 + 5)/2
Let g(m) be the second derivative of 3*m**5/20 + 17*m**4/4 + 79*m**3/2 + 189*m**2/2 + 1617*m. Let g(y) = 0. Calculate y.
-9, -7, -1
Suppose 0 = -2*v + 2700 - 1018. Suppose -25*u**2 - 30*u - 5*u**3 + v - 10*u - 861 = 0. Calculate u.
-2, -1
Let y(v) be the second derivative of v**4/22 + 4277*v**3/66 - 713*v**2/22 + 4624*v. Factor y(g).
(g + 713)*(6*g - 1)/11
Suppose -2*d + 52 + 146 = 0. Let c = -877 + 1077. Determine k, given that -12*k - 92*k**2 + 3*k**3 - d*k**2 + c*k**2 = 0.
-4, 0, 1
Let m(i) be the third derivative of i**5/33 + i**4/12 + 156*i**2 - 2*i. Factor m(o).
2*o*(10*o + 11)/11
Suppose c + 3*a - 6 = -27, 8 = -4*a. Let w be (-50)/9 - (-21 - c). Solve -14/9*s + 2/9*s**3 + w*s**2 + 8/9 = 0 for s.
-4, 1
Let j(s) = s**2 - 489*s + 1942. Let c be j(4). Factor -c*i**3 + 8/3 - 16/3*i - 22/3*i**2.
-2*(i + 2)**2*(3*i - 1)/3
Let s be (23 + -2 + -2)*1. Find k, given that s*k - 31 - 17*k + 47 - 16*k**2 - 2*k**3 = 0.
-8, -1, 1
Let u(s) be the third derivative of 9 + 2/105*s**7 - 4*s**2 - 8*s**3 + 0*s + 1/5*s**6 - 2/3*s**4 + 3/5*s**5. Let u(h) = 0. Calculate h.
-3, -2, 1
Let f(m) be the first derivative of -m**4 - 500*m**3/3 - 7936*m**2 - 15376*m - 1948. Factor f(n).
-4*(n + 1)*(n + 62)**2
Suppose 0 = -12*k + 658847 - 39851. Suppose 0 = -16*y - 15743 + k. Factor -y*t**4 - 2*t**5 + 4*t**5 + 2234*t**4.
2*t**4*(t - 3)
Suppose -4*w + 7*w - 39 = 0. Suppose -3*l = w - 25. Factor -12*u**3 + 8*u**2 + 4*u**5 - 1684*u**l + 1684*u**4.
4*u**2*(u - 1)**2*(u + 2)
Let s be (-44)/(-10)*((-175)/5)/(-7). Let i = s - -121. Factor -70*a + 10*a**2 - 68*a - 10 + i*a - 5*a**3.
-5*(a - 2)*(a - 1)*(a + 1)
Let s be 12/(-19)*(-21280)/6720. Factor 1083 + 1/3*i**s - 38*i.
(i - 57)**2/3
Let c(i) = i. Let l be c(0). Let h(b) be the third derivative of 0*b**4 - 15*b**2 + 0*b**3 + l*b**5 + 0*b + 0 + 0*b**7 + 1/80*b**6 - 1/224*b**8. Factor h(f).
-3*f**3*(f - 1)*(f + 1)/2
Let i(a) be the first derivative of a**4 + 236*a**3/3 - 2*a**2 - 236*a - 2724. Suppose i(u) = 0. Calculate u.
-59, -1, 1
Let o(z) = 2*z**2 + 6*z - 23. Let j(a) = a**2 - a - 1. Let l(f) = 3*j(f) - o(f). Let y be l(6). Factor 0*t - t**2 - 3*t**3 - 4*t - y*t - 8*t**2.
-3*t*(t + 1)*(t + 2)
Let n(z) be the first derivative of -3*z**4/4 - 361*z**3 + 3*z**2/2 + 1083*z - 2070. Factor n(r).
-3*(r - 1)*(r + 1)*(r + 361)
Let r = -1009 - -1017. Let p(z) be the third derivative of 21*z**2 + 0*z**3 - 1/30*z**6 + 0*z**5 + 0*z**4 + 1/84*z**r + 0 + 0*z**7 + 0*z. Factor p(s).
4*s**3*(s - 1)*(s + 1)
Let y = 148 - 135. Determine f, given that -46*f - 108 - 4*f - y*f**3 - 35*f - f**4 - 50*f - 63*f**2 = 0.
-4, -3
What is c in 88/9*c**3 + 296*c + 2/9*c**4 + 330 + 268/3*c**2 = 0?
-33, -5, -3
Let l = -48 - -91. Let h = l - 41. Factor h*r + 2*r**2 + 6*r - 10*r.
2*r*(r - 1)
Let s = 9872251/11 + -898859. Let t = s - -1382. Solve -26/11*r**3 - 6/11*r - 6/11*r**4 + 8/11*r**5 - t + 34/11*r**2 = 0 for r.
-2, -1/4, 1
Let g(v) be the second derivative of -v**6/150 - 11*v**5/20 + 74*v**4/15 - 8*v**3 - v - 1368. Factor g(f).
-f*(f - 4)*(f - 1)*(f + 60)/5
Factor -3/4*x**3 - 81 + 153/4*x - 3/2*x**2.
-3*(x - 4)*(x - 3)*(x + 9)/4
Let s(f) be the first derivative of f**3/3 - 28*f**2 + 343*f - 762. Let s(d) = 0. Calculate d.
7, 49
Factor -9/2*u**3 + 280900 - 1262990*u - 4769*u**2.
-(u + 530)**2*(9*u - 2)/2
Let -1488*o**3 + 13480812 - 28046*o**2 - 89396*o**2 - 64381*o**2 - 8335040*o - 57061164 - 4*o**4 - 5569*o**2 = 0. Calculate o.
-122, -6
Let w(a) = 1139*a + 5695. Let b be w(-5). Factor -1/2*s**2 + b + 0*s.
-s**2/2
Let g = 45 - 134/3. Let l = 4133 + -4133. Factor g*x**2 + 0 + l*x.
x**2/3
Suppose 4*p + 8 = 4*u, 3*u - 6 + 2 = 5*p. Let a be (-2)/4*p*-2 + 1. Factor -5 + 1 + 42*s + a*s**2 - 2 - 38*s.
2*(s - 1)*(s + 3)
Let n(x) be the second derivative of x**6/40 - 57*x**5/16 - x**4/16 + 95*x**3/8 - 37*x + 20. Factor n(l).
3*l*(l - 95)*(l - 1)*(l + 1)/4
Let m be 106/5 - (-56)/(-280). Suppose -w + 4*x = 18, 4*w + 19*x - m*x + 2 = 0. Factor 2/17*d**3 + 0 + 2/17*d + 4/17*d**w.
2*d*(d + 1)**2/17
Let j(s) = s**3 + 10*s**2 + 9*s + 5. Let c be j(-9). Suppose -2*r + 1 = r + 5*y, c*r = -4*y + 6. Factor h**r - 8*h - h**3 + 4*h + h + h**4 - 6*h**2.
h*(h - 3)*(h + 1)**2
Let q(a) be the third derivative of a**7/490 - a**6/28 + 3*a**5/140 + 27*a**4/28 + 265*a**2 - 3. Factor q(d).
3*d*(d - 9)*(d - 3)*(d + 2)/7
Let x(t) = -1. Let n(d) = d**2 - 68*d + 1151. Suppose -7*w + 20*w + 52 = 0. Let z(a) = w*n(a) + 20*x(a). Factor z(p).
-4*(p - 34)**2
Let k(t) be the first derivative of 3*t**4/16 + 191*t**3/2 + 2283*t**2/8 + 285*t + 3429. Factor k(h).
3*(h + 1)**2*(h + 380)/4
Let t(r) be the third derivative of 0*r**4 + 1/30*r**6 + r**2 + 5*r - 1/210*r**7 + 0 + 0*r**5 + 0*r**3. Solve t(v) = 0.
0, 4
Let l(b) be the third derivative of -b**5/30 + 4*b**4 + 100*b**3/3 - 3219*b**2. Determine r so that l(r) = 0.
-2, 50
Let j(c) be the third derivative of -c**5/100 - c**4/10 + 102*c**3 - 8*c**2 + 89*c - 2. Factor j(h).
-3*(h - 30)*(h + 34)/5
Let d(f) be the first derivative of 12 + 5/4*f**4 - f**5 + 0*f + 0*f**2 + 0*f**3. Factor d(p).
-5*p**3*(p - 1)
Let v(y) be the first derivative of -14*y**2 - 14/3*y**3 - 16*y - 1/2*y**4 - 17. Factor v(g).
-2*(g + 1)*(g + 2)*(g + 4)
Let c(t) be the second derivative of 3*t + 12*t**2 + 10/3*t**3 + 1/3*t**4 + 8. Let c(v) = 0. Calculate v.
-3, -2
Let b be (9 - 384/36)/((-2)/558). Let f = b - 2765/6. Determine d so that 32/3 + f*d**2 - 40/3*d = 0.
8/5
Let x = -1483/70 + 4519/210. Factor x*z**4 + 1/3*z**3 + 0 - 5/3*z**2 + z.
z*(z - 1)**2*(z + 3)/3
Let j(d) = 3*d**4 + 95*d**3 + 109*d**2 - 95*d - 104. Let c(x) = -2*x**4 - x**2 + 1. Let q(f) = -4*c(f) - j(f). Factor q(z).
5*(z - 20)*(z - 1)*(z + 1)**2
Let v(s) = -105*s**2 + 5964*s - 110266. Let w(g) = 206*g**2 - 11930*g + 220525. Let b(f) = -11*v(f) - 6*w(f). Factor b(l).
-(9*l - 332)**2
Let t(m) = 29*m + 210. Let p be t(-7). Suppose 0 = -2*g + p*g + n, -3*n = 3*g. What is s in 0*s**4 + 0 - 3/5*s**3 + 3/5*s**5 + 0*s + g*s**2 = 0?
-1, 0, 1
Suppose 88*l = 18*l. Let j(i) be the second derivative of 5/6*i**4 - 3/5*i**5 + 1/3*i**3 + l + 22*i + 0*i**2. Factor j(h).
-2*h*(h - 1)*(6*h + 1)
Let n(q) be the first derivative of 9/2*q**2 + 0*q**4 - 1/420*q**6 + 0*q - 11 + 1/70*q**5 - 4/21*q**3. Let r(c) be the second derivative of n(c). Factor r(b).
-2*(b - 2)**2*(b + 1)/7
Suppose -8*p + 3*p - 25 = 5*k, -4*k = p + 17. Let j be (4 + 7 + k)*1. Factor 5*b**2 - 5*b + b + j*b + 2*b.
5*b*(b + 1)
Let g = -617 - -622. Suppose 4*t = -2*k + 10, 1 = 3*k - g*t - 3. Factor 0*b + 8/15 - 2/5*b**2 - 2/15*b**k.
-2*(b - 1)*(b + 2)**2/15
Let o(t) be the third derivative of -5*t**8/112 + 32*t**7/35 - 769*t**6/200 + 359*t**5/50 - 71*t**4/10 + 4*t**3 - 511*t**2. Suppose o(r) = 0. Calculate r.
2/5, 1, 10
Let c(x) be the first derivative of -14 + 2/63*x**3 + 0*x - 1/1260*x**6 + 1/84*x**4 - 13*x**2 + 0*x**5. Let f(m) be the second derivative of c(m). Factor f(p).
-2*(p - 2)*(p + 1)**2/21
Let d(c) = -80*c + 23*c + 24*c + 20 + 32*c. Let w be d(17). Factor -4 + 4*s**2 - 10*s + 14*s**w - 12*s**3 + 8*s.
2*(s - 1)*(s + 1)*(s + 2)
Find d, given that -6864/5*d - 121/5*d**2 - 97344/5 = 0.
-312/11
Let n(w) be the second derivative of w**6/5 - w**5/5 - 39*w**4/16 - 9*w**3/2 + 20*w**2 - w + 9. Let t(y) be the first derivative of n(y). Factor t(j).
3*(j - 2)*(4*j + 3)**2/2
Let h(k) be the first derivative of -k**8/336 + k**7/84 + k**6/72 - k**5/12 + 83*k**3/3 - 36. Let v(a) be the third derivative of h(a). Factor v(u).
-5*u*(u - 2)*(u - 1)*(u + 1)
Let u(w) be the second derivative of w**7/13860 - w**6/792 - 3*w**5/55 - 61*w**4/6 - 171*w. Let t(x) be the third derivative of u(x). Factor t(r).
2*(r - 9)*(r + 4)/11
Suppose -67 = -3*f + 176. Suppose 0 = 77*z - f*z. Factor z + 1/3*w**5 + 1/3*w**2 + w**4 + 0*w + w**3.
w**2*(w + 1)**3/3
Let w(i) be the third derivative of -4/21*i**8 + 0*i + 40*i**4 - 1 + 24*i**3 + 80/21*i**7 + 27*i**2 - 133/6*i**6 + 41/3*i**5. Let w(r) = 0. Calculate r.
-1/4, 1, 6
Factor -48 - 24*j**2 - 7*j**2 + 10*j**2 - 9*j**2 + 221*j - 33*j.
-2*(j - 6)*(15*j - 4)
Let k(z) = -4*z**3 + 37*z**2 + 57*z - 270. Let s be k(10). Factor 2/5*n**3 - 2/5*n**2 + 0*n + s.
2*n**2*(n - 1)/5
Let y(c) be the second derivative of c**5/5 - 73*c**4/3 - 452*c**3/3 - 304*c**2 + 3405*c. Let y(u) = 0. What is u?
-2, -1, 76
Suppose 122/3*s**2 + 158/15*s**3 + 20 + 75