, -1, 1
Let m(r) be the third derivative of 0*r - 1/21*r**8 + 1/2*r**4 + 91/180*r**5 + 2/9*r**3 + 4*r**2 + 7/120*r**6 - 52/315*r**7 + 0. Determine u so that m(u) = 0.
-2, -2/3, -1/4, 1
Let o(v) be the third derivative of v**6/1020 + v**5/170 + v**4/68 + v**3/51 + 3*v**2. Let o(a) = 0. Calculate a.
-1
Let k = 65/134 + 1/67. Factor 0 - k*g - 1/4*g**2.
-g*(g + 2)/4
Find x such that -2*x - 4*x + x**3 + 8*x - 3*x**2 = 0.
0, 1, 2
Let d = 100/183 - 13/61. Let u**2 + 1/3 - u - d*u**3 = 0. Calculate u.
1
Solve 0 + 4/5*k**2 - 8/5*k = 0 for k.
0, 2
Let i(o) be the second derivative of 0 - o - 1/9*o**3 - 1/36*o**4 + 0*o**2. Find h, given that i(h) = 0.
-2, 0
Let a(r) be the second derivative of r**6/180 + r**5/45 - r**4/9 - 8*r**3/9 + 2*r**2 + r. Let y(v) be the first derivative of a(v). Solve y(o) = 0.
-2, 2
Suppose -6*r + 80 = -r. Find t such that 11*t**2 - 13*t + t**2 - 14*t - 2*t**3 + 3*t + r = 0.
2
Let p(f) be the first derivative of f**5 + 5*f**4/4 + 17. Determine h, given that p(h) = 0.
-1, 0
Let j(c) = -2*c**2 - 11*c + 8. Let v(r) = 3*r**2 + 12*r - 9. Let t(p) = 6*j(p) + 5*v(p). Factor t(n).
3*(n - 1)**2
Let d(i) be the first derivative of -2*i**5/35 + 3*i**4/14 - 4*i**3/21 - 39. Factor d(s).
-2*s**2*(s - 2)*(s - 1)/7
Suppose -5*c - 1 = 24. Let g be c/(-2 + -3 + 1). Determine q so that -2*q**2 - g*q**3 - 1/4*q**4 + 0 - q = 0.
-2, -1, 0
Let v be (-7)/(-28) + 50/(-8). Let o be (-1)/4 - v/24. Factor 0 - 2/9*m**5 - 2/9*m + 4/9*m**3 + o*m**2 + 0*m**4.
-2*m*(m - 1)**2*(m + 1)**2/9
Suppose b**4 + 107 + 7*b**3 - 107 + 6*b**2 = 0. What is b?
-6, -1, 0
Suppose 2*n + 3*n - 10 = -5*q, -4 = -4*q - 2*n. Solve 2*w**2 - 2*w**4 + 2*w**3 + 0*w**3 - 2*w + q*w**2 = 0 for w.
-1, 0, 1
Suppose 11*q - 10 = 6*q. Let i be q + (-22)/(-10) + -4. Factor 0*f + 1/5 - i*f**2.
-(f - 1)*(f + 1)/5
Let x(j) be the third derivative of 2*j**7/35 + 13*j**6/60 + 4*j**5/15 + j**4/12 - 19*j**2. Factor x(v).
2*v*(v + 1)**2*(6*v + 1)
Factor 4*z**3 - 3*z**4 + 4*z**2 + 2*z**3 + 1 - 2*z**4 - 6*z.
-(z - 1)**2*(z + 1)*(5*z - 1)
Let x(v) be the second derivative of 1/63*v**7 - 1/15*v**5 + 0 + 4/9*v**4 + 2/3*v**2 - 7/9*v**3 - 2/45*v**6 - v. Determine w, given that x(w) = 0.
-2, 1
Let c = 17 - 133. Let y = 583/5 + c. Find n, given that -y*n**2 - 3/5 + 6/5*n = 0.
1
Let k(r) = -r**5 + r**3 - r**2 - r - 1. Let l(u) = -10*u**5 - 8*u**4 + 6*u**3 + 2*u**2 - 2*u - 6. Let a(b) = 6*k(b) - l(b). Factor a(g).
4*g*(g - 1)*(g + 1)**3
Let f(n) be the second derivative of -8/63*n**7 - 1/6*n**2 + 5/36*n**4 - 2*n + 0 - 5/12*n**5 - 4/9*n**6 + 5/18*n**3. Factor f(y).
-(y + 1)**3*(4*y - 1)**2/3
Suppose -3*y + 6*y = 6. Let n(u) be the second derivative of -1/20*u**5 - 4/3*u**3 - 5/12*u**4 + 2*u - 2*u**y + 0. Factor n(i).
-(i + 1)*(i + 2)**2
Let q(c) = 8*c**4 + 4*c**2 + 6. Let h(o) = -o**4 - o**2 - 1. Suppose 0 = -4*z - 0*z + 24. Let i(x) = z*h(x) + q(x). Determine f so that i(f) = 0.
-1, 0, 1
Let h(a) = -4*a - 6 - a**3 + 6*a**2 + 6. Let y be h(5). Solve y*q**2 - 2*q**2 - q**2 = 0 for q.
0
Suppose 4*w - 35 = -3*q, -3*w + w - 10 = -4*q. Suppose 2*t - 2 = -3*z, w*z + 5*t - 2*t = 4. Let 2/5*d - 2/5*d**z - 2/5*d**3 + 2/5 = 0. Calculate d.
-1, 1
Factor 4*f**2 + f + 3*f**2 + 7*f - 5*f**2 + 8.
2*(f + 2)**2
Suppose 4*t = 4*s - 4, -2*t + 7 = 3*s - t. Factor -k**2 + 7 + 2*k**2 + 0 + s - 6*k.
(k - 3)**2
Let x(y) = -5*y**3 - 12*y**2 - 18*y - 8. Let d(q) = 9*q**3 + 24*q**2 + 36*q + 16. Let w(f) = 6*d(f) + 10*x(f). Let w(h) = 0. What is h?
-4, -1
Let f be (0 + 1)/((-2)/(-6)). Let b be 1*1/f*3. Factor r**2 - b + 3 - 3.
(r - 1)*(r + 1)
Let j = -131/882 + 10/49. Let c(v) be the third derivative of 0 + 0*v + j*v**4 - v**2 + 1/9*v**3 + 1/90*v**5. Suppose c(a) = 0. Calculate a.
-1
Let j(l) = l**4 - l**3 + l. Let v(m) = -6*m**4 + 8*m**3 - 2*m**2 - m. Let i(d) = j(d) + v(d). Solve i(h) = 0 for h.
0, 2/5, 1
Let k(l) = -l**2 - 7*l. Let d be k(-7). Suppose 4*h - 5*r + 13 = 0, -3*h + 0*h - 4*r + 29 = d. Find y such that -y + 7/2*y**h + 5/2*y**2 + 0 = 0.
-1, 0, 2/7
Suppose 5*a - 5*j = 30, 5*j - 3 = -2*a + 2. Let b = 165 + -823/5. Factor -2*v - 2*v**4 - 4*v**3 - b*v**a - 2/5 - 4*v**2.
-2*(v + 1)**5/5
Let m(k) be the second derivative of k**7/189 - 2*k**6/135 + k**5/90 + 6*k. Let m(o) = 0. What is o?
0, 1
Let r(p) = 4*p**2 + 2*p + 1. Let v be r(-1). Let f = 0 + 2. Factor 0 - 1/4*l**f - 1/2*l + 3/4*l**v.
l*(l - 1)*(3*l + 2)/4
Suppose -3*w - 2 = -c - 0*c, 0 = -3*c + 15. Let i(r) be the first derivative of 0*r - 1/6*r**6 + 1/4*r**4 + 1/3*r**3 - w - 1/5*r**5 + 0*r**2. Solve i(a) = 0.
-1, 0, 1
Let a(o) be the third derivative of -o**6/600 + 6*o**2. Determine i so that a(i) = 0.
0
Let i(w) be the third derivative of -2*w**5/35 + w**4/42 + 4*w**3/21 + 17*w**2. Find f such that i(f) = 0.
-1/2, 2/3
Let s be (-4 - -5)/(-1*(-4)/8). Let a = 724/5 + -144. Solve -a - 2/5*k**s + 6/5*k = 0 for k.
1, 2
Let a be 1/((-3)/2)*(-26)/234. Let v(z) be the first derivative of -4 - 2/9*z - a*z**3 + 2/9*z**2. Solve v(l) = 0.
1
Solve -10*y - 2*y**3 + 7*y**3 + 217*y**2 - 222*y**2 = 0 for y.
-1, 0, 2
Let v(p) be the second derivative of -p**5/70 + p**4/14 - 2*p**3/21 + 10*p. Factor v(i).
-2*i*(i - 2)*(i - 1)/7
Let p(y) = 3*y**2 - 2*y + 2. Let r(t) be the second derivative of t**4/3 - t**3/2 + 3*t**2/2 + t. Let m(k) = -6*p(k) + 4*r(k). Factor m(q).
-2*q**2
Let i(f) be the first derivative of 7/5*f**3 - 9/25*f**5 - 1/10*f**6 + 3 + 3/20*f**4 - 12/5*f + 0*f**2. Determine d so that i(d) = 0.
-2, -1, 1
Let m = 89/390 - 4/65. Let g(v) be the second derivative of 0 - 1/9*v**3 - m*v**2 - 2*v - 1/36*v**4. Suppose g(j) = 0. Calculate j.
-1
Let y be (-10)/6*(-7)/((-980)/(-24)). Suppose y*n**2 - 2/7*n + 0 = 0. Calculate n.
0, 1
Let a = 9 + -7. Factor -2 + 5*o**3 - 5*o - 8*o**a + 8*o - 2*o**3 + 4*o.
(o - 1)**2*(3*o - 2)
Solve -4*u**2 + 4*u + 3/4*u**4 + 4 - u**3 = 0.
-2, -2/3, 2
Suppose 3*h - 15 + 6 = 0. Find i, given that -39*i + 60*i**2 + 6 - i**3 - h*i**3 - 22*i**3 - i**3 = 0.
2/9, 1
Let b(l) be the second derivative of 1/30*l**5 + 0*l**2 + 0 - 2*l - 1/45*l**6 + 1/18*l**4 + 0*l**3 - 1/63*l**7. Factor b(u).
-2*u**2*(u - 1)*(u + 1)**2/3
Let a(t) = 2*t - 2. Let u be a(7). Let d(r) = r**3 - 13*r**2 + 13*r. Let y be d(u). Factor -3 - y*o + 6*o**3 - 7*o**3 - 3*o - 24*o**2 - 11*o**3.
-3*(o + 1)*(2*o + 1)**2
Let a(c) be the second derivative of -c**5/90 + 5*c**4/54 - 4*c**3/27 + 28*c. Factor a(n).
-2*n*(n - 4)*(n - 1)/9
Let j(p) be the third derivative of 3*p**7/140 + p**6/80 - 23*p**5/120 + 13*p**4/48 - p**3/6 - 12*p**2. Find o, given that j(o) = 0.
-2, 1/3, 1
Find h such that 4/3*h**4 + 20/3*h**3 + 12*h**2 + 28/3*h + 8/3 = 0.
-2, -1
Suppose 1/3 - 8/3*f**2 - 1/2*f - 2/3*f**4 - 5/2*f**3 = 0. What is f?
-2, -1, 1/4
Suppose -3*v + 19 = 4*q, -4*q = 5*v - 6 - 7. Let w(u) = u**2 - 6*u - 7. Let a be w(q). Let -1/2*f**2 + 1/2*f**5 + a - 3/2*f**4 + 0*f + 3/2*f**3 = 0. What is f?
0, 1
Let z(l) be the second derivative of 1/2*l**2 + 0 + 7/80*l**5 + 1/3*l**3 + 4*l - 19/48*l**4. Factor z(a).
(a - 2)*(a - 1)*(7*a + 2)/4
Let d = 9 + -5. Suppose -o**2 + 3*o**2 - 3*o**3 - o**3 + 3*o**4 - o**d = 0. Calculate o.
0, 1
Let l be ((-20)/8 - 0)/(4/(-8)). Let g(h) be the second derivative of 0*h**2 + 1/3*h**3 + 0*h**4 + 3*h - 2/5*h**l + 0. Let g(d) = 0. What is d?
-1/2, 0, 1/2
Let o(r) = -24*r + 1. Let j be o(-1). Suppose k + q + 0*q + 5 = 0, 0 = 4*k + 5*q + j. Find x, given that 1/2*x + k - 1/2*x**2 = 0.
0, 1
Let q(b) be the second derivative of b**5/210 - b**2/2 + 4*b. Let f(h) be the first derivative of q(h). Factor f(n).
2*n**2/7
Suppose 0 = 2*d + 9 - 57. Let o be 6/4 - 28/d. Factor 0 + 2/3*h**2 + 1/3*h + o*h**3.
h*(h + 1)**2/3
Let v(u) be the first derivative of -1/2*u**2 + 0*u + 6 + 2/5*u**5 - 5/4*u**4 + 4/3*u**3. Factor v(w).
w*(w - 1)**2*(2*w - 1)
Let x = -2 + 3. Let g(s) = 2*s**4 - 2*s**3 - 10*s**2 + 10*s + 10. Let r(b) = b**2 - b - 1. Let a(j) = x*g(j) + 10*r(j). Factor a(n).
2*n**3*(n - 1)
Let n(y) = -y**3 - y**2 + 1. Let h(a) = -32*a**3 - 127*a**2 - 65*a + 27. Let f(m) = -h(m) - 3*n(m). Factor f(d).
5*(d + 1)*(d + 3)*(7*d - 2)
Let a(l) = -7*l**3 + 12*l**2 + 7*l. Let o(x) = 15*x**3 - 23*x**2 - 15*x. Let d(v) = 14*a(v) + 6*o(v). Factor d(z).
-2*z*(z - 4)*(4*z + 1)
Suppose 8/11*p**4 + 0 + 6/11*p**3 + 0*p - 2/11*p**2 = 0. Calculate p.
-1, 0, 1/4
Solve 29 - 21*w**3 + 36*w - 5 - 24*w**2 + 18*w**2 + 3*w**5 = 0.