5*n - 1)/4
Let t(p) = 4*p**3 + 72*p**2 - 732*p + 2656. Let f(n) = 3*n**3 + 71*n**2 - 731*n + 2657. Let r(c) = 6*f(c) - 5*t(c). Solve r(s) = 0 for s.
11
Let x(t) be the second derivative of t**4/30 - 12*t**3/5 + 7*t**2 - 286*t. Let x(h) = 0. Calculate h.
1, 35
Let k(n) be the second derivative of n**5/60 - 7*n**4/36 + 11*n**3/18 - 5*n**2/6 - 3*n - 66. Find p, given that k(p) = 0.
1, 5
Let n(a) be the first derivative of 4*a**5/15 - 4*a**4/3 - 44*a**3/9 - 4*a**2 + 73. Factor n(r).
4*r*(r - 6)*(r + 1)**2/3
Let i = -66 + 68. Find x such that -2*x**5 + 36 - i*x**5 - 28*x**4 - 7*x**3 - 34*x**3 - 8*x**2 + 60*x - 15*x**3 = 0.
-3, -1, 1
Let l(w) be the second derivative of w**7/315 - 4*w**6/225 + w**5/50 + 2*w**4/45 - 4*w**3/45 - w - 343. Solve l(q) = 0 for q.
-1, 0, 1, 2
Let q be (-52)/(-90) - ((-15)/270)/(3/12). Factor 2/5*l**2 + 2/5 + q*l.
2*(l + 1)**2/5
Factor -32/15*w**3 - 22/5*w - 8/15 - 48/5*w**2.
-2*(w + 4)*(4*w + 1)**2/15
Let r(q) = 2*q + 4*q - 5 - 7*q**2 + q**2 - q**3. Let m be r(-7). Factor -m - 4*b - 7*b**2 + b**2 + b**2 + 3*b**2.
-2*(b + 1)**2
Let x = -91/54 - 8135/54. Let r = x + 153. Find n such that -r*n**5 + 0*n + 2/3*n**3 + 0*n**4 + 0 + 0*n**2 = 0.
-1, 0, 1
Let j(x) be the first derivative of 7*x**9/1296 + x**8/72 - x**7/840 - x**6/54 + x**5/90 - 6*x**3 + 2. Let s(q) be the third derivative of j(q). Factor s(p).
p*(p + 1)**2*(7*p - 2)**2/3
Let b = 24/59 + 3892/295. Let q = 16 - b. Determine f so that -3*f**2 + q*f**3 + 6/5*f + 0 - 3/5*f**4 = 0.
0, 1, 2
Let o(c) = -26*c**2 - 26*c. Let a be -4 - 1*-2 - 126/(-7). Let k(v) = 5*v**2 + 5*v. Let x(q) = a*k(q) + 3*o(q). Let x(d) = 0. Calculate d.
-1, 0
Let a(z) be the first derivative of -z**3/8 - 33*z**2/16 + 194. Factor a(p).
-3*p*(p + 11)/8
Let t(r) = 5*r**2 - 11*r - 50. Let h(y) = -15*y**2 + 34*y + 150. Let z(u) = 4*h(u) + 11*t(u). Factor z(f).
-5*(f - 5)*(f + 2)
Let u(q) = q**3 + 21*q**2 + 37*q - 15. Let d be u(-19). Find l such that -20*l - 55*l**3 - 6*l**d + l**4 + 70*l**3 = 0.
-1, 0, 2
Let n be 1612/91 - 4/(-14) - 2. Let a be (12/n)/(18/12). Solve a*d + 1/4*d**2 + 1/4 = 0.
-1
Factor -177*g + 148 - 36 + 68 - 3*g**2.
-3*(g - 1)*(g + 60)
Let h(n) = -2*n**2 + 110*n - 747. Let b be h(8). Suppose 1/7*g**b + 3/7*g**4 + 1/7*g**2 + 0*g + 3/7*g**3 + 0 = 0. What is g?
-1, 0
Let c(h) be the second derivative of -h**5/4 + 5*h**3/6 + 16*h + 1. Factor c(f).
-5*f*(f - 1)*(f + 1)
Let h(i) = 5*i**4 - 44*i**3 + 159*i**2 - 186*i - 12. Let t(z) = -10*z**4 + 87*z**3 - 317*z**2 + 373*z + 26. Let n(u) = 13*h(u) + 6*t(u). Solve n(v) = 0.
0, 3, 4
Suppose 234*l - 1634 = -464. What is t in 51/8*t**2 + 3/2 + 5*t + 1/8*t**l + 9/8*t**4 + 31/8*t**3 = 0?
-3, -2, -1
Let b be (4/8 - (6 - 3))/(3/(-6)). Determine t so that -6/7*t**4 + 0*t**2 + 0*t - 2/7*t**b + 0 - 4/7*t**3 = 0.
-2, -1, 0
Let q = -168 - -172. Let n(s) = -s**3 - 4*s**2 + 5*s. Let l be n(-5). Factor 3/2*v**q - 3/2*v**3 + 1/2*v**2 + l + 0*v - 1/2*v**5.
-v**2*(v - 1)**3/2
Let q(v) be the second derivative of -v**7/2205 - v**6/168 + v**5/105 - 7*v**4/4 - 3*v. Let g(i) be the third derivative of q(i). Factor g(x).
-2*(x + 4)*(4*x - 1)/7
Let c = 23 - 18. Suppose -4*v + 18 = c*v. Solve 0 + 0*g + 1/6*g**3 + 0*g**v = 0.
0
Let k(a) = -a**3 - a**2 + 7*a + 4. Let y be k(-6). Determine b, given that -180*b**3 + 14*b + 10*b**2 - y*b**2 - 2 - 43*b = 0.
-2/5, -1/6
Let s(h) be the first derivative of -h**5/330 + h**4/66 + h**3/11 + 5*h**2 - 8. Let b(a) be the second derivative of s(a). Factor b(f).
-2*(f - 3)*(f + 1)/11
Let f(y) be the first derivative of -y**6/4 + 27*y**5/10 - 9*y**4 + 8*y**3 - 524. Determine p so that f(p) = 0.
0, 1, 4
Suppose 5*w + 2*a = 104, -5 = -5*a + 5. Find p, given that -w*p**4 + 12*p**3 + 16*p**4 - 4*p**3 = 0.
0, 2
Let v(c) = -4*c - 46. Let h be v(-12). Find w such that 0*w**3 - 17*w**3 - 17*w**4 - 7*w**2 + 3*w**h - 5*w**5 + w**3 = 0.
-2, -1, -2/5, 0
Suppose -5*i = w + 50, -37*i = 7*w - 34*i + 30. Factor w - 3/8*u**3 - 3/8*u**2 + 0*u.
-3*u**2*(u + 1)/8
Factor -20*j**2 + 12*j**2 - 50 + 25*j - 2*j**2 - 130*j.
-5*(j + 10)*(2*j + 1)
Let q be 12/(-20) + 165/25. Let i(d) be the first derivative of -1/2*d**4 + 5 - 4/5*d**5 + 0*d + 0*d**2 - 1/3*d**q + 0*d**3. Solve i(a) = 0.
-1, 0
Let h = -401 - -1204/3. Let b(a) be the first derivative of -6 + h*a**3 + 0*a**2 - 1/4*a**4 + 0*a. Suppose b(z) = 0. What is z?
0, 1
Suppose -41*m + 40*m + 1 = 0. Let s(u) = 5*u. Let x be s(m). Factor 3*q**3 - 2*q + q**2 + 3*q**3 - x*q**3.
q*(q - 1)*(q + 2)
Suppose -s - 6 = -r + 3*s, 4*r + 2*s - 6 = 0. What is c in 2/9*c - 2/9*c**r + 0 = 0?
0, 1
Let g(q) = 3*q**4 + 9*q**3 - 6*q**2 - 30*q. Let l(a) = a**4 - a**3 - a. Let d(w) = -g(w) + 6*l(w). Factor d(z).
3*z*(z - 4)*(z - 2)*(z + 1)
Let y be (-109)/(-84) - (-375)/(-300). Let d(k) be the third derivative of -4*k**2 + 1/210*k**5 + 0*k + 4/21*k**3 + 0 + y*k**4. Factor d(l).
2*(l + 2)**2/7
Let t = -715/6 - -239/2. Let p(l) be the first derivative of -1/12*l**4 + 1/15*l**5 + 1/36*l**6 - 4 - t*l - 7/12*l**2 - 4/9*l**3. Factor p(f).
(f - 2)*(f + 1)**4/6
Suppose k - 15 = -4*k - 5*m, 5*k = 2*m + 15. Factor -4*a - 7*a + k*a**2 - 2*a + 18 - 2*a.
3*(a - 3)*(a - 2)
Let v be (4/(-9))/(62/9 + -7). What is x in -21 - 36*x - 66/7*x**2 - 3/7*x**v + 36/7*x**3 = 0?
-1, 7
Let x(d) = -4*d**3 + d**2 + 2*d. Let u(p) = 17*p**3 + 8*p**2 - 21*p. Let g(r) = -u(r) - 4*x(r). Factor g(j).
-j*(j - 1)*(j + 13)
Let f be (-2)/4 + (-57)/(-76). Let c(b) be the first derivative of b + 1/2*b**2 - f*b**4 - 1 - 1/3*b**3. Determine v so that c(v) = 0.
-1, 1
Solve 134/5*z - 8978/5 - 1/10*z**2 = 0.
134
Let v(l) be the third derivative of 0*l + 1/120*l**6 + 6*l**2 + 0*l**3 - 1/60*l**5 - 1/12*l**4 + 0. Factor v(w).
w*(w - 2)*(w + 1)
Solve 64/5*q + 2/5*q**2 + 512/5 = 0 for q.
-16
Determine n so that -7/5*n**3 + 0 + 12/5*n**2 + 4/5*n = 0.
-2/7, 0, 2
Let o be (3 + 132/(-20))*15/33. Let d = o - -76/33. Factor 2/3*b**3 + d*b**2 + 0 - 2/3*b**4 - 2/3*b**5 + 0*b.
-2*b**2*(b - 1)*(b + 1)**2/3
Suppose -10/7*x**3 + 36/7*x - 9/7 - 17/7*x**2 = 0. What is x?
-3, 3/10, 1
Let k(o) be the first derivative of 2*o**3/15 - 28*o**2/5 + 392*o/5 - 63. Determine i, given that k(i) = 0.
14
Suppose -95*v - 5*r - 24 = -97*v, 0 = -4*v - 2*r. What is c in 12*c + 6 - 9/2*c**3 + 3/2*c**v = 0?
-1, -2/3, 2
Let c be (21/49 - 0) + (3 - 3). Factor -c*m**2 - 3/7 + 6/7*m.
-3*(m - 1)**2/7
Let k(a) = -38*a - 44. Let l be k(-2). Suppose 45*n = l*n. Factor n + 0*g + 3/4*g**2.
3*g**2/4
Let q(b) = -3*b**4 - b**3 + 3*b**2 + b + 4. Let s(x) = -12*x**4 + 17*x**2 + 3*x + 3 + 4 - 5*x**2 - 3*x**3 + 8. Let z(u) = -15*q(u) + 4*s(u). Factor z(t).
-3*t*(t - 1)**2*(t + 1)
Let w(m) = -5*m**2 + 255*m - 215. Let r(l) = -l**2 + 42*l - 36. Let c(s) = -25*r(s) + 4*w(s). Factor c(p).
5*(p - 4)*(p - 2)
Suppose -24*i - 5*q = -28*i + 1, 0 = -5*i + q + 17. Find t, given that i*t + 8/3*t**2 + 3/2 = 0.
-3/4
Let u = 9/10295 - -570271/82360. Let x = u + -49/8. Suppose -14/5*y**3 - 32/5*y**2 - 22/5*y - x = 0. What is y?
-1, -2/7
Let n = 27 - 16. Let p(q) = 0 - 4*q**2 + 13*q - n + 2. Let a(h) = 12*h**2 - 40*h + 28. Let x(t) = 5*a(t) + 16*p(t). Factor x(s).
-4*(s - 1)**2
Let b(p) = 23*p**3 + 18*p**2 - 251*p + 57. Let d(h) = 24*h**3 + 19*h**2 - 253*h + 56. Let q(v) = 4*b(v) - 3*d(v). Solve q(i) = 0 for i.
-4, 1/4, 3
Factor -2/5*i**2 - 64/5 - 1/5*i**3 + 8*i.
-(i - 4)*(i - 2)*(i + 8)/5
Let u(b) = 81*b**3 - 42*b**2 - 1575*b + 996. Let s(j) = -23*j**3 + 12*j**2 + 450*j - 285. Let l(h) = -18*s(h) - 5*u(h). Factor l(g).
3*(g - 5)*(g + 5)*(3*g - 2)
Factor -36*m + 20 + 24*m**2 + 13*m**3 + 28*m**3 - 52 - 13*m**3.
4*(m + 1)**2*(7*m - 8)
Suppose -u + 11 = 3*o, -4*u = 5*o - 254 + 224. What is d in 2*d - 1/2*d**o - 2 = 0?
2
Let p(i) = -i**5 - 3*i**4 + 5*i**3 + 3*i**2 - 4*i. Let z(m) = 2*m**5 + 6*m**4 - 11*m**3 - 6*m**2 + 9*m. Let n(s) = 9*p(s) + 4*z(s). Factor n(d).
-d**2*(d - 1)*(d + 1)*(d + 3)
Determine f, given that 42/25 - 8/5*f**2 - 44/25*f**3 - 2/25*f**4 + 44/25*f = 0.
-21, -1, 1
Let t(s) be the third derivative of 1/2*s**3 + 0 + 11/48*s**4 - 7/24*s**5 - 6*s**2 + 0*s. Factor t(b).
-(5*b - 3)*(7*b + 2)/2
Let s(g) be the first derivative of -2*g**6/5 + 84*g**5/25 - 219*g**4/20 + 84*g**3/5 - 54*g**2/5 + 465. Let s(i) = 0. Calculate i.
0, 3/2, 2
Let x(j) be the first derivative of j**5/35 + 3*j**4/28 - 2*j**2/7 + 57. Find v such that x(v) = 0.
-2, 0, 