x so that 0*x - x - 2*x**2 - k*x + 2*x**3 = 0.
-1, 0, 2
Let y(i) be the first derivative of i**5/50 - i**4/10 + 2*i**3/15 + 3. Suppose y(t) = 0. What is t?
0, 2
Let s(d) = 8*d**2 - d - 3. Let x be s(-2). Let w be (-4)/(-8)*(x - 2). Let 2 - 21/2*p**3 - 2*p - w*p**2 = 0. Calculate p.
-1, -2/3, 2/7
Let n(r) = 5*r**3 + 8*r**2 + 2*r - 6. Let m(v) = v**3 + v**2 - 1. Let j(u) = -4*m(u) + n(u). Let t be j(-2). Solve -3*x - x**t + 2*x + 0*x = 0.
-1, 0
Factor 4/19*v + 2/19*v**4 + 10/19*v**2 + 8/19*v**3 + 0.
2*v*(v + 1)**2*(v + 2)/19
Factor 4*o - 4 + 2*o**2 - 4*o**3 + 7/4*o**4 - 1/4*o**5.
-(o - 2)**4*(o + 1)/4
Suppose 22 + 14*w**2 + 4*w + 8*w**3 + 2*w**4 - 22 - 16*w**4 - 12*w**5 = 0. Calculate w.
-1, -2/3, -1/2, 0, 1
Let c(k) be the second derivative of 0 + 0*k**2 + 1/63*k**7 + 1/9*k**3 + 2/9*k**4 + 2*k + 4/45*k**6 + 1/5*k**5. Factor c(o).
2*o*(o + 1)**4/3
Let q be 121/132 - (0 - 1/(-4)). Factor 2/3*m - 10/3*m**2 + q + 2*m**3.
2*(m - 1)**2*(3*m + 1)/3
Let z(n) = 4*n + 1. Let a = -2 + 3. Let x be z(a). Suppose o - 5*o**5 - 3*o - 2*o**2 + 6*o**3 + 2*o**4 + o**x = 0. What is o?
-1, -1/2, 0, 1
Solve -r**4 + 5 + 10*r - 4 + 2*r**3 - 12*r = 0 for r.
-1, 1
Let w(x) = 4*x**2 + 30*x + 14. Let n be w(-7). Factor 0*m**2 + 0 + 1/2*m**5 + n*m**3 + 1/2*m**4 + 0*m.
m**4*(m + 1)/2
Let h(f) be the third derivative of 7*f**6/300 - 37*f**5/150 + 19*f**4/30 - 8*f**3/15 - 32*f**2. Factor h(q).
2*(q - 4)*(q - 1)*(7*q - 2)/5
Let r(z) = -10*z**2 - 20*z + 30. Let x(d) = -5*d**2 - 10*d + 15. Let l(q) = 4*r(q) - 9*x(q). Factor l(b).
5*(b - 1)*(b + 3)
Suppose -3*q + 4 + 8 = 0. Let k(s) be the third derivative of 5/16*s**q + s**2 + 0*s - 3/10*s**5 + 7/48*s**6 - 1/35*s**7 + 0 - 1/6*s**3. Solve k(f) = 0.
1/4, 2/3, 1
Let q = 55 + -491/9. Suppose 0*f - 4/9*f**2 - 2/9*f**5 + q*f**4 + 2/9*f**3 + 0 = 0. What is f?
-1, 0, 1, 2
Suppose -3*t + 5*t - 12 = 0. Factor 2*z**4 + 8 - t*z**2 - 2*z**3 - 2*z**2 + 6*z**3 + 2*z**2 - 8*z.
2*(z - 1)**2*(z + 2)**2
Suppose 3*b = b + 6. Let z be 2/16*1008/63. Factor -4/3*c + 0 - 2/3*c**b + z*c**2.
-2*c*(c - 2)*(c - 1)/3
Let f(a) = a - 1. Let q(r) = -r**2 + 1. Let p(l) = 3*f(l) + 2*q(l). Let j(y) = 2*y**2 - 4*y + 2. Let g(h) = -5*j(h) - 6*p(h). Solve g(i) = 0 for i.
-2, 1
Let g(z) be the second derivative of -z**8/252 - z**7/315 + z**6/90 + z**5/90 + 2*z**2 + 3*z. Let v(x) be the first derivative of g(x). What is s in v(s) = 0?
-1, -1/2, 0, 1
Let c be (2/4)/((-8)/(-32)). Let g(n) be the second derivative of 1/6*n**3 - 1/42*n**7 - n + 1/15*n**6 + 0*n**c - 1/6*n**4 + 0*n**5 + 0. Factor g(u).
-u*(u - 1)**3*(u + 1)
Let f(m) be the second derivative of 7*m**6/480 - m**5/48 - m**4/48 + m**2/2 + 3*m. Let z(c) be the first derivative of f(c). Factor z(l).
l*(l - 1)*(7*l + 2)/4
Factor -4*w**5 + 4*w**4 - 42*w**2 + 42*w**2.
-4*w**4*(w - 1)
Let v(s) = 2*s**4 + 8*s**3 + 6*s**2 - 6*s - 2. Let y(a) = a**5 + a**4 + a**2 + 1. Let k(u) = v(u) - 2*y(u). Factor k(f).
-2*(f - 2)*(f - 1)*(f + 1)**3
Let g(k) be the third derivative of -k**6/24 + k**5/3 - 5*k**4/8 + 16*k**2. Suppose g(j) = 0. What is j?
0, 1, 3
Let p(d) be the second derivative of -1/6*d**4 + 0 - 2*d + 4/3*d**3 - 4*d**2. Factor p(a).
-2*(a - 2)**2
Let u(s) be the first derivative of 2*s**5/55 + 3*s**4/22 + 4*s**3/33 + 1. Find n, given that u(n) = 0.
-2, -1, 0
Let q(o) be the first derivative of -3*o**4/16 + o**3/4 + 3*o**2/4 - 38. Factor q(j).
-3*j*(j - 2)*(j + 1)/4
Let p be (10/4 + -2)/((-100)/(-35)). Let d(v) be the third derivative of -v**3 - 7/8*v**4 + p*v**6 + 0*v + 1/10*v**5 + 2*v**2 + 0. Let d(n) = 0. What is n?
-1, -2/7, 1
Factor -49 - 4*j**2 + 2*j**3 + 49 + 2*j**4.
2*j**2*(j - 1)*(j + 2)
Let g(a) be the third derivative of -a**7/1050 - a**6/600 + 6*a**2. Let g(i) = 0. Calculate i.
-1, 0
Let w(v) be the second derivative of -v + 3/4*v**5 + 3/10*v**6 + 1/6*v**3 + 0*v**2 + 0 + 7/12*v**4. Factor w(t).
t*(t + 1)*(3*t + 1)**2
Let r(t) be the third derivative of -5*t**6/48 - 13*t**5/24 + 29*t**4/48 - t**3/4 - 9*t**2. Determine z so that r(z) = 0.
-3, 1/5
Suppose 0 = -c + 2 + 4. Let n be (1 - 4/c)*1. Suppose 1/3*o**5 + 0 - 1/3*o**4 - n*o**3 + 1/3*o**2 + 0*o = 0. What is o?
-1, 0, 1
Let f(d) be the first derivative of -d**5/15 - d**4/4 - d**3/9 + d**2/2 + 2*d/3 - 5. Factor f(s).
-(s - 1)*(s + 1)**2*(s + 2)/3
Let u(n) be the second derivative of n**4/72 - n**3/12 + n**2/6 - n. Solve u(z) = 0.
1, 2
Let g(j) = 3*j - 10. Let d be g(4). Let -d - 1/2*c**3 + 3/2*c**2 + 0*c = 0. What is c?
-1, 2
Let v(b) be the first derivative of b**5/15 + 7*b**4/24 - b**3/3 + 3*b**2/2 + 6. Let i(u) be the second derivative of v(u). Factor i(n).
(n + 2)*(4*n - 1)
Let y(l) = -3*l**2 + 15*l - 12. Let d(x) = -x**2 + 7*x - 6. Let f(g) = 9*d(g) - 4*y(g). Suppose f(u) = 0. What is u?
-2, 1
Let s(f) be the third derivative of 0 - 1/24*f**4 - 1/336*f**8 + f**2 + 0*f + 2/105*f**7 + 0*f**3 + 1/15*f**5 - 1/20*f**6. Factor s(n).
-n*(n - 1)**4
Let f(j) be the first derivative of -j**6/60 - j**5/10 - j**4/6 - j**2 - 3. Let r(l) be the second derivative of f(l). Solve r(d) = 0 for d.
-2, -1, 0
Suppose -4*f - v + 70 = 0, -3*f - 12 = -5*v - 76. Let d be (2/f)/((-7)/(-21)). Factor -d*z**2 - 2/3*z - 1/3.
-(z + 1)**2/3
Suppose s - i - 171 = 0, 4*i = 4*s + s - 852. Let b = 1516/9 - s. Solve 2/9*c + 2/9*c**2 - b = 0 for c.
-2, 1
Let u(v) be the third derivative of 11*v**7/1575 + v**6/45 + 7*v**5/450 - v**4/90 + v**2 - 10. Factor u(q).
2*q*(q + 1)**2*(11*q - 2)/15
Let d be ((-4)/(-18))/(-1) - (-196)/126. Let r = 11/7 + -43/63. Factor 0 + 2/9*o**5 + d*o**3 + 8/9*o**2 + r*o**4 + 2/9*o.
2*o*(o + 1)**4/9
Let i = -4/69 - -77/138. Let n(j) be the first derivative of 0*j + 2 + i*j**4 + 0*j**2 + 2/3*j**3. Let n(p) = 0. What is p?
-1, 0
Let x(n) = -9*n**4 - 3*n**3 + n**2 - 5. Let f(w) = 4*w**4 + 2*w**3 + 2. Suppose 2*c = 4*t + 18, -c + 6*c = 25. Let g(s) = t*x(s) - 5*f(s). Solve g(m) = 0 for m.
-1, 0
Let x be (-3)/7 - (-558)/567. Let q = 55/18 - x. Factor q*p + 3/2*p**2 + 1.
(p + 1)*(3*p + 2)/2
Let q(h) = h - 1. Let c be q(3). Factor -f**4 - 6*f**c + 0*f**2 + 4*f**3 - 1 + 4*f - f**4 + f**4.
-(f - 1)**4
Let y(r) = 3*r**2 + 30*r - 48. Let q(w) be the second derivative of -w**4/12 - w**3/6 + 4*w. Let h(j) = -6*q(j) - y(j). What is i in h(i) = 0?
4
Suppose 0*x + 0*x**3 + 1/3 - 2/3*x**2 + 1/3*x**4 = 0. What is x?
-1, 1
Let w(d) be the second derivative of -d**5/270 + d**4/36 - 2*d**3/27 - d**2/2 - 2*d. Let h(k) be the first derivative of w(k). Factor h(z).
-2*(z - 2)*(z - 1)/9
Let a be (-21)/15 + (-4 - 1) + 8. What is i in 14/5*i + a*i**2 - 4/5 = 0?
-2, 1/4
Let y(i) = -i - 8. Let d be y(-11). Factor -2*j + 0*j**3 - j**3 - 1 + j**2 + d*j.
-(j - 1)**2*(j + 1)
Let f(l) = -2*l - 15. Let k be f(-9). Suppose -8/3*c - 2/9*c**k + 16/9 + 4/3*c**2 = 0. Calculate c.
2
Let b(z) = -6*z + 2. Let t be b(0). Suppose -2/3*o**t - 4/3*o + 0 = 0. Calculate o.
-2, 0
Suppose -2*t - 5*t = -147. Let p = -16 + t. Find i, given that 0*i + 1/3*i**4 + 4/3*i**3 - 1/3*i**2 - 4/3*i**p + 0 = 0.
-1, 0, 1/4, 1
Let y(z) = -z**3 + 6*z**2 + 8*z - 5. Suppose 2*n + 12 = 26. Let i be y(n). Suppose -r - 7/2*r**i + 0 + 2*r**3 = 0. What is r?
-1/4, 0, 2
Suppose 10/3*u + 58/3*u**4 + 74/3*u**3 + 14*u**2 + 4/15 + 28/5*u**5 = 0. What is u?
-1, -2/7, -1/6
Suppose -2*k - 5*w - 25 = -0*w, 5*w + 25 = 2*k. Solve k - 2/3*t**2 - 2/3*t = 0 for t.
-1, 0
Let d = -49 + 51. Let p = 33/26 + 16/13. What is r in 1/2*r**4 - 2*r**3 - r + p*r**d + 0 = 0?
0, 1, 2
Let v(t) = -t**3 - t**2 + t. Let w(r) = -r**2 - r + 1. Let y(i) = -5*i**3 - 10*i**2 + i + 4. Let s(a) = 4*w(a) - y(a). Let j(b) = s(b) + 6*v(b). Factor j(o).
-o*(o - 1)*(o + 1)
Let x(j) be the second derivative of -j**6/30 - 3*j**5/10 - 13*j**4/12 - 2*j**3 - 2*j**2 + 15*j. Determine u so that x(u) = 0.
-2, -1
Let l(a) be the third derivative of -a**9/8640 + a**8/5376 + a**7/5040 + a**4/8 - 2*a**2. Let x(w) be the second derivative of l(w). Factor x(i).
-i**2*(i - 1)*(7*i + 2)/4
Let t be -4 - (2 - 0)*1. Let s be ((-8)/(-18))/((-4)/t). Factor 2/3 + 0*u + s*u**4 - 4/3*u**2 + 0*u**3.
2*(u - 1)**2*(u + 1)**2/3
Let b be (-28)/6*12/(-16)*1. Let r = 2 + -1. Suppose r + 9/2*g + b*g**2 = 0. Calculate g.
-1, -2/7
Let u = -74 + 149/2. Suppose -5*r + 7 = -3. Find x such that -1/4*x + 0 - u*x**r - 1/4*x**3 = 0.
-1, 0
Factor -2/3*f**2 - 10/9*f + 2/9*f**3 - 4/9 + 2/9*f**4.
2*(f - 2)*(f + 1)**3/