
Let i(x) be the second derivative of -x**5/20 + x**3/6 - x. Suppose i(k) = 0. Calculate k.
-1, 0, 1
Let k = 15 - 9. Let f be k/(-33) + 40/99. Factor f - 4/9*g + 2/9*g**2.
2*(g - 1)**2/9
Let n(a) be the first derivative of 3*a**5/40 + 3*a**4/8 + 3*a**3/4 + 3*a**2/4 + 3*a/8 - 7. Factor n(j).
3*(j + 1)**4/8
Let j(q) be the second derivative of q**4/66 + 2*q**3/11 + 14*q - 1. Find f such that j(f) = 0.
-6, 0
Let n(q) be the third derivative of 1/330*q**5 + 0*q + 1/1155*q**7 + 1/330*q**6 - 7*q**2 + 0*q**3 + 0 + 0*q**4. Suppose n(h) = 0. Calculate h.
-1, 0
Let g(x) be the third derivative of x**7/42 - 4*x**6/45 + x**5/30 + x**4/3 - x**3/6 - 3*x**2. Let n(i) be the first derivative of g(i). Solve n(t) = 0 for t.
-2/5, 1
Let z(g) be the first derivative of 0*g - 1/21*g**6 - 4 + 1/14*g**4 + 0*g**2 - 2/21*g**3 + 2/35*g**5. Find n, given that z(n) = 0.
-1, 0, 1
Determine j, given that -941*j + 3*j**3 - 6*j**2 + 938*j + 6 + 0*j**3 = 0.
-1, 1, 2
Let i(q) be the second derivative of -q**6/120 + 3*q**5/80 - q**4/48 - q**3/8 + q**2/4 + 3*q. Suppose i(p) = 0. What is p?
-1, 1, 2
Suppose -2*f + 5 = -5. Solve 5*k**4 + k**f - 3*k**3 - 6*k**4 + 2*k**2 + 2*k + 0*k**3 - k**2 = 0.
-1, 0, 1, 2
Let h(d) be the third derivative of 3*d**2 - 1/1512*d**8 + 1/945*d**7 + 0*d + 0*d**3 + 0 + 0*d**4 + 0*d**6 + 0*d**5. Factor h(u).
-2*u**4*(u - 1)/9
Let y(m) = -12*m**5 - 40*m**4 - 20*m**3 - 3*m**2 - 3*m - 3. Let h(n) = 13*n**5 + 40*n**4 + 20*n**3 + 2*n**2 + 2*n + 2. Let b(k) = -3*h(k) - 2*y(k). Factor b(z).
-5*z**3*(z + 2)*(3*z + 2)
Let w = 55658/8127 + 10/1161. Let n = w - 130/21. Determine z, given that -z**4 + n - z**2 + z - 7/3*z**3 = 0.
-1, 2/3
Suppose 0 = b, 4*f + 5*b = 3*b. Let s(q) be the second derivative of 1/10*q**5 - 1/3*q**3 + 0 + 0*q**4 + f*q**2 - 2*q. Factor s(i).
2*i*(i - 1)*(i + 1)
Let h = 8 - 6. Suppose -g = -h*g. Suppose g*f + 2/7*f**3 + 0 + 2/7*f**2 = 0. Calculate f.
-1, 0
Let n = 3 + -3. Let s be (-2 + n + 1)*0. Factor 0 + 0*c**2 + s*c - 2/5*c**5 + 0*c**3 + 2/5*c**4.
-2*c**4*(c - 1)/5
Suppose 4*c = 5*c + 3*h, -8 = -c + 5*h. Determine k so that 17*k**2 - 3*k**2 + 11*k**2 + 8 - 7*k**c - 20*k - 7*k**2 + k**4 = 0.
1, 2
Let s(l) be the first derivative of 1 + 2/15*l**3 + 18/5*l + 6/5*l**2. Find q, given that s(q) = 0.
-3
Let x = -11 + 2. Let v = x + 13. Factor g**2 - g**v - 1/4*g + 1/4*g**3 + 0.
-g*(g - 1)*(g + 1)*(4*g - 1)/4
Let d be -3 + (-52)/(-16) + 3/(-12). Factor -1/7*c**4 + 0 - 4/7*c**3 - 4/7*c**2 + d*c.
-c**2*(c + 2)**2/7
Let f(v) = 9*v - 50. Let r be f(6). Let w(u) be the second derivative of 0*u**2 + 1/120*u**6 - 3/80*u**5 + 3*u + 0 + 0*u**3 + 1/24*u**r. Factor w(z).
z**2*(z - 2)*(z - 1)/4
Factor 22/9*d**2 - 40/9*d - 8/9.
2*(d - 2)*(11*d + 2)/9
Let d(u) be the first derivative of 2/5*u + 1 + 11/10*u**2 + 7/20*u**4 + 16/15*u**3. Factor d(q).
(q + 1)**2*(7*q + 2)/5
Suppose -3*s - 5 = i, -2*i - 1 = 2*s + 1. Let x(o) = -o**2 - o - 1. Let u(k) = -7*k**2 - 5*k - 4. Let z(r) = i*u(r) - 6*x(r). Factor z(b).
-(b - 2)*(b + 1)
Let t be (-14)/10 - -2*1. Let y = -267/5 - -54. Let 4/5*r**5 - r**3 + t*r**4 + 1/5*r + 0 - y*r**2 = 0. What is r?
-1, 0, 1/4, 1
Let g be 11/6 + 1/6. Let z(m) be the third derivative of 0 + 0*m**5 + 1/480*m**6 + 0*m + m**g + 0*m**4 + 0*m**3. Determine q, given that z(q) = 0.
0
Suppose -13 = -4*p + 5*x, -2*p + 0*x = -5*x - 9. Suppose -2*r + 8 = u + 3*u, 2*r - 8 = 0. Suppose -1/3*n**p + 0 + u*n = 0. What is n?
0
Let j(b) = 9*b + 4. Let y be j(-3). Let z = -91/4 - y. Suppose 1/4*h**3 - z - 3/4*h**2 + 3/4*h = 0. What is h?
1
Let d = 6 + -3. Let r(j) be the second derivative of -1/15*j**d + 0*j**4 + 0 + 0*j**2 + 1/50*j**5 + 2*j. Factor r(p).
2*p*(p - 1)*(p + 1)/5
Let t = 4 - 8. Let n be ((-10)/t)/1*2. Factor 0 - 2*r**2 + n*r**2 - 1 - 2*r**2.
(r - 1)*(r + 1)
Let h(a) be the first derivative of -a**6/60 + a**5/10 - a**4/4 + a**3/3 - a**2/4 - a - 3. Let x(c) be the first derivative of h(c). What is w in x(w) = 0?
1
Suppose 7*d**3 - 2*d**3 - 8*d**3 - d**3 - 12*d**2 + 16 = 0. What is d?
-2, 1
Factor -8/9*t**2 - 4/9 - 2*t.
-2*(t + 2)*(4*t + 1)/9
Let d(x) = -x**4 - x**3 - x - 1. Let y(m) = 2*m**4 - 3*m**2 + 2*m + 3. Let w(p) = 15*d(p) + 5*y(p). Let w(v) = 0. What is v?
-1, 0
Let h(w) be the second derivative of -1/1080*w**6 + w + 0 - 1/3*w**3 - 1/72*w**4 + 0*w**2 + 1/180*w**5. Let u(l) be the second derivative of h(l). Factor u(i).
-(i - 1)**2/3
Let j(x) = x**2 + x - 1. Suppose 0*z - 5 = 5*z. Let t(m) be the second derivative of m**3/6 + 2*m. Let y(l) = z*j(l) + t(l). Find u such that y(u) = 0.
-1, 1
Let y(q) be the second derivative of 1/2*q**3 + 0 + 0*q**5 + 0*q**4 - 3*q + 1/180*q**6 + 0*q**2. Let s(h) be the second derivative of y(h). Factor s(v).
2*v**2
Suppose 5*i + 2*b = 3*i + 174, 4*b + 372 = 4*i. Let v be 24/(-108) - (-74)/i. Factor -1/5*s**3 + 1/5*s**4 - 2/5 - v*s**2 + s.
(s - 1)**3*(s + 2)/5
Suppose 0*b + 0*b**2 - 2*b**3 - 2*b**2 + 0*b + 4*b = 0. What is b?
-2, 0, 1
Let y(q) be the first derivative of 2*q**2 + 2*q + 2/3*q**3 - 2. Let y(k) = 0. Calculate k.
-1
Factor -605 - 5*r**2 + 110*r + 7*r - 7*r.
-5*(r - 11)**2
What is o in 0 + 5/2*o**2 + 5*o = 0?
-2, 0
Let h(l) = -6*l + 3. Let m be h(4). Let n be ((-4)/6)/(2/m). Factor n - 3 - 2*d**2 - 2.
-2*(d - 1)*(d + 1)
Determine y, given that -13*y**3 + 8*y - 9*y**3 + 8*y**2 + 39*y**3 - 15*y**3 = 0.
-2, 0
Let g(p) = -9*p**4 - 15*p**3 - 15*p**2 - 3*p - 6. Let b(i) = i**4 + i**3 + i**2 + 1. Let o(s) = -6*b(s) - g(s). Factor o(v).
3*v*(v + 1)**3
Let a(v) be the third derivative of 0*v**4 + 0*v**3 + 1/756*v**8 + 1/189*v**7 - 6*v**2 + 1/270*v**5 + 0*v + 0 + 1/135*v**6. Determine m, given that a(m) = 0.
-1, -1/2, 0
Let -12 + 24*x**2 + 30*x**2 + 25*x + 21*x**3 + 3*x**2 - x = 0. What is x?
-2, -1, 2/7
Let c(p) be the second derivative of p**6/75 + 3*p**5/50 + 27*p. Factor c(z).
2*z**3*(z + 3)/5
Let o(u) be the second derivative of u**6/180 - u**5/45 + 3*u**2 - 2*u. Let y(r) be the first derivative of o(r). Factor y(l).
2*l**2*(l - 2)/3
Let a be (-3)/(-2)*14/3. Let m = a + -3. Suppose 0*y**3 + m*y**3 + y**2 - 3*y**3 = 0. What is y?
-1, 0
Let p(v) be the first derivative of v**9/1512 + v**8/840 - v**7/140 - v**6/180 + v**5/30 + 5*v**3/3 - 7. Let n(y) be the third derivative of p(y). Factor n(h).
2*h*(h - 1)**2*(h + 1)*(h + 2)
Suppose 4*o + u + 3 - 17 = 0, 5*u + 14 = o. Factor -1/3*c**5 + 1/3*c**2 - c**3 + 0*c + c**o + 0.
-c**2*(c - 1)**3/3
Let g(s) be the third derivative of -2*s**2 + 0 + 1/18*s**4 + 1/90*s**5 + 0*s + 1/9*s**3. Factor g(q).
2*(q + 1)**2/3
Suppose -3*k + 0*k = -9. Suppose 2*j**5 + 2*j**3 + 0*j**5 - 5*j**3 - j**k + 2*j = 0. Calculate j.
-1, 0, 1
Let v(s) be the third derivative of 0*s**4 + 0*s - 1/6*s**3 - 2*s**2 + 0 + 1/60*s**5. Find o such that v(o) = 0.
-1, 1
Let n(o) = -2*o + 8. Let j be n(10). Let m be (-15)/j + -3 + 2. Factor -1/2*i - m - 1/4*i**2.
-(i + 1)**2/4
Let z(h) be the first derivative of 3/7*h**2 - 5 + 4/7*h + 2/21*h**3. Factor z(j).
2*(j + 1)*(j + 2)/7
Let d be (-3)/(-3) + (-3 - -4). Suppose d*k + 4 = 4*k. Factor 0*h**2 + 3*h**2 - h**2 - k*h**3.
-2*h**2*(h - 1)
Let k = -18 - -20. Suppose 2*u - 3*u - k = -x, 4 = 2*u + 2*x. Factor u*c - 1/4*c**4 + c**3 + 0 - c**2.
-c**2*(c - 2)**2/4
Let i be 408/140 + (-18)/(-63). Find u such that -i*u + 4/5*u**2 + 16/5 = 0.
2
Let j = -2419/5 + 485. Factor 2/5*k**2 - 4/5*k - j.
2*(k - 3)*(k + 1)/5
Let k be 0*(2 + (-12)/8). Let t(m) be the third derivative of -m**2 + 0 + 1/120*m**6 + 0*m**4 + 1/210*m**7 + 0*m**5 + 0*m**3 + k*m. Solve t(q) = 0 for q.
-1, 0
Let f be -1 - 1 - (-3 + 1). Factor 2/11*t**3 + 0 + f*t**2 - 2/11*t.
2*t*(t - 1)*(t + 1)/11
Let h(t) be the first derivative of t**5/90 - t**4/36 - 2*t**3/9 - 3*t**2/2 - 3. Let p(i) be the second derivative of h(i). Determine x, given that p(x) = 0.
-1, 2
Suppose 0 = 6*o - 4*o - 3*t + 6, -2*o = t - 2. What is i in i**2 - 1/2*i**3 + o + 0*i = 0?
0, 2
Let d(p) be the third derivative of -4*p**2 - 7/90*p**5 + 0 + 2/9*p**4 + 0*p - 1/36*p**6 + 4/9*p**3. Determine g, given that d(g) = 0.
-2, -2/5, 1
Suppose -4*u - 2*o + 4 = 0, 0 = 33*u - 34*u + 5*o + 23. Suppose -9/7*a + 6/7*a**2 + 3/7*a**5 - 9/7*a**4 + 3/7 + 6/7*a**u = 0. Calculate a.
-1, 1
Let q(j) be the second derivative of -3/25*j**5 + 1/5*j**2 - 2*j + 0 + 2/5*j**3 - 3/25*j**6 + 4/15*j**4. Determine p, given that q(p) = 0.
-1, -1/3, 1
Suppose -