**2 + 15*g. Let f be k(-6). Factor f + 0*d**2 + 1/6*d**3 - 1/6*d.
d*(d - 1)*(d + 1)/6
Let a be 28/(-18)*(-732)/854. Factor 4/3 - 2/3*c**3 - a*c**2 + 2/3*c.
-2*(c - 1)*(c + 1)*(c + 2)/3
Let p = -12 + 23. Suppose 15 = p*v - 6*v. Find x, given that -x + x**2 + 3*x**3 + v*x**4 - 3*x + 4*x + x**5 = 0.
-1, 0
Suppose 24 - 22*l - 4*l**3 - 16*l**2 - 19*l + 62*l - 25*l = 0. Calculate l.
-3, -2, 1
Let t(g) = g**3 + g**2. Let c(j) = -j**3 + j. Let o(k) = 12*k**3 + 8*k**2 - 7*k - 3. Let u(z) = -4*c(z) - o(z). Let x(p) = 5*t(p) + u(p). Factor x(l).
-3*(l - 1)*(l + 1)**2
Suppose -4*w + 1 = a - 27, -3*w = -4*a - 40. Suppose -4*j + w = 4*u, 4*j = u + 14 - 6. Solve -4/3 - j*v - 14/3*v**3 + 8*v**2 = 0.
-2/7, 1
Solve -2*y + 1/3*y**2 - 40/3 = 0.
-4, 10
Let v = 284 - 284. Let f(w) be the first derivative of v*w + 0*w**2 + 7 - 2/5*w**5 + 0*w**3 + 1/2*w**4. Suppose f(u) = 0. Calculate u.
0, 1
Let b be -11 + 0 + -1 + 12. Let 6/13*l**3 - 6/13*l**2 - 2/13*l**4 + 2/13*l + b = 0. Calculate l.
0, 1
Let k(o) be the third derivative of -o**6/120 + 2*o**5/15 + 2*o**4 + 440*o**2. Factor k(w).
-w*(w - 12)*(w + 4)
Let y(l) be the second derivative of 1/4*l**4 + 3/2*l**3 + 3*l**2 + 0 + 3*l. Suppose y(h) = 0. Calculate h.
-2, -1
Let s(r) be the first derivative of 66*r**5/35 + r**4/2 - 26*r**3/7 - r**2 + 12*r/7 - 125. Suppose s(d) = 0. What is d?
-1, -6/11, 1/3, 1
Let h(k) = -k**4 + 2*k**3 + 7*k**2 + 4*k - 4. Let t(i) = i**4 - 2*i**3 - 8*i**2 - 5*i + 5. Let l(p) = -5*h(p) - 4*t(p). Suppose l(b) = 0. What is b?
-1, 0, 3
Suppose 0 = -5*r + 6*r - 4*q - 21, 3 = 3*r + 3*q. Solve -5*d**2 - 70*d + 2*d**5 + r*d**2 + 72*d + 2*d**2 - 4*d**3 - 1 - d**4 = 0 for d.
-1, 1/2, 1
Suppose 0 = 8*w - 0*w - 1136. Let k = 143 - w. Factor 5/2*h - 3/2*h**2 - k.
-(h - 1)*(3*h - 2)/2
Factor -8/5*q + 0 - 1/5*q**2.
-q*(q + 8)/5
Let w(t) = 8*t**2 - 15*t + 3. Let d(v) be the first derivative of 35*v**3 - 195*v**2/2 + 40*v + 6. Let j(q) = 3*d(q) - 40*w(q). Factor j(b).
-5*b*(b - 3)
Let j(v) be the first derivative of 5/6*v**6 + 0*v + 5/3*v**3 - v**5 + 5*v**2 - 15/4*v**4 - 59. Solve j(o) = 0.
-1, 0, 1, 2
Let c(s) = 1. Let k(y) = y**2 + 48*y - 161. Let u(r) = -40*c(r) - 5*k(r). Determine a so that u(a) = 0.
-51, 3
Let t(i) = i**2 + 13*i + 9. Let c(s) be the first derivative of s + 1/2*s**2 + 1/3*s**3 - 13. Let a(d) = 3*c(d) + t(d). Solve a(m) = 0.
-3, -1
Determine m, given that 16/5*m**4 - 702/5*m - 216/5*m**2 - 648/5 + 2/5*m**5 + 12/5*m**3 = 0.
-3, 4
Let r(m) = m**2 + 28*m + 54. Let u be r(-26). Let 2/3*c**3 + 4/3*c + 0 - 2*c**u = 0. What is c?
0, 1, 2
Let b(i) = -6*i**2 + 6*i + 8. Let l(q) be the second derivative of -5*q**4/12 + 7*q**3/6 + 9*q**2/2 + 25*q. Let r(t) = 3*b(t) - 4*l(t). Factor r(c).
2*(c - 6)*(c + 1)
Let a(s) be the second derivative of -s**7/210 - s**6/45 - s**5/30 + 11*s**3/6 + 11*s. Let r(q) be the second derivative of a(q). Factor r(l).
-4*l*(l + 1)**2
Let i(b) be the first derivative of b**6/27 + 64*b**5/45 + 313*b**4/18 + 1852*b**3/27 + 1036*b**2/9 + 784*b/9 - 397. What is s in i(s) = 0?
-14, -2, -1
Let f(a) = 1. Let r(c) be the second derivative of -11/4*c**4 - 2*c + 0 + 1/5*c**5 + 12*c**3 - 10*c**2. Let h(x) = 4*f(x) + r(x). Suppose h(z) = 0. What is z?
1/4, 4
Let t(x) = -x**2 + 6*x + 3. Let n be t(7). Let m be (72/n)/((-9)/12). Let 11*r**4 - m*r**4 + 10*r**4 = 0. Calculate r.
0
Let o(k) be the first derivative of -k**4/2 - 35*k**3/9 - 8*k**2 + 3*k - 54. Let o(x) = 0. What is x?
-3, 1/6
Let r(i) be the second derivative of i**5/10 - i**4/3 + 12*i + 4. Factor r(q).
2*q**2*(q - 2)
Find w such that 52/5 - 54/5*w + 2/5*w**2 = 0.
1, 26
Let s(q) be the third derivative of -q**7/1260 - q**6/18 - 91*q**5/60 - 169*q**4/9 - 2197*q**3/36 - 113*q**2. Find v, given that s(v) = 0.
-13, -1
Let c(b) be the third derivative of -2*b**7/105 + b**6/30 + b**5/15 - b**4/6 - 39*b**2. Solve c(u) = 0.
-1, 0, 1
Let n = -589/2 - -296. Let p(f) be the first derivative of -3/2*f**3 + n*f - 2 + 3/2*f**2. Let p(u) = 0. Calculate u.
-1/3, 1
Let z(r) be the first derivative of -6/55*r**5 + 4 + 15/11*r**2 - 3/22*r**4 + 12/11*r + 6/11*r**3. Determine k so that z(k) = 0.
-1, 2
Let -36*d**2 - 2*d**5 - 2746*d**4 + 2766*d**4 + 4*d**5 + 14*d**3 = 0. What is d?
-9, -2, 0, 1
Let a(g) be the second derivative of 3*g + 0 + 4/3*g**3 - 1/3*g**4 - 2*g**2. Determine i so that a(i) = 0.
1
Find y, given that -3*y + 10*y**3 + 15*y - 2*y**2 - 12*y**3 + 0*y = 0.
-3, 0, 2
Let d(z) = 3*z - 2*z + 1 - 2*z. Let h(o) be the third derivative of -o**5/10 - o**4/4 - 30*o**2. Let u(r) = 4*d(r) + h(r). Suppose u(b) = 0. What is b?
-2, 1/3
Let t(k) be the first derivative of k**6/300 - 2*k**5/75 + k**4/20 - 13*k**2/2 + 15. Let v(b) be the second derivative of t(b). Determine l so that v(l) = 0.
0, 1, 3
Let r(n) be the first derivative of 36*n**2 + 4/3*n**3 + 324*n + 14. Factor r(u).
4*(u + 9)**2
Let c(p) = -9*p**3 - 15*p**2 + 18*p - 6. Let q(n) = n**3 + n**2 - n + 1. Let y = 25 - 31. Let d(h) = y*q(h) - c(h). Solve d(o) = 0.
-4, 0, 1
Let r(j) be the second derivative of -j**8/560 + j**6/40 + j**5/20 - 5*j**3/6 - 18*j. Let l(p) be the second derivative of r(p). Factor l(y).
-3*y*(y - 2)*(y + 1)**2
Let l(m) be the first derivative of -m**6/4 - 3*m**5/10 + 9*m**4/8 + 5*m**3/2 + 3*m**2/2 + 70. Solve l(u) = 0 for u.
-1, 0, 2
Let a = 18 - 17. Let g be 12/5 - 3 - (a - 2). Factor -1/5*j**5 + 3/5*j**3 + 0 + g*j - 1/5*j**4 + j**2.
-j*(j - 2)*(j + 1)**3/5
Let k(a) = 2*a**2 - 11*a + 6. Let i be k(6). Let -9*g**5 + 6 + 280*g**2 - 24*g**4 - i*g**3 + 35*g - 262*g**2 - 14*g = 0. Calculate g.
-1, -2/3, 1
Let w(c) be the first derivative of 1/11*c**2 - 1/22*c**4 + 0*c + 11 + 0*c**3. Factor w(j).
-2*j*(j - 1)*(j + 1)/11
Let t = 18 - 6. Factor -4*z**4 - 18 + 8*z**2 + 8*z**3 - t*z + 2 + 4*z**2 - 4*z.
-4*(z - 2)**2*(z + 1)**2
Suppose 75 = 74*u - 59*u. Let c(v) be the first derivative of 0*v + 1/4*v**3 - 1/12*v**6 + 1/8*v**2 - 3/20*v**u + 1/16*v**4 + 1. Let c(n) = 0. Calculate n.
-1, -1/2, 0, 1
Let l(h) be the third derivative of -h**6/180 - h**5/15 - 11*h**4/36 - 2*h**3/3 - h**2 + 23. Find v, given that l(v) = 0.
-3, -2, -1
Let b(k) = k**2 + 16*k - 11. Let f be b(-17). Let p be (3/f)/((-4)/(-16)). Factor 0 - 4/3*y**p + 1/3*y + y**3.
y*(y - 1)*(3*y - 1)/3
Let p = 968/365 - 33/73. Determine y so that 36/5 - p*y**2 - 1/5*y**3 - 24/5*y = 0.
-6, 1
Let c(t) be the first derivative of 5*t**3/3 + 210*t**2 - 19. Factor c(j).
5*j*(j + 84)
Let q(i) be the second derivative of i**7/70 - i**6/60 - i**5/15 + i**4/12 + i**3/6 - 53*i**2/2 + 22*i. Let p(l) be the first derivative of q(l). Factor p(x).
(x - 1)**2*(x + 1)*(3*x + 1)
Let v = -6084869/1354050 - -31/25075. Let s = 1/135 - v. Solve 3/2*k**5 - 6*k**3 + 3 + 0*k**4 + s*k - 3*k**2 = 0 for k.
-1, 1, 2
Let b(k) be the first derivative of -k**6/2 + 18*k**5/5 - 33*k**4/4 + 6*k**3 - 78. Solve b(l) = 0.
0, 1, 2, 3
Suppose 197*n = 248*n. Find u such that 4/3*u**2 + 2*u - 4/3 - 8/3*u**3 + n*u**4 + 2/3*u**5 = 0.
-2, -1, 1
Let o be ((-21)/(-14) - 0)/15. Let i(a) be the second derivative of o*a**3 - 7*a + 0 + 1/20*a**4 + 0*a**2. Factor i(l).
3*l*(l + 1)/5
Suppose 36*c + 71*c - 670 = -27*c. Let -14/5*p**2 + 7/5*p**4 - 2/5*p**3 + 1/5*p**c + 7/5 + 1/5*p = 0. What is p?
-7, -1, 1
Let h(m) = 5*m**2 + 10*m + 5. Let y(p) = -11*p - 5. Let t(r) = 2*r + 1. Let i(k) = -6*t(k) - y(k). Let v(x) = h(x) + 10*i(x). Factor v(q).
5*(q - 1)*(q + 1)
Let j = -2998 - -2998. Let w(g) be the third derivative of 0*g**3 + 9*g**2 + 1/600*g**6 + 0 - 1/300*g**5 + 0*g**4 + j*g. Factor w(t).
t**2*(t - 1)/5
Suppose a - 4 = u, 0 = -4*a - 0*u - u + 6. Let m be 0 - -6 - (44/17 + -2)*10. Factor -4/17 - m*z + 2/17*z**a.
2*(z - 2)*(z + 1)/17
Let w = -1890 + 1893. Factor 2/11*q**2 + 0*q**w - 2/11*q**4 + 0*q + 0.
-2*q**2*(q - 1)*(q + 1)/11
Let s(w) be the first derivative of -3*w**4/4 - w**3 + 24*w**2 - 60*w - 66. Factor s(r).
-3*(r - 2)**2*(r + 5)
Let u be (2/(-14))/(50/(-12) + 4). Solve -u*r + 2/7*r**2 + 0 = 0 for r.
0, 3
Let d(s) = -22*s - 2. Let q be d(1). Let a = 26 + q. Find f such that -4*f**a + 76 + 3*f**2 - 75 = 0.
-1, 1
Let u(m) be the second derivative of -m**5/20 + m**3/2 - 6*m**2 - 7*m. Let v(l) be the first derivative of u(l). What is j in v(j) = 0?
-1, 1
Suppose -51*l = -57*l + 6. Let n(d) be the first derivative of -1/12*d**4 + 5/9*d**3 - 1/2*d**2 - l - 3*d. What 