 453149276*m**3 - 453143704*m**3 + 530*m = 0.
-466, 0, 2/3, 1
Let x = 82 + -76. Let a be 1/(-3) + 26/x. Determine j so that 6*j**3 + 4*j**2 - 6*j - 10*j**4 + 13*j**a - 7*j**2 = 0.
-2, -1, 0, 1
Let b(m) = 2*m. Let y be b(2). Suppose 2*k = y*n + 158, -3*n - 306 = k - 5*k. Factor -29 + 19 + 95*l + k*l**3 - l + l - 160*l**2.
5*(l - 1)**2*(15*l - 2)
Let f(z) be the third derivative of -z**5/60 + 2*z**2. Let u(o) = -2641 - 4*o + 2642 + 2*o + o**2 + 3*o**2. Let r(t) = 3*f(t) + u(t). Factor r(v).
(v - 1)**2
Let n(g) be the second derivative of g**5/25 + 19*g**4/5 + 384*g**3/5 - 14336*g**2/5 - 1351*g + 3. Factor n(d).
4*(d - 7)*(d + 32)**2/5
Let s(z) be the first derivative of -z**4/32 - 35*z**3/6 - 3773*z**2/16 + 41503*z/4 + 6085. Suppose s(i) = 0. What is i?
-77, 14
Let o(v) be the third derivative of v**5/150 - 457*v**4/10 + 626547*v**3/5 - 5*v**2 - 439*v. What is d in o(d) = 0?
1371
Factor 9*i**3 + 24361803 + 407410*i - 127965*i + 84164*i - 6*i**3 + 1809*i**2.
3*(i + 201)**3
Let a = 5555/9 + -27586/45. Factor -1 - 4/5*p**2 + a*p.
-(p - 5)*(4*p - 1)/5
Let k(v) = v**4 - v**2 + 2*v - 1. Let b(w) = -4*w**4 - 58*w**3 + 66*w**2 + 116*w + 2. Let z(u) = b(u) + 2*k(u). Factor z(j).
-2*j*(j - 2)*(j + 1)*(j + 30)
Suppose 1870*w - 1357*w = 1026. Let 0 + 5/2*i**3 - 5/2*i**5 + 0*i + 0*i**4 + 0*i**w = 0. What is i?
-1, 0, 1
Let l(c) be the third derivative of c**6/660 - 2*c**5/165 + c**4/33 + 10*c**3/3 - c**2 + 4. Let p(o) be the first derivative of l(o). What is h in p(h) = 0?
2/3, 2
Let l(t) be the third derivative of -t**8/42 - 2*t**7/21 + 8*t**6/15 + 13*t**5/15 - 7*t**4/3 - 16*t**3/3 - 1642*t**2. What is v in l(v) = 0?
-4, -1, -1/2, 1, 2
Let c(r) be the second derivative of 11/15*r**4 + 8/5*r**2 + 3 - 2/25*r**6 - 2/105*r**7 + 7*r + 1/25*r**5 + 8/5*r**3. Find d, given that c(d) = 0.
-2, -1, 2
Solve 1/3*d**5 - 14*d**4 - 294 - 413*d + 146*d**3 + 124/3*d**2 = 0 for d.
-1, 2, 21
Let m(s) be the first derivative of 15*s**4/4 - 85*s**3/3 - 80*s**2 + 140*s + 5348. Find d, given that m(d) = 0.
-2, 2/3, 7
Suppose -c + 2 = 4, 0 = q - 4*c - 30. Find v such that -17*v**4 + 12*v + q*v**2 - 60*v**3 + 11*v**4 + 66*v**3 - 2*v**5 = 0.
-3, -1, 0, 2
Let v(s) = 11*s**3 + 2165*s**2 - 396*s - 376. Let r be v(-197). Factor -2/9*q**2 - r + 4*q.
-2*(q - 9)**2/9
Let x = 751 + -748. Suppose 0*s**x - 16 - 6241*s + 4*s**2 + 4*s**3 + 6225*s = 0. What is s?
-2, -1, 2
Let l = 106134 - 106134. Factor l*g**2 - 48/5*g + 3/5*g**3 + 0.
3*g*(g - 4)*(g + 4)/5
Let s(m) = 4*m**2 - 6. Let o(u) = 21*u**2 - u - 31. Let j = -207 - -196. Let x(a) = j*s(a) + 2*o(a). Determine y, given that x(y) = 0.
-2, 1
Let x(i) be the second derivative of i**4/4 - 5*i**3 - 33*i**2/2 - 286*i. Factor x(s).
3*(s - 11)*(s + 1)
Let q(d) = -3*d - 2. Let j be q(-1). Let v be j - -1 - (262*-2)/4. Let v*t**2 + 180*t + 17 + 272*t**2 + 3 = 0. What is t?
-2/9
Find k, given that 1/3*k**2 + 688/3*k + 118336/3 = 0.
-344
Let y(v) be the first derivative of v**4/2 - 7*v**2 + 12*v - 3761. Determine b, given that y(b) = 0.
-3, 1, 2
Let c = 3045 - 1267. Suppose -c + 2*i + i**2 + 1778 = 0. What is i?
-2, 0
Let y(f) be the first derivative of f**4/3 + 52*f**3/9 - 56*f**2 + 144*f + 368. Factor y(i).
4*(i - 3)*(i - 2)*(i + 18)/3
Let d(x) be the third derivative of -20/3*x**3 + 2*x - 1/30*x**5 - 3/4*x**4 + 0 + 5*x**2. Determine g, given that d(g) = 0.
-5, -4
Factor -3/2*y**2 - 18*y - 48.
-3*(y + 4)*(y + 8)/2
Let t(g) = 13*g**2 - 96*g + 12. Let p(h) = 115*h**2 - 865*h + 105. Let r(w) = -4*p(w) + 35*t(w). Determine q so that r(q) = 0.
0, 20
Let v(c) = c**2 + 247*c - 2836. Let u be v(11). Let d(a) be the second derivative of 1/2*a**3 - 19*a + 3/2*a**u + 1/16*a**4 + 0. Find k, given that d(k) = 0.
-2
Let s(b) be the first derivative of 6*b**6 + 832*b**5/7 + 4548*b**4/7 + 2816*b**3/7 + 512*b**2/7 - 414. Let s(m) = 0. Calculate m.
-8, -2/7, -2/9, 0
Suppose -f = 2*v - 8, -10*v - 5*f + 28 = -6*v. Factor 38*z**2 - z + 2*z + 3*z**3 - 4*z**4 + z**5 - 5*z - 34*z**v.
z*(z - 2)**2*(z - 1)*(z + 1)
Let y(n) be the second derivative of n**6/60 + 201*n**5/20 + 12639*n**4/8 - 41607*n**3 + 385641*n**2 + 17*n - 166. Factor y(r).
(r - 6)**2*(r + 207)**2/2
Find t such that 4/3*t**2 + 0 - 1/3*t**5 - 2*t**3 - 5/3*t**4 + 8/3*t = 0.
-2, 0, 1
Let t(p) be the second derivative of 3*p**7/35 - 37*p**6/75 + 29*p**5/25 - 7*p**4/5 + 13*p**3/15 - p**2/5 - 841*p. Factor t(h).
2*(h - 1)**4*(9*h - 1)/5
Let n = 445826 - 445822. Factor -9/2*k**2 + 0*k + 0 - 6*k**3 - 3/2*k**n.
-3*k**2*(k + 1)*(k + 3)/2
Determine c, given that 235/2*c**4 + 0*c**3 + 0*c + 0 + 5/4*c**5 + 0*c**2 = 0.
-94, 0
Let p(f) be the second derivative of -1/20*f**5 + 1/3*f**3 - 2 - 1/4*f**4 + 1/10*f**6 - 1/42*f**7 - 99*f + 0*f**2. Let p(v) = 0. Calculate v.
-1, 0, 1, 2
Suppose 3*d = -o + 4*d + 55, 2*d = -3*o + 175. Suppose 4*m - 76 = -3*j, -j + 2*j = 3*m - o. Factor -t + m*t**3 - 9*t**2 + t - 16*t**3.
3*t**2*(t - 3)
Factor 1331*v**3 - 68*v + 1337*v**3 - 108*v**2 + 24 - 2684*v**3.
-4*(v + 1)*(v + 6)*(4*v - 1)
Let c(i) = -3*i**4 + i**3 + i**2 - 5*i. Suppose -p - 2*h = -0*h - 8, 0 = -p + 3*h - 7. Let u(y) = 3*y**4 + 6*y. Let f(z) = p*u(z) + 3*c(z). Factor f(v).
-3*v*(v - 1)**2*(v + 1)
Let g(x) = -55*x + 4899. Let y be g(89). Let n(j) be the second derivative of -5/19*j**2 - 2/19*j**3 - 1/114*j**y + 2*j + 0. Factor n(q).
-2*(q + 1)*(q + 5)/19
Let y = 56884066/278213 + -16/21401. Let a = -204 + y. Factor -16/13*j**2 + a*j**3 - 4/13 + 14/13*j.
2*(j - 1)**2*(3*j - 2)/13
Let p(c) = -c**3 - 5*c**2 + 6*c + 5. Let l = -119 + 113. Let h be p(l). Solve -3*t**2 - 11 + h*t**2 + 9 = 0.
-1, 1
Let u(n) be the second derivative of 3*n**5/140 - 1037*n**4/28 + 2071*n**3/14 - 3105*n**2/14 + 128*n + 2. Suppose u(d) = 0. What is d?
1, 1035
Determine q, given that 22/3 - 1/3*q**4 + 35/3*q + q**2 - 11/3*q**3 = 0.
-11, -1, 2
Let p(c) be the second derivative of c**4/21 - 10*c**3/7 - 152*c**2/7 - 1849*c. Factor p(q).
4*(q - 19)*(q + 4)/7
Let p(n) be the first derivative of n**7/210 + n**6/2 + 161*n**5/10 - 529*n**4/6 + 2*n**3/3 + 31*n - 10. Let u(s) be the third derivative of p(s). Factor u(y).
4*(y - 1)*(y + 23)**2
Let w(q) be the second derivative of q**5/100 - q**4/10 - 7*q**3/30 + 662*q. Let w(t) = 0. Calculate t.
-1, 0, 7
Let g(f) be the second derivative of 0*f**2 - 1/4*f**5 + 35/6*f**4 + 0 - 55*f + 0*f**3. Determine p so that g(p) = 0.
0, 14
What is y in 0*y**3 - 6 + 1/6*y**4 - 25/6*y**2 + 10*y = 0?
-6, 1, 2, 3
Let b(o) = -17*o + 3. Let q be b(0). Factor 2*g**2 - 35*g**2 - 4*g**4 - 320*g + 287 - 15*g**2 + 481 - g**q + 37*g**3.
-4*(g - 4)**3*(g + 3)
Suppose 52*h + 75*h = 179 + 75. Let c(z) be the first derivative of 0*z - 1/2*z**4 + 0*z**h + 0*z**3 - 1/3*z**6 + 20 - 4/5*z**5. Find q such that c(q) = 0.
-1, 0
Let n(s) be the second derivative of -s**4/28 - 113*s**3/14 - 24*s**2 + 4941*s. Determine a, given that n(a) = 0.
-112, -1
Suppose -364*g = -353*g + 77. Let z(l) = -2*l**3 - 14*l**2 - 3*l - 19. Let n be z(g). Factor 1/6*h**3 - 2/3*h**n - 1/6*h + 0 + 2/3*h**4.
h*(h - 1)*(h + 1)*(4*h + 1)/6
Let h be (58/60 + (-37)/(-111))*258. Let m = -335 + h. Determine y so that 4/5 + m*y**3 - 2/5*y - 4/5*y**2 = 0.
-1, 1, 2
Let x(g) = 13*g**4 - 54*g**3 - 22*g**2 - 54*g - 6. Let s(j) = 15*j**4 - 63*j**3 - 21*j**2 - 55*j - 7. Let p(d) = 6*s(d) - 7*x(d). Factor p(y).
-y