- o**5/90 - 5*o**4/6 + 24*o**2. Let d(w) be the second derivative of u(w). Factor d(y).
-2*(y + 1)**2*(y + 2)/3
Let d(n) be the first derivative of 29 - 1/6*n**3 + 1/12*n**6 + 0*n**2 - 1/8*n**4 + 0*n + 1/10*n**5. Suppose d(s) = 0. Calculate s.
-1, 0, 1
Let t(s) be the first derivative of -10/3*s**2 + 40/9*s**3 + 1/3*s**5 + 0*s - 8 - 25/12*s**4. Suppose t(m) = 0. What is m?
0, 1, 2
Let b(c) be the third derivative of -c**8/672 + 11*c**7/210 - c**6/6 - c**5/60 + 41*c**4/48 - 5*c**3/3 + c**2 + 46*c. Solve b(g) = 0 for g.
-1, 1, 20
Let u(w) be the first derivative of w**3/3 - 20*w**2 + 161. What is c in u(c) = 0?
0, 40
Let d(a) be the third derivative of -a**7/5040 - a**6/360 - a**5/80 + a**4/8 - 3*a**2. Let t(k) be the second derivative of d(k). Factor t(m).
-(m + 1)*(m + 3)/2
Suppose 2*p - 3*x + 23 = 38, -3*p = -5*x - 25. Factor -8/7*i**2 + p + 4/7*i**5 - 4/7*i + 0*i**3 + 8/7*i**4.
4*i*(i - 1)*(i + 1)**3/7
Let f(w) be the third derivative of 1/21*w**3 + 0*w**5 + 1/210*w**6 + 0*w + 19*w**2 - 1/735*w**7 - 1/42*w**4 + 0. Factor f(z).
-2*(z - 1)**3*(z + 1)/7
Let x be (9/(-4))/(246/(-328)). Let r = 13/2 + -5. Suppose n**2 - 1/4*n**5 - r*n**x + 0 + n**4 - 1/4*n = 0. What is n?
0, 1
Let h(w) = -w**2 - 3. Let o(k) = -k**2 - 1. Let d = -31 + 33. Let z(i) = d*h(i) - 4*o(i). Factor z(b).
2*(b - 1)*(b + 1)
Let 4 - 152/3*d**2 - 20/3*d - 72*d**3 - 20/3*d**5 - 116/3*d**4 = 0. What is d?
-3, -1, 1/5
Let l(m) be the third derivative of 0 + 0*m + 1/450*m**5 + 11*m**2 + 0*m**3 + 1/36*m**4. Determine n so that l(n) = 0.
-5, 0
Let y(u) be the third derivative of -u**6/180 + u**4/9 - 290*u**2. Factor y(h).
-2*h*(h - 2)*(h + 2)/3
Suppose -3*w - 5*q = -70, w + q + 6 = 28. Let i be (30/(-25))/((-6)/w). Factor 6*l**3 + l**i - 1 + 1 + 4*l**2 - 2*l**3.
l**2*(l + 2)**2
Let g = 61 + -2. Let i = -57 + g. Factor 2/9*x**i + 2 - 4/3*x.
2*(x - 3)**2/9
Let h be -6 - (-728)/119 - 66/(-17). Factor 759*j**2 + j**3 + 3*j**3 - 755*j**2 - 4*j - 4*j**h.
-4*j*(j - 1)**2*(j + 1)
Let h be (2*-1 - 20/(-12))*0. Let x(n) be the first derivative of h*n**2 + 1/4*n**4 - 2 + 1/10*n**5 + 0*n + 1/6*n**3. Suppose x(b) = 0. What is b?
-1, 0
Let g(u) be the first derivative of 2/5*u**2 - 19 - 2/5*u - 1/5*u**4 + 0*u**3 + 2/25*u**5. Factor g(w).
2*(w - 1)**3*(w + 1)/5
Let j(o) be the third derivative of o**8/13440 - o**7/7560 - o**6/1440 + o**5/360 - 7*o**4/24 - 4*o**2. Let z(h) be the second derivative of j(h). Factor z(d).
(d - 1)*(d + 1)*(3*d - 2)/6
Let 1/3*n**2 - n - 10/3 = 0. Calculate n.
-2, 5
Let p(b) = b**3 + 10*b**2 + 10*b + 13. Let x be p(-9). Find v, given that 13*v**4 - 7*v**2 - 4*v - 30*v**x + v**2 + 19*v**4 = 0.
-1, 0, 2
Let r(y) be the second derivative of -y**6/30 + 7*y**5/40 - y**4/8 - 86*y. Factor r(m).
-m**2*(m - 3)*(2*m - 1)/2
Let r(t) be the third derivative of t**6/135 + 4*t**5/135 - 11*t**4/108 + t**3/9 + 12*t**2 - 1. Factor r(w).
2*(w + 3)*(2*w - 1)**2/9
Let x(p) = p**3 + 5*p**2 - 4*p + 16. Let h be x(-6). Suppose -9*m = -10*m + h. Factor 0*y + 4/7*y**2 + 0*y**3 - 2/7*y**m - 2/7.
-2*(y - 1)**2*(y + 1)**2/7
Let o + 1/2*o**4 - 3/2*o**2 + 0*o**3 + 0 = 0. Calculate o.
-2, 0, 1
Let p(k) be the third derivative of -k**8/1008 + k**6/36 + k**5/9 + 5*k**4/24 + 2*k**3/9 + 21*k**2 + 2. Factor p(d).
-(d - 4)*(d + 1)**4/3
Suppose 0 = -41*h - 117 + 117. Let -c**3 - 2*c**2 + h*c + 1/2 + c**5 + 3/2*c**4 = 0. Calculate c.
-1, 1/2, 1
Factor -f - 1327*f**2 + 2 + 1326*f**2 + 10.
-(f - 3)*(f + 4)
Let p(j) be the third derivative of j**6/120 - j**5/60 + j**4/24 - j**3/6 + 5*j**2. Let m(z) = -z**3 + 6*z**2 - 6*z + 6. Let c(a) = m(a) + 6*p(a). Factor c(y).
5*y**3
Let d(r) be the third derivative of r**4 + 2*r**3 + 1/40*r**6 - 9*r**2 + 0*r + 0 + 1/4*r**5. Factor d(u).
3*(u + 1)*(u + 2)**2
Let a be (-342)/(-19) + 14 + -32. What is b in a*b**3 - 16/5*b**2 + 0 + 4/5*b**4 + 0*b = 0?
-2, 0, 2
Let u(m) be the third derivative of 1/42*m**7 - 25/96*m**4 + 1/24*m**6 - 5/12*m**3 - 28*m**2 - 1/24*m**5 + 0*m + 5/1344*m**8 + 0. Let u(y) = 0. Calculate y.
-2, -1, 1
Let f be 7 - 17 - (-2 - 8). Let m(c) be the second derivative of 0 - 1/36*c**4 + 1/6*c**2 - 6*c + f*c**3. Solve m(g) = 0.
-1, 1
Let u(v) be the third derivative of -v**8/1680 + 71*v**7/1050 - 51*v**6/25 - 108*v**5/25 + 280*v**2 - 2. Factor u(o).
-o**2*(o - 36)**2*(o + 1)/5
Let q = 60/73 + -201/511. Solve q*d**2 + 0*d + 3/7*d**3 + 0 = 0 for d.
-1, 0
Let j(v) be the third derivative of -5*v**2 + 0 + 1/9*v**5 - 13/18*v**4 + 0*v - 4/3*v**3. Factor j(i).
4*(i - 3)*(5*i + 2)/3
Let p(k) be the third derivative of 1/15*k**6 - 2/105*k**7 + 0*k**4 + 0*k**5 + 0*k + 0*k**3 + 7*k**2 + 0. Find r such that p(r) = 0.
0, 2
Let i(c) be the second derivative of -5/3*c**4 + 24*c + 20/3*c**3 + 0*c**2 + 1/6*c**6 + 0 - 1/2*c**5. What is s in i(s) = 0?
-2, 0, 2
Let k(r) = -5*r + 42. Let y be k(6). Let z(t) be the first derivative of -5 - 36*t**2 - 45*t**3 - y*t - 75/4*t**4. Solve z(p) = 0 for p.
-1, -2/5
Let f(t) be the first derivative of -t**5/25 - 4*t**4/5 - 46*t**3/15 + 72*t**2/5 - 81*t/5 + 300. Solve f(a) = 0.
-9, 1
Suppose 5*d - 2 - 3 = 0. Let j(c) = c**2 - c + 1. Let w(t) be the first derivative of -4*t**3/3 + 3*t**2/2 - 5*t + 3. Let k(g) = d*w(g) + 5*j(g). Factor k(v).
v*(v - 2)
Let w(m) be the first derivative of -m**6/15 + 3*m**5/10 - m**4/6 - m**3 + 2*m**2 - 12*m - 15. Let u(t) be the first derivative of w(t). Factor u(n).
-2*(n - 2)*(n - 1)**2*(n + 1)
Let v(t) = t**3 + 5*t**2 + 8*t + 2. Let j(u) = u + 1. Let f(c) = -5*j(c) + v(c). Let r be f(-4). Solve r - 4*p**2 - 8*p + 1 + 2 + 8*p**2 = 0 for p.
1
Let f(t) be the second derivative of t**6/45 - 2*t**5/3 + 3*t**4 - 52*t**3/9 + 17*t**2/3 - 38*t + 1. Suppose f(a) = 0. Calculate a.
1, 17
Suppose 5*u - 3 = 4*m - 13, 5*u = m - 10. Suppose m*i + 3*i - 9 = 0. Factor 0*l**2 + i*l**2 - 47*l + 35*l + 12.
3*(l - 2)**2
Let n(t) = -t**2 + 8*t + 15. Let r be n(8). Suppose r*q - 3*q = 36. Factor 0*c**q + 2/15 + 0*c + 2/15*c**4 - 4/15*c**2.
2*(c - 1)**2*(c + 1)**2/15
Let j be (2 + -3)/(-3 + 10/4). Suppose -45*c**3 + 5*c**4 - 32*c + 91*c**2 + 132*c - 16*c**j + 25*c = 0. What is c?
-1, 0, 5
Let y be 18/10 + (-17 - -17). Let d = 256/5 - 51. Factor d*b**3 + y*b + 6/5*b**2 + 0.
b*(b + 3)**2/5
Let y(p) be the first derivative of -5*p**3 + 55*p**2/2 - 30*p + 147. Factor y(s).
-5*(s - 3)*(3*s - 2)
Let x(w) = -w**3 - 28*w**2 - w - 24. Let l be x(-28). Let p(k) be the first derivative of 0*k + 0*k**2 + 5 + 3/5*k**5 - 3*k**4 + l*k**3. Factor p(s).
3*s**2*(s - 2)**2
Let h(m) be the first derivative of -1/25*m**5 + 6/5*m**3 + 11 - 1/5*m**4 + 7/5*m - 2*m**2. Find z, given that h(z) = 0.
-7, 1
Let h(x) be the third derivative of -5*x**8/336 + 23*x**7/210 + x**6/12 + 73*x**2 + 1. Factor h(b).
-b**3*(b - 5)*(5*b + 2)
Let i(q) be the second derivative of 5*q**7/378 - 11*q**6/216 - 14*q**5/135 - q**4/18 + 11*q**2/2 - 6*q. Let h(a) be the first derivative of i(a). Factor h(p).
p*(p - 3)*(5*p + 2)**2/9
Let i be (-3)/(-4 - -3) - 7. Let v be 0 + 4 + 8 + i. Determine q, given that 0*q**2 + v*q**4 + 0 - 7/2*q**5 + 0*q - 2*q**3 = 0.
0, 2/7, 2
Let d(k) be the second derivative of -k**7/210 + k**5/20 - k**4/12 + k**2 + 5*k. Let m(p) be the first derivative of d(p). Let m(l) = 0. What is l?
-2, 0, 1
Suppose 0 = 5*d - 3*y - 30, -2*d - 3*d - y + 10 = 0. Suppose 3*r**4 + 3*r**3 - 6*r**5 - 7*r**2 + r + 4*r**2 + 12*r**d - 10*r = 0. Calculate r.
-1, 0, 1, 3/2
Let p = -710 + 710. Let i(k) be the first derivative of 5*k**3 + 3*k**2 + 3*k**4 + 3/5*k**5 + 7 + p*k. Let i(h) = 0. What is h?
-2, -1, 0
Let c(t) = -10*t - 58. Let h = 114 - 120. Let i be c(h). Suppose 1/3*k**i - 1/3*k**4 + 1/3*k - 1/3*k**3 + 0 = 0. Calculate k.
-1, 0, 1
Let y = -57/109 + 845/1199. Let r = 6384/11 - 580. Factor 6/11*t - y*t**3 + r + 0*t**2.
-2*(t - 2)*(t + 1)**2/11
Let u(b) be the second derivative of 0*b**2 + 0 - 7*b - 5/48*b**4 + 5/12*b**3. Factor u(q).
-5*q*(q - 2)/4
Let o(p) be the third derivative of -p**7/630 - p**6/45 + 43*p**5/180 - 29*p**4/36 + 4*p**3/3 + 293*p**2. Find x such that o(x) = 0.
-12, 1, 2
Factor -130*q + 11*q**2 + 44 - 4 - 46*q**2.
-5*(q + 4)*(7*q - 2)
Let p = 1481 - 48877/33. Let n = p + 107/66. Solve n*j**2 - 3*j - 9/2 = 0.
-1, 3
Let z(x) be the second derivative of -2*x**7/105 + 7*x**6/75 - x**5/25 - 11*x**4/30 + 4*x**3/15 + 4*x**2/5 - 4*x - 1. Let z(o) = 0. Calculate 