(r - 41)/7
Factor 28322 + 1/2*v**2 + 238*v.
(v + 238)**2/2
Let d(r) be the second derivative of -r**4/6 - 170*r**3/3 + 696*r**2 + 436*r + 2. Factor d(w).
-2*(w - 4)*(w + 174)
Let p(g) be the first derivative of -g**4/42 + 15*g**3/7 + 46*g**2/7 - 226*g + 8. Let l(n) be the first derivative of p(n). Factor l(f).
-2*(f - 46)*(f + 1)/7
Let f(t) be the first derivative of t**3 + 27/2*t**2 - 67 + 54*t. Factor f(q).
3*(q + 3)*(q + 6)
Let g(i) be the first derivative of 7*i**6/3 + 262*i**5/5 + 423*i**4 + 1368*i**3 + 1080*i**2 - 37. Factor g(m).
2*m*(m + 6)**3*(7*m + 5)
Find s such that -29*s**3 + 169*s**2 - 77*s**2 - 62*s**2 - s = 0.
0, 1/29, 1
Let t(a) = -88*a - 52. Let d(f) = f**2 + f - 18. Let g(n) = 2*d(n) + t(n). Determine h, given that g(h) = 0.
-1, 44
Let h(g) = -g**3 - 4*g**2 - g - 4. Let t be h(-4). Suppose -350 = -2*v - t*v - 2*p, v - 179 = p. Factor 183*q**4 - v*q**4 - 6*q**2 + 0 + 0 - 3*q + 3*q**5.
3*q*(q - 1)*(q + 1)**3
Let w be ((-412)/4635*9/(-2)*2)/((-72)/(-20)). Let 20/3*a + 58/9 + w*a**2 = 0. Calculate a.
-29, -1
Let f(z) be the second derivative of -z**7/63 - 4*z**6/45 + 11*z**5/6 - 31*z**4/9 - 40*z**3/3 - z - 1104. Solve f(k) = 0.
-10, -1, 0, 3, 4
Let j(o) be the second derivative of 0*o**3 + 64/21*o**4 + 0*o**2 - 48/35*o**5 + 13*o - 1/147*o**7 + 3 + 6/35*o**6. Factor j(p).
-2*p**2*(p - 8)**2*(p - 2)/7
Factor -1/4*h**3 + 9*h**2 + 0 - 17*h.
-h*(h - 34)*(h - 2)/4
Let f = 3340/161 - 14929/805. Suppose -19/5*c**2 + f*c**3 - 1/5*c**4 + 9/5*c + 0 = 0. What is c?
0, 1, 9
Let w be 1638558/1491412 - 2/92. Let 20/13 - 66/13*z - w*z**2 = 0. What is z?
-5, 2/7
Let s(g) be the second derivative of -g**5/40 + 313*g**4/8 - 97969*g**3/4 + 30664297*g**2/4 + 1613*g. Factor s(a).
-(a - 313)**3/2
Suppose -33*c = -36*c + 456. Suppose -142*y + c*y = 40. Find b such that 4/5 + 3/5*b**2 + 2/5*b**3 - 8/5*b - 1/5*b**y = 0.
-2, 1, 2
Let i be (-16)/4 - ((-14912)/28 + 16/56). Factor 2/7*g**2 + i - 172/7*g.
2*(g - 43)**2/7
Suppose 21*r + 7532 = 7*r. Let s = 542 + r. Solve 2/5*c**s + 2/5 + 0*c**3 + 0*c - 4/5*c**2 = 0 for c.
-1, 1
Let y(q) be the third derivative of 0*q**4 + 1/120*q**6 + 11*q**2 + 31/6*q**3 - 7/40*q**5 + 0*q + 0. Let k(w) be the first derivative of y(w). Factor k(g).
3*g*(g - 7)
Let x be 1*0/(56 + -60). Factor 0 + 0*r**2 + 5/4*r**4 + x*r + 5/2*r**3.
5*r**3*(r + 2)/4
Let i(m) be the second derivative of 5*m**4/12 - 1405*m**3/6 - 705*m**2 + 58*m - 1. Determine v so that i(v) = 0.
-1, 282
Let c = 1 + 6. Determine g so that 2*g + 5*g + 0*g - g + c - g**2 = 0.
-1, 7
Let t(v) = 3*v - 3. Let u(d) = -d**2 - d + 1. Let z = 46 - 47. Let k be (-6)/((-4)/(z - 1)). Let i(x) = k*u(x) - t(x). Solve i(f) = 0 for f.
0
Suppose 12*y = -13 + 95 - 22. Let m(k) be the third derivative of -1/735*k**7 + 0*k + 0*k**6 - 1/21*k**3 + 0*k**4 + 1/105*k**y + 11*k**2 + 0. Factor m(d).
-2*(d - 1)**2*(d + 1)**2/7
Let v(i) = -i**3 + 57*i**2 - 59*i + 3. Let y be v(1). Factor y*t + 10/11*t**4 + 8/11*t**2 - 18/11*t**3 + 0.
2*t**2*(t - 1)*(5*t - 4)/11
Let p = 1326117 + -17239513/13. Factor -242/13*b**2 + 1860/13*b - 450/13 + p*b**3.
2*(b - 15)**2*(4*b - 1)/13
Let r(a) be the first derivative of -50 - 3*a**5 - 3*a**2 - 7*a**3 - 1/2*a**6 - 27/4*a**4 + 0*a. Factor r(f).
-3*f*(f + 1)**3*(f + 2)
Let s(o) be the third derivative of -o**7/315 + 2*o**6/45 + 7*o**5/30 - 2*o**4/9 - 20*o**3/9 - 4*o**2 + 201*o. Find i such that s(i) = 0.
-2, -1, 1, 10
Let z(m) be the third derivative of -m**8/112 + 87*m**7/70 - 1929*m**6/40 + 1333*m**5/20 + 5547*m**4/4 + 28*m**2 - 148*m + 1. Let z(k) = 0. Calculate k.
-2, 0, 3, 43
Let w(u) = 7*u**2 + 22334*u - 15545783. Let a(d) = -2*d**2 - 5584*d + 3886444. Let k(b) = -15*a(b) - 4*w(b). Factor k(c).
2*(c - 1394)**2
Let g be (385/42)/(7000/8800). Factor 440/21*d + g - 40/21*d**3 + 52/7*d**2 + 2/21*d**4.
2*(d - 11)**2*(d + 1)**2/21
Let u(f) = -10*f**2 - 55*f - 42. Let w(k) = 17*k**2 + 106*k + 84. Let p(z) = 5*u(z) + 3*w(z). Let p(t) = 0. What is t?
-42, -1
Suppose 505 = 3*a - 4*h + 520, 2*a = -h + 12. Factor -1305*x**2 - 60 - 405/2*x**a - 550*x.
-5*(x + 6)*(9*x + 2)**2/2
Suppose 3*t = -3103*j + 3107*j - 30, 3*j + t = 3. Let b(l) be the first derivative of -1/35*l**5 + 44 - 4/7*l**2 + 1/14*l**4 + 4/7*l + 1/7*l**j. Factor b(r).
-(r - 2)*(r - 1)**2*(r + 2)/7
Let g be 22270/3 - (-13 + 185/15). Solve -7084*y**5 + 4 + 495*y**2 + 1246*y**3 + 79*y**2 + g*y**5 + 1094*y**4 + 86*y = 0 for y.
-1, -2/17, -1/10
Let x be ((-1 + 2)*-2)/2*-30. Factor 21*o - 2038*o**2 + 1017*o**2 + 1018*o**2 - x.
-3*(o - 5)*(o - 2)
Let o be (1518/(-2530))/(-2 - ((-2)/4 - 0)). Factor -2 + o*c**2 - 8/5*c.
2*(c - 5)*(c + 1)/5
Find s, given that -4/3*s**4 + 64/3*s**2 + 4*s**5 + 128/3*s - 200/3*s**3 + 0 = 0.
-4, -2/3, 0, 1, 4
Let l(z) be the first derivative of 3/4*z**4 + 1/10*z**6 + 0*z**2 - 9/20*z**5 + 12*z - 1/2*z**3 - 13. Let c(f) be the first derivative of l(f). Factor c(t).
3*t*(t - 1)**3
Let y(v) be the second derivative of -v**6/30 + 47*v**5/20 + v**4/3 - 94*v**3/3 + 1768*v. Determine a so that y(a) = 0.
-2, 0, 2, 47
Let k(j) be the third derivative of -j**6/30 - 67*j**5/15 - 125*j**4/2 - 366*j**3 + 635*j**2 + 2*j. Find r such that k(r) = 0.
-61, -3
Let s(d) = -656*d - 57716. Let x be s(-88). Factor -44/3*j**2 - 76/3*j - 4/3*j**3 - x.
-4*(j + 1)**2*(j + 9)/3
Let 14*y + 12*y + 4*y**2 + 17*y + 57*y - 2*y - 156 = 0. What is y?
-26, 3/2
Let i be 1346*1/144 + (-20)/160. Let t = -41/9 + i. Factor t*k**2 + 2/3*k**3 + 10*k + 6.
2*(k + 1)*(k + 3)**2/3
Let a = 21463 - 21460. Let h(d) be the first derivative of -5/14*d**4 - 4/21*d**a + 5/7*d**2 + 4/7*d + 11. Factor h(l).
-2*(l - 1)*(l + 1)*(5*l + 2)/7
Let l(k) be the third derivative of -1/12*k**5 + 248*k**2 - 1/24*k**6 + 0 + 0*k**3 + 5/24*k**4 + 1/42*k**7 + 2*k. Let l(b) = 0. Calculate b.
-1, 0, 1
Let m be 42/8 + -1 + (-213)/852. Let v be 6/(-8 + 92)*m. Factor 0*x**2 + 0 - 8/7*x + v*x**3.
2*x*(x - 2)*(x + 2)/7
Let c(j) be the first derivative of -4*j**3/3 - 566*j**2 - 2248*j - 1123. Solve c(h) = 0 for h.
-281, -2
Solve 841 + 146*m**3 - 4*m**4 + 420*m**2 - 201 - 948*m - 30*m**3 - 224*m = 0.
-5, 1, 32
Suppose 146/5*p**2 + 92/5*p**3 - 452/5*p + 6/5*p**4 + 208/5 = 0. Calculate p.
-13, -4, 2/3, 1
Let y(d) be the second derivative of 131 - d - 3/20*d**5 - 15/2*d**2 - 3/4*d**4 + 9/2*d**3. Factor y(a).
-3*(a - 1)**2*(a + 5)
Let r = 198026 - 198024. Suppose -16*m - 286/3*m**r + 16*m**3 + 96 - 2/3*m**4 = 0. Calculate m.
-1, 1, 12
Determine f so that -192 - 1416/5*f - 249/5*f**4 + 6/5*f**5 + 1236/5*f**2 + 66*f**3 = 0.
-2, -1/2, 2, 40
Let t be ((-304)/475)/(4/6*(-30)/100). Factor t*u - 18/5*u**2 - 1 - 1/5*u**4 + 8/5*u**3.
-(u - 5)*(u - 1)**3/5
Let k(w) be the first derivative of w**6/9 - 22*w**5/15 - 605*w**4/6 - 2662*w**3/3 + 1190. Factor k(r).
2*r**2*(r - 33)*(r + 11)**2/3
Let w = -417257/2765 + 59/553. Let i = w - -151. Factor 1/5*h**4 - 1/5*h**3 + 1/5*h + 0 - i*h**2.
h*(h - 1)**2*(h + 1)/5
Factor -36/7*q + 216/7 - 3/7*q**3 - 30/7*q**2.
-3*(q - 2)*(q + 6)**2/7
Let a(f) = -309*f - 24. Let y be a(1). Let i = y - -336. Determine o so that -3/5*o**5 - 3/5*o**4 + 3/5*o**2 - 6/5*o + 9/5*o**i + 0 = 0.
-2, -1, 0, 1
Let s be (40/(-45))/(575/(-207)). Let b(v) be the first derivative of s*v**5 + 0*v + 1/5*v**4 + 1/5*v**2 - 8/15*v**3 + 12 - 1/5*v**6. Solve b(j) = 0.
-1, 0, 1/3, 1
Let c be 31/2046*1837 - 26. Solve -4*k - c*k**2 + 10/3 + 1/2*k**3 = 0 for k.
-2, 2/3, 5
Let r be 12488/(-196) + 37 - -31. Solve -16/7*y - r - 2/7*y**2 = 0 for y.
-5, -3
Let l = 158489 - 158489. Determine o, given that l + 0*o - 3/4*o**4 + 0*o**2 + 3/2*o**3 = 0.
0, 2
Let t = 426359 + -426357. Find d such that 225/7*d**5 + 4/7 + 105*d**4 + 417/7*d**t + 859/7*d**3 + 72/7*d = 0.
-1, -2/15
Factor -40881*n**4 + 20441*n**4 + 20438*n**4 - 90*n**2 + 44*n + 48*n**3.
-2*n*(n - 22)*(n - 1)**2
Let h(y) be the first derivative of y**6/360 + y**5/30 + y**4/8 + 5*y**3/3 + 11*y - 74. Let j(n) be the third derivative of h(n). Find r such that j(r) = 0.
-3, -1
Let k(m) be the second derivative of 5/2*m**2 + 42*m + 2 - 7/12*m**3 + 1/24*m**4. Solve k(p) = 0.
2, 5
Let i be 13 - (25/(-6525)*-18 - (-1500)/116). Find y, given that -36/5*y**2 - 6/5*y**5 - 64/5*y**4 - 94/5*y**3 + i + 0*y = 0.
-9, -1, -2/3, 0
Let t(m) be the third derivative of m**8/98 - 4*m**7/147 - 5*m**6/84 + 4*m**5/21 + 5*m**4/28 - 6*m**3/7 - 10*m**2 +