 -58 - 23/2*u**4 + 172*u + 161/2*u**3 - 365/2*u**2 - 1/2*u**5 = 0.
-29, 1, 2
Suppose 0*n - n - 10 = -2*p, 4*n - 4*p = -20. Suppose n = -4*f + 3*g + 3, -5*f + 3*g + 9 = g. Factor 21/4*d**f + 33/4*d + 12*d**2 + 3/2.
3*(d + 1)**2*(7*d + 2)/4
Let x(n) = -9*n**4 - 9*n**3 - 58*n**2 - 57*n + 1. Let b(d) = -d**4 - d**3 - 7*d**2 - 7*d. Let z(t) = -51*b(t) + 6*x(t). What is r in z(r) = 0?
-1, 2
Let y(h) = h**3 + 3*h**2 - 2*h + 9. Let u be y(-4). Let r = u + 25. Determine o so that -30*o**2 + r*o**3 + 16*o - 2 - 2*o + 4*o**4 - 12*o**4 = 0.
1/4, 1
Let i(r) be the first derivative of -6*r - 21 - 2*r**3 + 3*r**4 - 15/2*r**2 + 12/5*r**5 + 1/2*r**6. Factor i(a).
3*(a - 1)*(a + 1)**3*(a + 2)
Let c = 19 - 16. Find s such that 8367*s**3 - 37580*s**c + 526*s + 24 - 1498*s - 29836*s**3 + 13122*s**2 = 0.
2/27
Factor -1/6*q**2 + 58/3*q - 1682/3.
-(q - 58)**2/6
Let 8*j**2 - 20*j**2 - 8*j + 49*j**4 - 45*j**4 = 0. Calculate j.
-1, 0, 2
Factor -2/3*a**4 - 1/3*a + 0*a**3 + 1/3*a**5 + 0 + 2/3*a**2.
a*(a - 1)**3*(a + 1)/3
Let u(w) be the second derivative of w**6/1260 + w**5/60 - 2*w**4/21 + 3*w**3/2 - 36*w. Let r(d) be the second derivative of u(d). Factor r(b).
2*(b - 1)*(b + 8)/7
Let l be (-1)/((-3)/15 + 76/(-20)). Let 3/4*m**2 + 0 - l*m**3 + m = 0. Calculate m.
-1, 0, 4
Suppose 30 = 5*l + p, 3*l + 4*p - 1 = -0*l. Solve -14*d**5 + 2*d**5 + 2*d**3 + l*d**5 + 3*d**3 = 0.
-1, 0, 1
Suppose -3*k + 4*k + c = -10, 4*k + 5*c = -40. Let m be ((-9)/(-6))/((-5)/k). Solve m - 3*j**2 + 3*j**2 - j**2 + 1 = 0 for j.
-2, 2
Let u(v) be the first derivative of 3*v**4/16 + 2*v**3 + 15*v**2/2 + 12*v + 38. Factor u(n).
3*(n + 2)**2*(n + 4)/4
Solve 232*t**4 - 64*t - 272*t**2 - 50*t**5 + 62*t**4 - 34*t**4 - 168*t**3 = 0 for t.
-2/5, 0, 2, 4
Let l(f) be the first derivative of f**5/4 - 125*f**4/16 + 315*f**3/4 - 1215*f**2/8 - 3645*f/2 - 74. Solve l(y) = 0 for y.
-2, 9
Let u(h) be the first derivative of -h**4/4 + h**3 - 3*h**2/2 + h + 70. Find o such that u(o) = 0.
1
Suppose 55 = 5*b + 3*u + 2*u, -3*u = -12. Suppose -b*i + 6 = -5*i. Determine l so that -5*l**i + l**2 - 60*l + 17*l**2 + 40 + 12*l**2 = 0.
2
Suppose -17*f = -5*f - 36. Suppose 6*w + 2 = 2*w - 2*z, f*w - 3 = 3*z. Factor w*a**2 - 2/3*a**3 + 0 + 1/3*a**4 + 0*a.
a**3*(a - 2)/3
Let b(n) be the third derivative of 0*n + 1/12*n**3 + 0 + 1/24*n**4 - n**2 + 1/120*n**5. Let b(k) = 0. Calculate k.
-1
Let b(v) = 8*v + 26. Let z be b(-3). Let x(f) be the third derivative of 0 + 1/96*f**4 + 0*f + 1/48*f**3 + f**z + 1/480*f**5. Suppose x(n) = 0. What is n?
-1
Let h(q) = -q**3 + 3*q**2 - 1. Let s be h(2). Let k(l) = -l**3 + 4*l**2 + 13*l - 6. Let x be k(6). Factor 12/5*j**5 - 3/5*j**s + x + 0*j**2 + 9/5*j**4 + 0*j.
3*j**3*(j + 1)*(4*j - 1)/5
Suppose 0 + 0*q + 2/3*q**4 - 22/3*q**3 - 8*q**2 = 0. What is q?
-1, 0, 12
Let l(b) = 6*b - 89. Let h(o) = 18*o - 266. Let g(j) = 3*h(j) - 10*l(j). Let f be g(15). Solve 0*i + 2/7*i**f + 0 = 0 for i.
0
Let f be (-15 - -7) + 15 - 34/5. Factor -6/5 - 1/5*w + f*w**2.
(w - 3)*(w + 2)/5
Let t be -6*(-1)/(60/50). Let j(v) be the second derivative of 1/2*v**2 + 4*v + 1/20*v**t - 1/12*v**4 + 0 - 1/6*v**3. Suppose j(m) = 0. What is m?
-1, 1
Let o(n) be the third derivative of 0 + 0*n**4 + 0*n + 1/15*n**5 + 1/60*n**6 + 5*n**2 - 1/105*n**7 + 0*n**3. Determine x so that o(x) = 0.
-1, 0, 2
Suppose -f + m = -0*f + 6, 0 = -2*f - 3*m + 13. Let b(r) = 14*r**2 - r - 1. Let n be b(f). Factor -2*a - n*a**2 - 10*a + 2*a**2 - 3*a**5 + 6*a**4 + 9*a**3.
-3*a*(a - 2)**2*(a + 1)**2
Let h(b) be the first derivative of 5*b**4/2 - 2*b**3/3 + 9*b**2/2 + 5. Let j(l) = l**3 - l**2 + l. Let c(g) = 3*h(g) - 21*j(g). Let c(o) = 0. Calculate o.
-1, -2/3, 0
Suppose -5*w = x - 1, 2 = 3*w + 3*x - 1. Let t(d) be the second derivative of -2/3*d**3 + 3*d + 1/10*d**5 + 1/6*d**4 + 0 + w*d**2. Factor t(f).
2*f*(f - 1)*(f + 2)
Let x(i) = 7*i - 3 - 10*i**2 + 3. Let w(d) = 9*d**2 - 6*d. Suppose -68 = -8*n - 12. Let u(z) = n*w(z) + 6*x(z). Let u(q) = 0. What is q?
0
Let r(n) be the third derivative of -n**8/168 - 2*n**7/35 - 13*n**6/60 - 2*n**5/5 - n**4/3 + 8*n**2 + 2. Suppose r(f) = 0. What is f?
-2, -1, 0
Let m(v) be the third derivative of v**6/960 - 17*v**5/96 - 3*v**2 - 75*v. Solve m(s) = 0.
0, 85
Let h be 14*(-4 - (-54)/4). Suppose -3*q + 3*q**2 - h*q**3 + 3*q + 136*q**3 = 0. Calculate q.
-1, 0
Suppose -3*s + 196 + 155 = -j, 12 = -4*j. Let m be -8 + s/14 - 16/154. Solve m*y**2 - 2/11 + 0*y = 0 for y.
-1, 1
Solve 50/3 + 5/3*r**3 - 5/3*r - 50/3*r**2 = 0.
-1, 1, 10
Factor 0 + 0*i - 142/5*i**3 - 2/5*i**4 - 28*i**2.
-2*i**2*(i + 1)*(i + 70)/5
Let f(q) be the third derivative of 13*q**2 + 5/6*q**3 + 0 + 1/12*q**5 + 5/12*q**4 + 0*q. Find c, given that f(c) = 0.
-1
Let x(z) be the first derivative of -z**3/21 - 3*z**2/14 + 10*z/7 + 82. Factor x(w).
-(w - 2)*(w + 5)/7
Let f = -2/207 - -247/4140. Let u = 1/4 - f. Factor -u*d**2 - 4/5*d - 3/5.
-(d + 1)*(d + 3)/5
Determine g so that 5/3*g**4 - 7/3*g**3 + 2/3*g**2 + 0*g + 0 = 0.
0, 2/5, 1
Suppose -4*d - n = -2*d - 5, 0 = 3*d - 2*n + 10. Let x(a) be the first derivative of -2 + d*a**3 - 1/2*a**2 + 1/4*a**4 + 0*a. Find r, given that x(r) = 0.
-1, 0, 1
Suppose -p = 4*p - 20. Suppose -9*c = -p*c - 10. Factor -3 + 6*f**2 - f**2 + 9 - c*f**2 + 9*f.
3*(f + 1)*(f + 2)
Let x(y) = -9*y - 169. Let n be x(-19). Let l(d) be the first derivative of 1/6*d**4 - 8/9*d**3 + 0*d + 4/3*d**2 - n. Suppose l(b) = 0. What is b?
0, 2
Solve -8*u**2 + 16*u**3 + 33*u + 36 + 4*u**4 - 49*u - 32*u = 0 for u.
-3, 1
Suppose 0 = 25*b - 30*b + 25. Suppose 0*x = b*x - 15. Determine w, given that -12*w + 84*w**2 + 708 - 135*w**x + 147*w**5 - 708 - 84*w**4 = 0.
-1, 0, 2/7, 1
Suppose 78*g - 132*g = -162. Let y(q) be the second derivative of -2*q + 0 + 0*q**g - 1/66*q**4 + 0*q**2 + 0*q**5 + 1/165*q**6. Factor y(j).
2*j**2*(j - 1)*(j + 1)/11
Let g(z) be the third derivative of z**9/1512 + 13*z**8/840 + 4*z**7/35 + z**6/5 - 13*z**3/6 - 11*z**2. Let v(d) be the first derivative of g(d). Factor v(i).
2*i**2*(i + 1)*(i + 6)**2
Let l(k) = -2*k**2 + 11*k + 96. Let j(r) = r**2 - 6*r - 48. Let a(v) = 15*j(v) + 6*l(v). What is s in a(s) = 0?
-4, 12
Let p(a) be the first derivative of 5*a**4/4 - 70*a**3/3 + 110*a**2 - 200*a + 86. Find m such that p(m) = 0.
2, 10
Let p = 10423/3 + -3474. Factor -p*o**3 + 0 + 1/9*o**5 - 2/9*o**4 + 4/9*o**2 + 4/9*o.
o*(o - 2)**2*(o + 1)**2/9
Let b be 72/4*((-28)/70 - 142/(-330)). Factor -10/11*t**2 - 14/11*t - b - 2/11*t**3.
-2*(t + 1)**2*(t + 3)/11
Suppose 5*n + 5 = 6*n. Factor 4 - 8*f**3 + 32*f**2 - 40*f**2 + 2*f**n + 4*f**4 + 2*f**5 + 4*f.
4*(f - 1)**2*(f + 1)**3
Factor 40 + 40*y**3 + 14*y**2 - 4*y - 28*y**2 - 26*y**2 - 36*y**3.
4*(y - 10)*(y - 1)*(y + 1)
Factor -2/3*d**4 - 16*d**2 - 64/3*d - 32/3 - 16/3*d**3.
-2*(d + 2)**4/3
Let t(x) be the third derivative of x**5/330 - x**4/44 - 70*x**3/33 + 983*x**2. Factor t(q).
2*(q - 10)*(q + 7)/11
Suppose 7 - 22 = -3*g. Suppose 0 = g*m - 2*m. Factor 7*t - 6*t + m*t**2 - t**2.
-t*(t - 1)
Let m(r) be the first derivative of 9*r**5/5 - 33*r**4/4 + 2*r**3 + 24*r**2 - 655. Factor m(j).
3*j*(j - 2)*(j + 1)*(3*j - 8)
Factor -858*j**2 - 4*j**3 - 60*j + 0*j**3 + 890*j**2.
-4*j*(j - 5)*(j - 3)
Let b = 175 - 172. Let v(p) be the second derivative of 3*p + 0 + 3/4*p**4 + 0*p**2 - 1/2*p**b. What is j in v(j) = 0?
0, 1/3
Factor -16/11*c**2 + 34/11*c - 20/11 + 2/11*c**3.
2*(c - 5)*(c - 2)*(c - 1)/11
Let u(g) be the second derivative of 3/4*g**4 - 3/10*g**6 + 0 + 17*g + 33/80*g**5 + 0*g**2 - 1/2*g**3 - 1/8*g**7. Find h such that u(h) = 0.
-2, -1, 0, 2/7, 1
Let f(u) = -u**2 - 17*u - 25. Let s be f(-15). Suppose 5*r = -l + 10, -4*r - 2 = -s*r. Factor -24/7*k + 12/7*k**3 + l + 4*k**2.
4*k*(k + 3)*(3*k - 2)/7
Let v(x) be the first derivative of x**4/3 + 4*x**3/3 + 2*x**2 + 4*x - 6. Let f(t) be the first derivative of v(t). Suppose f(y) = 0. What is y?
-1
Let s(d) be the third derivative of d**5/60 + 11*d**4/4 + 363*d**3/2 + 4*d**2 + 16*d. Solve s(b) = 0.
-33
Let l(n) = n**3 + 5*n**2 + 2*n - 9. Let t be l(-4). Let o be 7/7 - (0 + t). Solve 3/2*d + 3/2*d**4 - 3/2*d**o - 3/2*d**3 + 0 = 0.
-1, 0, 1
Suppose 0 = x + 1 + 5. Let n be 0*x/24 + (-4)/(-5). Let 2/5*w**2 + 2/5 - n*w = 0. Calculate w.
1
Determine j, given that 71*j**2 + 4*j**5 - 10*j**4 - 2*j**3 + j - 10 - 51*j**2 - 3*j**5 = 0.
-1, 1, 10
Let f(m) be th