
Let f(z) be the first derivative of 0*z**2 + 0*z - 2/35*z**5 + 1/7*z**4 + 4 + 0*z**3. Suppose f(s) = 0. Calculate s.
0, 2
Let h be -1*2 + (7 - 3). Suppose 12 = 5*m + h. Determine v so that 2/7*v**m + 0*v + 0 - 2/7*v**3 = 0.
0, 1
Let j = -31/2 + 16. Let p(y) be the second derivative of -y + j*y**2 + 1/3*y**3 + 1/12*y**4 + 0. Let p(n) = 0. What is n?
-1
Let t(p) be the second derivative of 3/10*p**3 + 0 + 2*p + 3/10*p**2 + 3/20*p**4 + 3/100*p**5. Factor t(f).
3*(f + 1)**3/5
Factor -5*r**4 - 15 + 22*r**2 - 10*r - 3*r**2 + 10*r**3 + r**2.
-5*(r - 3)*(r - 1)*(r + 1)**2
Suppose -7*o**2 - 12*o + 19 + 9*o**2 - 1 = 0. What is o?
3
Let d(w) = -221*w**3 + 221*w**2 + 5*w - 27. Let s(y) = -111*y**3 + 111*y**2 + 3*y - 13. Let l(c) = 3*d(c) - 5*s(c). Find r such that l(r) = 0.
-1/3, 2/3
Let t(n) be the second derivative of n**7/84 + 7*n**6/240 - n**5/15 - n**4/12 + 9*n**2/2 - 6*n. Let x(h) be the first derivative of t(h). Solve x(s) = 0.
-2, -2/5, 0, 1
Let d be (-204)/54 + (-2)/9. Let t = d + 7. What is q in -4*q**3 - 5*q**4 + 6*q**3 + t*q**4 = 0?
0, 1
Factor -3*x**2 + 10*x + 2*x + 0*x + 0*x.
-3*x*(x - 4)
Find q, given that 1/4*q**4 - 4*q - 9/4*q**3 + 0 + 6*q**2 = 0.
0, 1, 4
Let t be 3 + -7 + (12/4 - -4). Let f(q) be the third derivative of -3/20*q**4 + 1/50*q**5 + 0*q + 1/75*q**6 + 0 + 2/15*q**t + 3*q**2. Factor f(y).
2*(y - 1)*(y + 2)*(4*y - 1)/5
Find m, given that 4/13*m**2 + 0*m - 2/13*m**4 + 0*m**3 - 2/13 = 0.
-1, 1
Let x(c) be the first derivative of 5*c**6 + 17*c**5 + 75*c**4/4 + 5*c**3 - 5*c**2/2 + 13. Solve x(i) = 0 for i.
-1, 0, 1/6
Factor 1/3*z**4 + 0 - 1/3*z**2 + 0*z + 1/3*z**3 - 1/3*z**5.
-z**2*(z - 1)**2*(z + 1)/3
Let m(p) be the third derivative of p**8/1008 + p**7/630 - p**6/180 - p**5/90 + p**4/72 + p**3/18 + 2*p**2. Determine y, given that m(y) = 0.
-1, 1
Let r = -1 + 4. Factor -3*t**2 + 0*t**r + t**3 - t + 2*t**2 + t**4.
t*(t - 1)*(t + 1)**2
Let x = 134 + -130. Let m(b) be the third derivative of 0*b**x + 1/240*b**5 + 1/840*b**7 + 0*b + 0*b**3 + 0 + b**2 + 1/240*b**6. Find f, given that m(f) = 0.
-1, 0
Let j = 29 - 25. Factor 2/7*p**j + 2/7*p**3 - 2/7*p + 0 - 2/7*p**2.
2*p*(p - 1)*(p + 1)**2/7
Let v(k) be the third derivative of -k**5/30 - k**4/9 - k**3/9 + 7*k**2. Factor v(z).
-2*(z + 1)*(3*z + 1)/3
Let m(t) be the first derivative of t**5/60 - 3*t**2/2 - 1. Let c(u) be the second derivative of m(u). Solve c(p) = 0 for p.
0
Suppose 4*l + 375 = l + 2*m, 266 = -2*l - 4*m. Let n = l + 385/3. Let 0 - 2/3*y - 2*y**2 - n*y**3 = 0. Calculate y.
-1, -1/2, 0
Let y be (-12)/(-9)*(-8)/(-16). Let f(i) be the first derivative of -2 - 1/9*i**3 + 1/2*i**2 - y*i. Factor f(w).
-(w - 2)*(w - 1)/3
Let y(s) = s - 3. Let m be y(-3). Let w = 9 + m. Determine b, given that 3 + w*b**2 - 2 + b**2 + 4*b = 0.
-1/2
Let n(o) be the third derivative of o**6/660 - o**5/22 + 25*o**4/44 - 125*o**3/33 + 14*o**2. Let n(f) = 0. Calculate f.
5
Solve 41 + 62 + 92*j**2 + 240*j - 3 - 8*j**2 + 8*j**3 = 0 for j.
-5, -1/2
Let h be (16/12)/(88/48). What is m in -2/11*m**3 + 82/11*m**2 - 48/11*m + h + 50/11*m**5 - 90/11*m**4 = 0?
-1, 2/5, 1
Let z(x) be the second derivative of -x**4/6 + x**3/3 + 13*x. Let z(v) = 0. Calculate v.
0, 1
Find t such that 2*t**2 - 12 + 4*t + 12 + 2*t = 0.
-3, 0
Let s(t) be the first derivative of -32/5*t**2 + 81/10*t**4 + 8/5*t + 7 + 6*t**3. Factor s(g).
2*(g + 1)*(9*g - 2)**2/5
Factor 75*v**5 + 12*v + 37*v**3 - 52*v**3 - 210*v**4 + 111*v**3 + 111*v**3 - 84*v**2.
3*v*(v - 1)**2*(5*v - 2)**2
Let s(x) be the second derivative of 2/5*x**6 + 0*x**3 + 0*x**2 - 1/21*x**7 + 4/3*x**4 + 0 - 6/5*x**5 - x. Find m such that s(m) = 0.
0, 2
Let a = -35 - -24. Let t = 15 + a. Factor -u**3 - u**5 - u**4 + 2*u**5 - u**2 + 2*u**t.
u**2*(u - 1)*(u + 1)**2
Let m be -9 + 332/36 + 4/9. Factor -4/3 + 2/3*l**2 - m*l.
2*(l - 2)*(l + 1)/3
Let p be 9/(-2)*(-4)/6. Suppose -6*r**2 - 6*r**2 + 2*r**5 + 3*r + r**5 + 4*r**3 + 14*r**p - 12*r**4 = 0. What is r?
0, 1
Let v be (-2)/(-5) + 68/255. Let u(m) be the first derivative of -2/5*m**5 - 3/2*m**4 - v*m**3 - 1 + 4*m + 3*m**2. Suppose u(k) = 0. Calculate k.
-2, -1, 1
Let r(h) be the first derivative of h**3 + 81*h**2/10 + 6*h - 11. Factor r(u).
3*(u + 5)*(5*u + 2)/5
Let c(t) be the third derivative of -t**5/210 + 2*t**4/21 + 40*t**2. Factor c(o).
-2*o*(o - 8)/7
Let t(v) = v - 1. Let x(h) = 5*h - 6. Let j(i) = -11*t(i) + 2*x(i). Let p(s) = -2*s**2 - 2*s - 8. Let d(m) = 6*j(m) - p(m). Solve d(q) = 0.
1
Find o, given that 3/7*o**3 - 6/7*o**2 + 0 + 3/7*o = 0.
0, 1
Let k = 48 - 46. Let v(p) be the second derivative of 1/7*p**k + 1/70*p**5 - 1/42*p**4 + 0 - 1/21*p**3 + p. Determine h so that v(h) = 0.
-1, 1
Let w = -46 + 46. Factor 0*s + w + 1/4*s**2.
s**2/4
Let j be 2/8 - 231/(-84). Let o(v) be the second derivative of v**2 + 3*v + 0 + 0*v**j - 1/6*v**4. Find k such that o(k) = 0.
-1, 1
Let r(x) be the third derivative of x**10/30240 - x**9/7560 + x**7/1260 - x**6/720 - x**4/24 - x**2. Let y(w) be the second derivative of r(w). Factor y(l).
l*(l - 1)**3*(l + 1)
Let r(c) = -3*c**3 + 7*c**2 + 12*c - 23. Let w(o) = -o**2 - 1. Let t(k) = r(k) + w(k). Let t(h) = 0. Calculate h.
-2, 2
Let q be 5*9/(-60) + 13/12. Factor -v**2 + 2/3 - 1/3*v**3 + 1/3*v + q*v**4.
(v - 2)*(v - 1)*(v + 1)**2/3
Let p(y) = y**3 - 4*y**2 + 3*y - 2. Let s(c) = c**3 - c**2 - 1. Let j(k) = -p(k) + 2*s(k). Find h such that j(h) = 0.
-3, 0, 1
Let s = -158/3 + 53. Determine x so that -1/3*x**3 + s - x + x**2 = 0.
1
Suppose 2*z - 4 = -4*h - 0, -2*h - 4*z = 10. Factor 0*m + 4*m**3 - 2*m**h + 0*m**3 + 8*m**2 + 8*m.
2*m*(m + 2)**2
Let f(v) be the first derivative of v**5/10 - v**4/2 + 2*v**3/3 + 7. Factor f(t).
t**2*(t - 2)**2/2
Factor -4*c**5 + c**5 + 3*c**2 - c**4 + 3*c**3 - 2*c**4 + 0*c**3.
-3*c**2*(c - 1)*(c + 1)**2
Let j = -16 - -10. Let m be (j/(-4))/(6/8). Suppose -5*i**2 + 4*i**2 + m*i**2 - 3*i**2 - 2*i**3 = 0. Calculate i.
-1, 0
Suppose -2*u + 5*c = 11, 2*c + 3*c = 4*u + 7. Find p, given that -p**5 + p**4 - p**3 + u*p**5 + 0*p**2 - p**2 = 0.
-1, 0, 1
Let l(p) = p**3 - 4*p**2 - 4*p - 5. Suppose 2*h - 7 - 3 = 0. Let s be l(h). Suppose g**2 + s*g**2 + 0*g**2 + g**4 - 2*g**3 = 0. What is g?
0, 1
Let g(t) be the second derivative of 0*t**3 + 0*t**2 + 0 + 1/42*t**4 + 3*t. Suppose g(a) = 0. What is a?
0
Let v = -1 + 1. Let q(p) be the second derivative of 0 - 1/20*p**5 - 5/84*p**7 + 0*p**4 - p + 0*p**3 - 7/60*p**6 + v*p**2. Factor q(k).
-k**3*(k + 1)*(5*k + 2)/2
Determine z so that -1 - 4/3*z - 1/3*z**2 = 0.
-3, -1
Let t(i) be the second derivative of 0 + 0*i**3 - 1/21*i**7 + 0*i**5 + 2*i + 0*i**2 + 0*i**4 - 1/30*i**6. Factor t(y).
-y**4*(2*y + 1)
Let m(j) be the first derivative of 0*j**4 - 1 + 1/3*j**3 + 0*j**2 + 1/240*j**5 + 0*j + 1/720*j**6. Let p(u) be the third derivative of m(u). Factor p(y).
y*(y + 1)/2
Let h(n) be the first derivative of -3*n**4 - 8/3*n**3 + 0*n**2 + 0*n + 9. Factor h(j).
-4*j**2*(3*j + 2)
Let z(n) = 76*n**2 - 12*n - 32. Let r(p) = 7*p**2 - p - 3. Let v(h) = -32*r(h) + 3*z(h). Find c, given that v(c) = 0.
0, 1
Let r(u) = 4*u**4 + 2*u**3 - 12*u**2 - 8*u + 18. Let w(y) = -17*y**4 - 8*y**3 + 48*y**2 + 32*y - 73. Let x(h) = -9*r(h) - 2*w(h). Factor x(b).
-2*(b - 2)*(b - 1)*(b + 2)**2
Let m(z) be the third derivative of z**6/120 - z**4/8 + z**3/3 + 2*z**2. Factor m(c).
(c - 1)**2*(c + 2)
Let b be 2 - 2/(-4 - -2). Determine u, given that -8*u**2 - 4*u**3 + 0*u**3 + 3*u**b - 8*u - u**3 = 0.
-2, 0
Let u(q) be the third derivative of -q**6/360 - q**5/30 - q**4/8 + 60*q**2. Factor u(p).
-p*(p + 3)**2/3
Let i(n) be the third derivative of 1/80*n**6 + 4*n**2 - 7/48*n**4 - 1/6*n**3 + 0*n - 1/60*n**5 + 0. Factor i(o).
(o - 2)*(o + 1)*(3*o + 1)/2
Suppose -n + 6 = 2*n. Factor 2 - x**n - x + 2 - 4.
-x*(x + 1)
Let w(k) = 15*k**4 + 295*k**3 - 85*k**2 + 85. Let r(j) = -j**4 - 21*j**3 + 6*j**2 - 6. Let d(p) = -85*r(p) - 6*w(p). Factor d(x).
-5*x**3*(x - 3)
Factor h**2 - 3*h**3 + 2*h**4 - 4*h**2 + 6*h**3 - 2*h.
h*(h - 1)*(h + 2)*(2*h + 1)
Let i(x) = 5*x**2 + 4. Let t be i(-3). Let a be 22/14 + 21/t. Determine f so that -2 + 5/2*f**3 - 1/2*f**a - 4*f - 1/2*f**5 + 1/2*f**4 = 0.
-1, 2
Let g be (-2)/7 + 9/7. Suppose -15 = -4*c + g. Factor -4/3*y - 2/3*y**2 + 4/3*y**3 - 1/3 + y**c.
(y - 1)*(y + 1)**2*(3*y + 1)/3
Let s(o) be the first derivative of -o**5/10 + o**3/3 - o/2 - 5. 