2, -1
Let w = 19/106 - 2/159. Find c, given that -1/6*c - 1/6*c**4 - 1/3 + 1/2*c**2 + w*c**3 = 0.
-1, 1, 2
Let m be ((-8)/(-10))/(4/2). Let r(k) be the first derivative of 0*k**3 + 0*k**2 + 1/4*k**4 + 0*k - m*k**5 - 2 + 1/6*k**6. Factor r(l).
l**3*(l - 1)**2
Let j(c) be the third derivative of 4913*c**7/665 - 1156*c**6/285 - 476*c**5/95 - 32*c**4/19 - 16*c**3/57 + 26*c**2. What is o in j(o) = 0?
-2/17, 2/3
Let y(d) be the third derivative of 2*d**2 + 1/12*d**4 + 0 + 0*d + 1/30*d**5 + 0*d**3 - 1/60*d**6 - 1/105*d**7. Suppose y(m) = 0. Calculate m.
-1, 0, 1
Let t(u) = u. Let p be t(4). Let m(w) be the first derivative of 4/5*w**5 - 2 + 0*w + 0*w**2 + 1/3*w**6 + 1/2*w**p + 0*w**3. Solve m(c) = 0.
-1, 0
Let c(g) = 5*g**5 + 10*g**3 - 3*g - 4. Let p(u) = 6*u**5 + u**4 + 11*u**3 + u**2 - 4*u - 5. Let o(t) = 5*c(t) - 4*p(t). Factor o(b).
b*(b - 1)**4
Let p = 17 - 12. Suppose p*a + 2 = 4*a + 5*c, 0 = 3*a + c - 10. Suppose 4 + 4*n**2 - 4 + 2*n**a = 0. Calculate n.
-2, 0
Factor 15*h**4 + 54*h**3 - 15*h**3 - 14*h + 12*h**2 + 2*h.
3*h*(h + 1)*(h + 2)*(5*h - 2)
Let y(i) be the first derivative of -i**3/7 - 9*i**2/14 - 6*i/7 - 11. Factor y(x).
-3*(x + 1)*(x + 2)/7
Let q(c) = -8*c**4 - 4*c**3 - 8*c**2 - 6*c. Let f(o) = o**4 + o**2 + o. Let s = -28 + 27. Let p(l) = s*q(l) - 6*f(l). Let p(w) = 0. Calculate w.
-1, 0
Let k(u) = -41*u**4 + 4*u**2 - 5*u - 5. Let o(l) = 21*l**4 - 2*l**2 + 3*l + 3. Let s(m) = 3*k(m) + 5*o(m). Find x, given that s(x) = 0.
-1/3, 0, 1/3
Let j(p) = p**2 - 14*p - 19. Let d be j(16). Let v be (-2)/d + 114/65. Let 2/5*n**2 + v + 8/5*n = 0. Calculate n.
-2
Let p(i) be the third derivative of i**9/3024 + i**8/840 + i**7/840 - i**3/2 - 2*i**2. Let v(u) be the first derivative of p(u). Find w such that v(w) = 0.
-1, 0
Let y(z) be the second derivative of z**8/6048 + z**7/945 + z**6/360 + z**5/270 + z**4/12 + z. Let t(p) be the third derivative of y(p). Factor t(g).
2*(g + 1)**2*(5*g + 2)/9
Let l(h) be the first derivative of h**4/10 + 2*h**3/5 + 11. Factor l(p).
2*p**2*(p + 3)/5
Suppose -13 = -j - 11. Let n(y) be the first derivative of -2 + 1/2*y + y**3 - y**j + 1/10*y**5 - 1/2*y**4. Factor n(b).
(b - 1)**4/2
Suppose 6*b - 3*b = -2*l, -3*b + 4*l + 18 = 0. Let g(n) be the first derivative of b + 1/6*n**2 + 2/3*n - 1/9*n**3. Factor g(c).
-(c - 2)*(c + 1)/3
Let k(n) = -3*n**3 - 7*n**2 + 7*n - 1. Let s(t) = -t**3 - t + 1. Let q(r) = k(r) - 4*s(r). Find j, given that q(j) = 0.
1, 5
Factor 2/5*y**5 + 2/5*y + 0 - 8/5*y**2 + 12/5*y**3 - 8/5*y**4.
2*y*(y - 1)**4/5
Suppose 4*k - 16 = -0*k. Let -2 - 4*f - k*f + 2*f**2 + 6*f - 2 = 0. Calculate f.
-1, 2
Let s(a) be the second derivative of 1/27*a**4 + 0 - 3*a - 1/90*a**5 + 0*a**2 - 1/27*a**3. Determine t, given that s(t) = 0.
0, 1
Factor -543*g**2 - 183*g**3 - 708*g**2 - 6900*g - 6*g**4 - 150*g**2 - 489*g**2 - 3000.
-3*(g + 10)**3*(2*g + 1)
Let u(h) be the third derivative of -h**7/4200 + h**6/1800 + h**3/6 + 2*h**2. Let x(l) be the first derivative of u(l). Solve x(n) = 0.
0, 1
Let p(l) be the third derivative of l**7/35 - l**6/40 + 19*l**2. Suppose p(d) = 0. Calculate d.
0, 1/2
Factor -6*b**4 + 0*b**4 + 3*b**3 - 8*b**5 + 6*b**5 - 9*b**3 - 2*b**2.
-2*b**2*(b + 1)**3
Let g(l) be the second derivative of l**5/100 - l**4/12 + 7*l**3/30 - 3*l**2/10 + 10*l. Suppose g(v) = 0. What is v?
1, 3
Let x(t) be the first derivative of -32*t**6/9 + 128*t**5/15 - 5*t**4 - 8*t**3/9 + 2*t**2/3 - 7. Let x(l) = 0. Calculate l.
-1/4, 0, 1/4, 1
Let o(l) be the third derivative of l**5/30 + l**4/12 + 2*l**3/3 - 6*l**2. Let t(x) = 8*x**2 + 7*x + 17. Let h(p) = -9*o(p) + 2*t(p). Factor h(i).
-2*(i + 1)**2
Find o such that 0*o + 2/9*o**4 + 4/9*o**2 + 0 + 2/3*o**3 = 0.
-2, -1, 0
Let z = -7 + 11. Suppose 2*k = -0*s - s + 13, -11 = -z*k + s. Find v such that -10*v**2 - 3*v + 4*v**3 + 8*v**k + 2*v**4 - v = 0.
-1, -2/5, 0, 1
Suppose 6*q - 2*q = 5*k + 37, 4*q = -5*k - 13. Let x(u) = -u**2 + 13. Let b be x(q). Suppose 1/4*t**5 + 1/4*t**2 + 0 + 0*t - 1/4*t**3 - 1/4*t**b = 0. What is t?
-1, 0, 1
Let h(c) = -3*c**2 + 9*c - 1. Let s(v) be the second derivative of -v**2/2 + 2*v. Let x(p) = -h(p) - 5*s(p). Find f, given that x(f) = 0.
1, 2
Let a = -175 + 353/2. Factor -27/2*s**2 + a*s**3 + 81/2*s - 81/2.
3*(s - 3)**3/2
Let n(v) = 9*v**4 - 6*v**3 - 19*v**2 + 4*v + 4. Let g(a) = 8*a**4 - 7*a**3 - 18*a**2 + 3*a + 3. Let r(h) = -4*g(h) + 3*n(h). Factor r(z).
-5*z**2*(z - 3)*(z + 1)
Let y = 1 + -1. Let s = -27 - -83/3. Factor 0*n + s*n**2 + y.
2*n**2/3
Let u = -390 - -1952/5. Factor -u*f**2 - 4/5*f + 2/5*f**3 + 0.
2*f*(f - 2)*(f + 1)/5
Determine n, given that 1/4*n**3 + 1/4*n**2 - 1/4*n**5 + 0*n + 0 - 1/4*n**4 = 0.
-1, 0, 1
Factor 0 - 6*f - 4 + f**2 - 2*f**2 - f**2.
-2*(f + 1)*(f + 2)
Let l be (-87)/29 - 21/(-5). Factor 3/5*d**3 + 3/5*d**4 - 9/5*d**2 - 3*d - l.
3*(d - 2)*(d + 1)**3/5
Let n = 61/42 + 3/14. Let 2/3 + 4/3*w**2 + n*w + 1/3*w**3 = 0. What is w?
-2, -1
What is l in 0 + 1/10*l**2 - 1/10*l**3 + 1/5*l = 0?
-1, 0, 2
Let l(c) = -3*c**2 + 18*c + 21. Let j(t) = t + 1. Let d(w) = -12*j(w) + l(w). Suppose d(k) = 0. Calculate k.
-1, 3
Let u be (-25)/(-21) + (-13)/(-91). Solve -u + 26/3*r - 40/3*r**2 = 0.
1/4, 2/5
Determine w, given that 43/7*w**2 + 16/7*w - 144/7*w**5 - 264/7*w**4 - 4/7 - 97/7*w**3 = 0.
-1, -2/3, 1/4
Let m(q) be the second derivative of 1/9*q**3 - 1/18*q**4 - 3*q + 0*q**2 + 0. Factor m(i).
-2*i*(i - 1)/3
Let w(y) be the first derivative of y**5/3 + 11*y**4/6 + 11*y**3/3 + 10*y**2/3 + 4*y/3 - 14. Find r, given that w(r) = 0.
-2, -1, -2/5
Factor 2*t**3 + 6*t**4 - 18*t**2 + 18 + 5*t**3 - 10 - 3*t**3.
2*(t - 1)**2*(t + 2)*(3*t + 2)
Factor 12*n**2 + 8*n**3 + 270 - 4*n**4 - 270.
-4*n**2*(n - 3)*(n + 1)
Suppose j - 8 = -3*j. Factor k**4 + 6 - k**3 - 3*k - 3*k**j - 4 + k + 3*k.
(k - 2)*(k - 1)*(k + 1)**2
Let x = -17 - -24. Factor -1 + 3*v**2 + 3*v - 4*v - 6*v**3 + x*v**3 - 2*v**2.
(v - 1)*(v + 1)**2
Let f(b) = 3*b**3 - 5*b**2 + 4*b + 4. Let s(o) = -2*o**2 + 0*o**2 + 3*o**2 - 1 + 0 - o - o**3. Let u(i) = f(i) + 4*s(i). Factor u(r).
-r**2*(r + 1)
Let o(t) be the third derivative of -t**8/252 + 4*t**7/315 + t**6/90 - 2*t**5/45 - 2*t**2. Let o(c) = 0. What is c?
-1, 0, 1, 2
Let u be 1*((-285)/(-120) - 6/16). Solve 0 - 2/9*s**u + 0*s = 0 for s.
0
Let i = 1759/2 + -879. Determine n so that i*n**2 - 1/6*n - 1/2 + 1/6*n**3 = 0.
-3, -1, 1
Suppose 18*l - 5 + 5 = 0. Determine z so that 0 - 2/3*z**3 - 2/3*z**2 + l*z = 0.
-1, 0
Let w(d) be the second derivative of -d**6/30 - 3*d**5/20 - d**4/4 - d**3/6 - d. Suppose w(g) = 0. Calculate g.
-1, 0
Let w be 1/2 - (-28)/8. Determine y, given that 3*y + 2*y**2 - 3*y**2 + 2 - w*y = 0.
-2, 1
Suppose -8 = -5*d + 2. Factor j**4 + j**5 + 3*j**3 + 0*j**4 - 4*j**3 - j**d.
j**2*(j - 1)*(j + 1)**2
Factor z**2 - 2*z**2 + 0*z**2 - 2*z.
-z*(z + 2)
Let a(c) be the first derivative of -2/3*c**3 + 1/9*c**6 + 1/6*c**4 - 2/3*c**2 + 2/5*c**5 + 0*c - 5. What is y in a(y) = 0?
-2, -1, 0, 1
Let h = -4932/7 + 705. Suppose h*l**5 + 9/7*l**4 + 0*l + 0 + 6/7*l**3 + 0*l**2 = 0. Calculate l.
-2, -1, 0
Factor 3*d**3 + 44 - 50 - 4*d**2 - 15*d - 7*d**2 + 3*d**4 + 2*d**2.
3*(d - 2)*(d + 1)**3
Determine o so that 0*o**2 + 0*o - 4/13*o**3 + 0 - 2/13*o**4 = 0.
-2, 0
Let k(g) be the first derivative of -4 - 2/9*g**3 - 8/3*g - 4/3*g**2. Factor k(o).
-2*(o + 2)**2/3
Suppose -4*k + 31 - 7 = 0. Let j be 12/7 + (-4)/(-14). Factor k*g**j + 2*g + 6*g**3 - g**2 - 2 + 5*g**2.
2*(g + 1)**2*(3*g - 1)
Find n such that 0*n + 3*n**3 - 3/5*n**4 - 12/5*n**2 + 0 = 0.
0, 1, 4
Factor 0 - 60*s + 20*s**2 - 36 - 11*s**2 - 2*s**3 + 14*s**2.
-(s - 6)**2*(2*s + 1)
Suppose 0 = -4*j + k + 3, -6*j - k - 3 = -3*j. Suppose 0*l**4 - 2/7*l**3 + 2/7*l**5 + 0*l + 0 + j*l**2 = 0. What is l?
-1, 0, 1
Suppose -h + 8*a + 6 = 6*a, 4*h - 14 = -2*a. Suppose 0*w + 2/5*w**3 + 4/5*w**2 + 0 - 8/5*w**h - 6/5*w**5 = 0. What is w?
-1, 0, 2/3
Let v(q) be the second derivative of -q**5/50 + q**4/15 - 3*q. Factor v(p).
-2*p**2*(p - 2)/5
Determine j so that 22/5*j**2 + 0 - 16/5*j**3 - 8/5*j**4 - 6/5*j = 0.
-3, 0, 1/2
Suppose -5*g + 2*y = 8, 2*g - g = -y + 4. Let t(v) be the second derivative of 0*v**3 - 3*v + 1/30*v**5 + 0*v**2 + 1/90*v**6 + 1/36*v**4 + g. Factor t(z).
z**2*(z + 1)**2/3
Factor 8*p + 16/3 + 3*p**2.
(3*p + 4)**2/3
Let d(z) = -2*z + 2. Let n be d(-1). Suppose 36*k**4 - 13*k*