 third derivative of d(t). Suppose s(f) = 0. What is f?
0, 1, 2
Let u(m) be the first derivative of -5*m**7/42 + 2*m**6/3 - 5*m**5/4 + 5*m**4/6 + 12*m - 4. Let l(p) be the first derivative of u(p). Factor l(s).
-5*s**2*(s - 2)*(s - 1)**2
Let i(w) be the first derivative of w**5/15 + w**4/4 - 2*w**2/3 - 742. Factor i(a).
a*(a - 1)*(a + 2)**2/3
Let x(v) be the first derivative of v**6/180 + v**5/24 + v**4/8 + 7*v**3/36 + v**2/6 - 12*v - 7. Let a(s) be the first derivative of x(s). Factor a(i).
(i + 1)**3*(i + 2)/6
Let r(x) = 7*x**3 - 51*x**2 + 160*x - 157. Let y(v) = -3*v**3 + 25*v**2 - 80*v + 78. Let n(z) = -2*r(z) - 5*y(z). Factor n(j).
(j - 19)*(j - 2)**2
Suppose -5*o - 2*a = 0, -3*o = -0*a + a - 1. Let m = 9894 + -89044/9. Factor -m*x**o + 0*x + 0 - 2/9*x**3.
-2*x**2*(x + 1)/9
Find r such that 3*r**2 + 0 - 15/4*r**4 + 6*r - 3/4*r**5 - 9/2*r**3 = 0.
-2, 0, 1
Suppose p - 2*g + 4 = 0, 4*g + 0 = -2*p + 16. Factor 16 - 6*k**3 + p*k**3 + 20*k**2 - 32*k + 0*k**2.
-4*(k - 2)**2*(k - 1)
Suppose -n - 2*b - 15 = -2*n, -3*n - 2*b + 5 = 0. Factor -7 + 15 - 2*z**2 + n*z**2 + z**2 + 12*z.
4*(z + 1)*(z + 2)
Determine d so that 1156/7 - 136/7*d + 4/7*d**2 = 0.
17
Find s such that 6*s - 8849 - 2*s**2 + 8865 + s**2 = 0.
-2, 8
Let i(n) be the third derivative of -1/60*n**6 - 1/42*n**5 - 1/84*n**4 + 0 - 1/245*n**7 + 0*n**3 + 0*n - 5*n**2. Factor i(s).
-2*s*(s + 1)**2*(3*s + 1)/7
Suppose -j = i - 13, 3*i - 34 + 5 = -j. Factor -1 - 23 - 36*x + i*x - 4*x**2.
-4*(x + 1)*(x + 6)
Let m be (-369)/1353*-11*1. Factor -2/7*l**m - 6/7 - 2/7*l**2 + 10/7*l.
-2*(l - 1)**2*(l + 3)/7
Factor -186/7*i + 16*i**2 + 36/7 - 18/7*i**3.
-2*(i - 3)**2*(9*i - 2)/7
Suppose 57 - 30 = 9*m. Let c(n) be the third derivative of 0*n**m - 1/21*n**7 - 11*n**2 + 5/24*n**6 + 5/24*n**4 + 0*n + 0 - 1/3*n**5. Factor c(t).
-5*t*(t - 1)**2*(2*t - 1)
Solve 1/6*r**4 + 2/3*r - 10/3 - 4/3*r**3 + 5/2*r**2 = 0.
-1, 2, 5
Let g(r) be the second derivative of r**4/3 + 40*r**3/3 + 200*r**2 + 60*r. Factor g(w).
4*(w + 10)**2
Let m(f) be the third derivative of 0*f**3 - 1/1365*f**7 + 0*f**4 - 1/390*f**6 - 9*f**2 + 1/2184*f**8 + 0*f + 0 + 0*f**5. Suppose m(k) = 0. Calculate k.
-1, 0, 2
Factor -29/6*c**3 + 3/2*c**4 - 1/6*c**5 - 5*c + 4/3 + 43/6*c**2.
-(c - 4)*(c - 2)*(c - 1)**3/6
Let w be (-2)/(-5) - (-48)/5. Suppose -3*h - k = -6*k - w, -5*h = 4*k + 8. Suppose h*p + 37*p**2 + 2*p - 39*p**2 = 0. What is p?
0, 1
Let d be 1*(7 - 1)*(-7)/(-441). Factor -10/21*r + d*r**2 + 0.
2*r*(r - 5)/21
Let v(y) be the first derivative of 3 + 0*y**3 - 1/35*y**5 + 1/7*y + 1/7*y**2 - 1/14*y**4. Factor v(g).
-(g - 1)*(g + 1)**3/7
Suppose -3*p + 11 = -2*p + 2*o, -5*p + 4*o - 15 = 0. Let f be (p/3)/((-5)/(-30)). Factor f*r**3 - 2*r + 0*r**4 - r**2 + 2 + r**4 - 2.
r*(r - 1)*(r + 1)*(r + 2)
Let s(f) be the third derivative of f**8/1680 + f**7/378 + 7*f**6/1620 + f**5/270 - 25*f**4/24 + 8*f**2. Let x(n) be the second derivative of s(n). Factor x(r).
4*(r + 1)*(3*r + 1)**2/9
Factor 0*o + 4/5*o**2 - 2/5*o**4 + 0 + 2/5*o**3.
-2*o**2*(o - 2)*(o + 1)/5
Let o(n) be the third derivative of -n**7/210 - 7*n**6/180 - 2*n**5/15 + 5*n**4/24 + 12*n**2. Let b(r) be the second derivative of o(r). Factor b(s).
-4*(s + 1)*(3*s + 4)
Let p = 12 - 15. Let y be ((-12)/7)/(p/21). Determine j, given that -12*j**2 + 4*j**5 - j**5 + 0*j**5 - y*j**4 + 18*j**3 + 0*j**5 + 3*j = 0.
0, 1
Let x(b) = 15*b + 17. Let i be x(1). Suppose -64 = -48*v + i*v. Factor 4/9*f - 4/9*f**3 + 2/9*f**2 + 0 - 2/9*f**v.
-2*f*(f - 1)*(f + 1)*(f + 2)/9
Let l(k) be the first derivative of -4/9*k - 1/3*k**2 - 16 + 1/18*k**4 + 0*k**3. Solve l(a) = 0 for a.
-1, 2
Let w = -5/382 + 201/764. Solve -3/8 - w*x + 1/8*x**2 = 0.
-1, 3
Let c(q) = -56*q**2 + 9*q + 13. Let r(o) = -13*o**2 + 2*o + 3. Let d(f) = 6*c(f) - 26*r(f). Find m such that d(m) = 0.
-1, 0
Suppose 3*t - 8*t - 13 = -4*i, -i + 7 = -5*t. Suppose -5*r = -2*n + 42, i*n - 3 = -3*r + 7. Let -d**2 - n*d**2 - 3*d + 15*d**2 = 0. What is d?
0, 1
Suppose -4*w = -w - 6. Suppose 0 = -14*n + 4*n + 40. Determine i so that -18*i + 6*i**3 - 2*i**2 - w*i**n - 4*i**2 + 4*i**3 = 0.
-1, 0, 3
Let r be ((-1)/(-1))/(6/(-108)). Let t = 20 + r. Factor g**3 - 4 - g**2 - g**2 - 7*g**t + 12*g**2.
(g - 1)*(g + 2)**2
Let a be 3/(-1)*(-2)/3*1. Suppose i**3 - 3*i**5 + 9*i**4 - 4*i**2 - 5*i**a - 4*i**3 + 6*i = 0. Calculate i.
-1, 0, 1, 2
Let h(k) be the second derivative of k**6/1440 - k**5/96 + k**4/24 - 11*k**3/3 + 21*k. Let v(i) be the second derivative of h(i). Let v(y) = 0. Calculate y.
1, 4
Let v(f) = f**4 - 15*f**3 + 11*f**2 - 5*f + 5. Let y(z) = z**4 - 13*z**3 + 10*z**2 - 4*z + 4. Let g(x) = 4*v(x) - 5*y(x). Determine u so that g(u) = 0.
0, 2, 3
Suppose -6*m + 8 + 28 = 0. Let q(o) = 44*o**2 - 19*o + 11. Let k(g) = 11*g**2 - 5*g + 3. Let v(f) = m*q(f) - 22*k(f). Factor v(x).
2*x*(11*x - 2)
Let h(l) be the third derivative of -l**6/40 - l**5/20 - 3*l**3/2 + 2*l**2. Let z(i) be the first derivative of h(i). Factor z(p).
-3*p*(3*p + 2)
Let x be 2*4 + 3168/(-504). Find a such that -4/7*a + 12/7*a**2 + 0 + 4/7*a**4 - x*a**3 = 0.
0, 1
Let r(j) = -210*j**2 - 1261*j - 4. Let w be r(-6). What is n in 0*n - 2/11*n**3 + 0 + 4/11*n**w = 0?
0, 2
Let m(s) be the first derivative of s**5/10 + 17*s**4/8 - s**3/6 - 17*s**2/4 - 59. Factor m(i).
i*(i - 1)*(i + 1)*(i + 17)/2
Let r = 92 - 88. Suppose 0 = 4*a + 4*p - 0*p + r, 0 = -a + 2*p + 8. Solve -1/8 - 1/8*n**a + 1/4*n = 0.
1
Let w(p) be the third derivative of -5/24*p**6 + 19/30*p**5 + 0*p - 1/336*p**8 - 7/6*p**4 + 29*p**2 + 4/105*p**7 + 4/3*p**3 - 1. Factor w(f).
-(f - 2)**3*(f - 1)**2
Let f(g) be the first derivative of 3*g**4/7 + 37*g**3/7 + 123*g**2/14 + 24*g/7 + 102. Factor f(x).
3*(x + 1)*(x + 8)*(4*x + 1)/7
Let v(h) be the second derivative of -4/3*h**2 + 1/9*h**4 - 9*h + 0 - 2/9*h**3. Factor v(k).
4*(k - 2)*(k + 1)/3
Let r(m) be the first derivative of -2/3*m**6 + 15 - 4/5*m**5 + 2*m**4 + 0*m**3 + 0*m + 0*m**2. Factor r(b).
-4*b**3*(b - 1)*(b + 2)
Let g(k) = k**3 - k**2. Let j(q) = 6*q**3 + 50*q**2 + 48*q + 16. Let l(c) = 6*g(c) + j(c). Solve l(p) = 0 for p.
-2, -1, -2/3
Suppose 0 = 8*a - 4*a - 180. Solve 4 - 7*w**2 + 43*w - 110*w + 25*w**2 + a*w = 0.
2/9, 1
Suppose 0 = -o + 256*o + 70*o - 650. Factor -2/5*d + 2/5*d**3 + 2*d**2 - o.
2*(d - 1)*(d + 1)*(d + 5)/5
Let t = 48 - 73. Let r be (-5)/t + 78/10. Factor x**3 - 3*x**3 - r*x - 8*x**2 - 2*x**3 - 4*x**2.
-4*x*(x + 1)*(x + 2)
Let m(d) = 2*d**2 + 36*d + 14. Let s(k) = k - 1. Let a(z) = -2*m(z) - 28*s(z). What is g in a(g) = 0?
-25, 0
Let q = -502 - -10043/20. Let g(y) be the first derivative of q*y**4 + 0*y**3 + 3 + 0*y - 3/10*y**2. Find b such that g(b) = 0.
-1, 0, 1
Let i be (1 + 0)*(7 - (16 - 9)). Let h(x) be the second derivative of x + 0*x**3 + i + 1/42*x**4 + 0*x**2 - 1/70*x**5. Let h(a) = 0. Calculate a.
0, 1
Let u(v) be the third derivative of v**8/32 - 19*v**7/140 - 13*v**6/80 + 19*v**5/40 + 3*v**4/8 + 542*v**2. What is r in u(r) = 0?
-1, -2/7, 0, 1, 3
Let f(u) be the first derivative of 3*u**4/4 - 20*u**3 + 57*u**2/2 - 231. Factor f(s).
3*s*(s - 19)*(s - 1)
Suppose n = -13*n - 11*n + 2*n. Factor 0*p - 3/2*p**4 + 1/2*p**5 + 0*p**2 + n + p**3.
p**3*(p - 2)*(p - 1)/2
Let h(n) be the first derivative of -17*n**6/60 - 7*n**5/8 - 19*n**4/24 - n**3/12 + 23*n - 32. Let t(p) be the first derivative of h(p). Factor t(r).
-r*(r + 1)**2*(17*r + 1)/2
Let a(v) be the first derivative of -49*v**3 + 63*v**2 - 27*v + 58. Solve a(q) = 0 for q.
3/7
Let 12/5 - 34/5*h - 4/5*h**2 + 42/5*h**3 = 0. Calculate h.
-1, 3/7, 2/3
Let j(o) be the first derivative of -3*o**4 + 3*o**5 - 40 - o**3 + 42 + 2*o**3 - o**6. Factor j(f).
-3*f**2*(f - 1)**2*(2*f - 1)
Let a be (-1)/1 + -2 + 27/9. Let j(o) be the first derivative of 0*o**2 - 1/4*o**4 - 2/5*o**5 + a*o - 1/6*o**6 + 0*o**3 + 2. Factor j(k).
-k**3*(k + 1)**2
Let z(j) be the third derivative of -j**5/12 - 3*j**4/8 + j**3/3 - 158*j**2. Find f such that z(f) = 0.
-2, 1/5
Let b(c) be the second derivative of -15*c**5/4 - 15*c**4/2 - 4*c**3 - 15*c - 2. Factor b(n).
-3*n*(5*n + 2)*(5*n + 4)
Let h(g) = 0*g + 2*g - g + 10. Let c be h(-7). Factor -33*m - c*m**2 + 31*m + m**3 - 2*m**3.
-m*(m + 1)*(m + 2)
Let o be -1 - 2*(-12)/8. Suppose 4*j = o*j + 16. Factor -3*t**3 - t**5 + 2 + j*t**2 + 5*t - 6*t**2 - 4*t**4 - t**3.
-(t - 1)*(t + 1)**3*(t + 2)
Le