(n - 1)*(n + 13)/5
Let u(i) be the second derivative of i**7/126 - i**6/30 + i**4/9 - 1348*i. Factor u(y).
y**2*(y - 2)**2*(y + 1)/3
Let k(x) = 7*x**2 - 22*x + 44. Let w be k(11). Let c = 649 - w. Determine v, given that c + 0*v - 1/2*v**2 = 0.
0
Suppose -11*t = -57*t + 138. Let i(w) = 2*w**2 + 6*w + 3. Let m be i(-3). Factor 3/2*b**4 - t*b + m*b**3 - 3/2*b**2 + 0.
3*b*(b - 1)*(b + 1)*(b + 2)/2
Let d(r) be the second derivative of -r**4/12 - 71*r**3/3 - 140*r**2 + 802*r. Solve d(i) = 0 for i.
-140, -2
Let m = -390266 + 390270. What is c in 2*c**2 + 0*c - 2/3*c**m + 0 + 4/3*c**3 = 0?
-1, 0, 3
Suppose -4*j = 2*j - 36. Suppose 0 = -3*f + a + 10, -3*f - 3*a = j - 0. Factor 20*c**f - c**4 - 24*c**2 + 5*c**4.
4*c**2*(c - 1)*(c + 1)
Let -334/3*h**3 + 232/3*h - 32 + 188/3*h**2 - 5*h**5 - 209/3*h**4 = 0. What is h?
-12, -2, -1, 2/5, 2/3
Let t(d) be the third derivative of -d**6/30 - 302*d**5/15 - 11840*d**4/3 - 87616*d**3 - 160*d**2. Factor t(s).
-4*(s + 6)*(s + 148)**2
Factor -1236/7*j + 3/7*j**3 + 1248/7 + 300/7*j**2.
3*(j - 2)**2*(j + 104)/7
Suppose -4 = 4*n + 4*j - 20, -2*j = -3*n + 2. Factor -3 - 2 - 3 + 22*b - 84*b**n + 58*b + 12*b.
-4*(b - 1)*(21*b - 2)
Suppose 0 = 295*j + 279*j - 1096 - 1200. Suppose -104/15*x**2 + 2/3*x**5 + 4/15*x**j - 4/5 - 62/15*x - 4*x**3 = 0. Calculate x.
-1, -2/5, 3
Suppose -6*q - 24 = -5*b, -8*q + 13*q + 20 = -4*b. What is j in -2/3*j**5 - 8/3*j**4 + 10/3*j**3 + b*j + 0*j**2 + 0 = 0?
-5, 0, 1
Let u(l) = 3*l**2 + 892*l - 885. Let h(v) = -24*v**2 - 6246*v + 6195. Let i(k) = -2*h(k) - 15*u(k). Factor i(q).
3*(q - 295)*(q - 1)
Let j(w) = -1 - 3*w + w**2 - 4*w**2 + w**3 + 2*w**2. Let p(y) = -7*y**3 + 37*y**2 - 113*y + 5. Let u(v) = 5*j(v) + p(v). Factor u(o).
-2*o*(o - 8)**2
Let d = 4442 + -4426. Let h(z) be the second derivative of 0*z**4 + 0 + 0*z**5 - 1/180*z**6 + 1/252*z**7 + 0*z**3 + 0*z**2 + d*z. Factor h(j).
j**4*(j - 1)/6
Suppose 0 = -j - 9 + 6. Let h be 1 - (j + 1/1). Factor -9*d**3 - 2*d**2 + d**4 + 6*d**2 + 8*d**h + 5*d**3.
d**2*(d + 2)**2
Let l(b) = b**3 + 18*b**2 + 81*b - 2. Let q be l(-10). Let x be (90/q)/((-11)/((-1320)/(-126))). Factor -20/7*d - x - 2/7*d**2.
-2*(d + 5)**2/7
Let a(q) be the first derivative of -3*q**5/5 - 57*q**4/4 + 4*q**3 + 114*q**2 + 2286. Factor a(k).
-3*k*(k - 2)*(k + 2)*(k + 19)
Let k(w) = -28698*w - 172186. Let c be k(-6). Determine y so that 0 + 8/3*y**5 - 2/3*y**c + 0*y - 8/3*y**3 + 2/3*y**4 = 0.
-1, -1/4, 0, 1
Let r(u) be the first derivative of 5/2*u + 104 + 3/2*u**2 + 1/6*u**3. Determine i, given that r(i) = 0.
-5, -1
Let g(q) be the second derivative of q**4/12 + 85*q**3/2 - 128*q**2 + 76*q - 18. Determine a so that g(a) = 0.
-256, 1
Suppose 3*r - 20 + 5 = 0. Let m be (-66)/165 - (0 - 17/r). Factor 129*h**2 - 129*h**2 + 6*h**m - 3*h**4.
-3*h**3*(h - 2)
Let o(b) = 7*b**5 - 71*b**4 - 10*b**3 + 68*b**2 - 3. Let v(p) = -8*p**5 + 72*p**4 + 12*p**3 - 68*p**2 + 4. Let m(s) = 4*o(s) + 3*v(s). Let m(r) = 0. What is r?
-1, 0, 1, 17
Factor 2/5*z**2 - 632/5 - 126*z.
2*(z - 316)*(z + 1)/5
Solve 38/9*w**2 - 64/9*w - 2/3*w**3 + 32/9 = 0.
1, 4/3, 4
Let u = 434 - 334. Find a such that 140*a**2 + u*a**3 - 275*a - 50*a**4 - 67*a**5 + 72*a**5 + 10*a**3 - 250 = 0.
-1, 2, 5
Let p(y) = -12*y + 36. Let j be p(2). Factor 235*z**2 - 237*z**2 - j*z - 1458 - 45*z - 51*z.
-2*(z + 27)**2
Solve -1628*o**2 + 4205*o**4 - 420*o**3 + 82 - 4209*o**4 - 1212*o - 82 = 0 for o.
-101, -3, -1, 0
Let b be 75/4 - (-2)/8. Suppose 0 = i + i + 4*s - 36, 0 = -3*i - 3*s + 42. Factor -15 - b + i*r**2 + 29 - 5*r**4.
-5*(r - 1)**2*(r + 1)**2
Let t = -318081 - -318083. Let v be 16/3*(-6)/(-44). Factor 14/11*d**t - v*d - 8/11 - 4/11*d**3.
-2*(d - 2)**2*(2*d + 1)/11
Let h(i) = -i**2 - 5586*i + 1556862. Let d(a) = 5585*a - 1556855. Let v(k) = 6*d(k) + 5*h(k). Factor v(f).
-5*(f - 558)**2
Let q be (-10 + 120/18)/((-4)/(-6)). Let v be 34/(-4) - 50/q. Determine h so that -9 - v*h**4 + 33/2*h + 1/2*h**2 - 13/2*h**3 = 0.
-3, 2/3, 1
Factor 11/2*g**2 + 1/6*g**4 - 20/3*g + 8/3 - 5/3*g**3.
(g - 4)**2*(g - 1)**2/6
Let i(n) = -2*n**3 - 16*n**2 + 40*n + 16. Let o be i(-10). Factor 3*j**2 - 8*j**4 - 4*j**5 - o*j + 13*j**2 - 24*j**3 + 36*j**3.
-4*j*(j - 1)**2*(j + 2)**2
Suppose y + 2*y - 2*m + 8 = 0, 0 = 3*m - 12. Let n(z) be the first derivative of 1/12*z**3 - 1/4*z**2 - 9 + y*z. Let n(c) = 0. What is c?
0, 2
Let o(j) = 2*j**2 - 21*j - 62. Let f be (1/2)/(35/910). Let x be o(f). Factor 7/10*i**2 + x*i + 4/5.
(i + 4)*(7*i + 2)/10
Suppose 0 = a + 3*i + 21 - 90, 4*a = -i + 287. Let g be 2/30 - 4/a*-6. Factor -4/5*y**2 - g + 1/5*y**3 + y.
(y - 2)*(y - 1)**2/5
Let g(y) be the third derivative of 7*y**6/60 + 17*y**5/90 - 23*y**4/18 + 8*y**3/9 - 39*y**2 - 6. Solve g(r) = 0 for r.
-2, 4/21, 1
Suppose 0 = 51*i - 95 - 4 + 14 - 68. Solve 15/8*u**2 - i - 3/4*u - 3/8*u**3 = 0 for u.
-1, 2, 4
Let w(l) be the first derivative of -l**7/42 + l**5/12 + 3*l**2 + 4*l + 19. Let k(p) be the second derivative of w(p). Factor k(y).
-5*y**2*(y - 1)*(y + 1)
Let q(o) be the first derivative of -1/2*o**4 - 1/6*o**3 + 0*o - 225 + 3/4*o**2. Factor q(r).
-r*(r + 1)*(4*r - 3)/2
Factor -1552/3*v**2 - 2/3*v**3 - 301088/3*v + 0.
-2*v*(v + 388)**2/3
Factor -2845/2 + 1425*d - 5/2*d**2.
-5*(d - 569)*(d - 1)/2
Let z be (2/8)/(140 + -136). Let q(s) be the first derivative of z*s**4 + 2 - 5/12*s**3 + s**2 - s. Suppose q(v) = 0. Calculate v.
1, 2
Let t be 6/7 + (-1422)/1659. Let w(v) be the third derivative of 0*v - 1/36*v**4 + 2/9*v**3 + t - 7*v**2 - 1/45*v**5 + 1/180*v**6. Factor w(p).
2*(p - 2)*(p - 1)*(p + 1)/3
Let r(o) = -o**3 + 10*o**2 + o - 7. Let l be r(10). Suppose 35 = 8*q + l. Factor 28*z - q*z**2 - 21 - 1 - 2.
-4*(z - 6)*(z - 1)
Let d(h) = h**3 + 5*h**2 - 6*h - 6. Let r(i) = 3*i**2 - 30*i - 6. Let w be r(10). Let p(k) = k**3 + 4*k**2 - 5*k - 5. Let g(f) = w*p(f) + 5*d(f). Factor g(y).
-y**2*(y - 1)
Let u = 2082 + -1377. Factor -15356 - u*t + 46561 + 5*t**2 - 85*t.
5*(t - 79)**2
Let i(y) = 6*y**2 - 64*y + 45. Let h be i(10). Suppose 0 = -n - 1, 3*r - n = 40. Factor -r*t**2 - h*t**2 - 10*t + 2*t**2 + t**2 - 5*t**3.
-5*t*(t + 1)*(t + 2)
Let g(h) be the second derivative of h**6/30 - 7*h**5/20 + 7*h**4/12 + 5*h**3/2 + 2775*h. Find v, given that g(v) = 0.
-1, 0, 3, 5
Let g(u) be the second derivative of u**6/24 + u**5/12 - 17*u**2 - 39*u. Let r(p) be the first derivative of g(p). Determine o, given that r(o) = 0.
-1, 0
Let b(w) = -5*w + 44. Let j be b(8). Suppose -3*n = -j*k, 0 = -15*n + 16*n + k. Suppose 2*q**4 - 14/5*q**3 + 0 + 8/5*q**5 + n*q - 4/5*q**2 = 0. Calculate q.
-2, -1/4, 0, 1
Suppose -372 - 1872/5*r - 3/5*r**3 - 477/5*r**2 = 0. Calculate r.
-155, -2
Let j(v) = 12*v**3 + v**2 + 2*v - 1. Let q be j(1). Let n = q - 7. Factor 3*c**2 - 9*c**3 - 4*c**2 - c**4 + n*c**3.
-c**2*(c + 1)**2
Let a(q) be the second derivative of -q**6/90 - 23*q**5/30 + 4*q**4 + q**3/3 + 3*q**2/2 - q - 25. Let p(v) be the second derivative of a(v). Factor p(s).
-4*(s - 1)*(s + 24)
Let v(k) be the second derivative of -k**5/160 - 9*k**4/16 - 81*k**3/4 - 729*k**2/2 - 7*k + 2. Determine i, given that v(i) = 0.
-18
Let j be (-14)/5*(6030/(-210) + 28). Suppose 1/7 + 1/7*w**4 + 0*w + 0*w**3 - 2/7*w**j = 0. Calculate w.
-1, 1
Solve -20*t**3 - 4*t**5 - 6*t**4 - 2*t**4 + 144*t + t**4 - t**5 + 132*t**2 + 6*t**5 = 0 for t.
-4, -1, 0, 6
Suppose 2*v + 165 - 171 = 0. Solve -m**3 + 16 + 112*m + 13*m**5 - 11*m**4 - 78*m**2 - 79*m**v + 118*m**2 = 0 for m.
-2, -1, -2/13, 2
Factor 119*u - 159/4 + 3/4*u**2.
(u + 159)*(3*u - 1)/4
Let s(d) be the second derivative of -1/30*d**3 + 1/100*d**5 + 0 + 0*d**4 + 0*d**2 - d. Factor s(j).
j*(j - 1)*(j + 1)/5
Let a = 1143/6104 + 3/12208. Let x(v) be the second derivative of 0 - a*v**2 + 7/96*v**4 + 1/24*v**3 - 30*v + 1/80*v**5. Factor x(z).
(z + 1)*(z + 3)*(2*z - 1)/8
Factor 39*q - 26*q - 19*q**2 - 11*q**3 + 4*q**4 - 17*q.
q*(q - 4)*(q + 1)*(4*q + 1)
Let w(n) = 5*n**2 - 52*n + 22. Let y be w(10). What is m in 49*m**3 + 201*m**2 - 3247 - 1056*m - 1119*m**y + 2863 - 292*m**3 = 0?
-2, -8/9
Let b(g) be the second derivative of -g**5/80 - 19*g**4/48 - g**3 + 90*g**2 + 705*g. Let b(u) = 0. What is u?
-12, 5
Let n = 169/1304 + 72179/6520. Factor -52/5 + 1/5*t**3 - 17/5*t**2 + n*t.
(t - 13)*(t - 2)**2/5
Let b(m) be the first derivative of -75/14*m**2 - 123 + 24/7*m + 3/7*m**3. What i