
Let r = 82/105 + 8/105. Suppose -9 = 4*n - 9. Factor 0*g + n*g**4 + 4/7*g**2 - r*g**3 + 0 + 2/7*g**5.
2*g**2*(g - 1)**2*(g + 2)/7
Suppose 11*o + 156 = -42. Let q = -18 - o. Factor 1/5*f**2 + q + 0*f.
f**2/5
Let v(i) be the first derivative of -2/9*i**2 - 6 + 0*i**3 - 2/9*i + 1/9*i**4 + 2/45*i**5. Suppose v(u) = 0. Calculate u.
-1, 1
Let s(h) = -5*h**3 + 2*h**2 - 4. Let c be s(3). Let q = 123 + c. Suppose 3/4*d**3 - 3/8*d**q - 3/8*d**4 + 0*d + 0 = 0. Calculate d.
0, 1
Let b(a) be the third derivative of a**8/1008 - a**6/60 + 2*a**5/45 - a**4/24 + a**2 - 59. Factor b(t).
t*(t - 1)**3*(t + 3)/3
Let u(g) = 32*g**3 + 252*g**2 + 948*g + 1280. Let x(h) = 13*h**3 + 101*h**2 + 379*h + 512. Let b(t) = 5*u(t) - 12*x(t). Determine r so that b(r) = 0.
-4
Let b(h) be the first derivative of -5*h**4/4 + 130*h**3/3 - 120*h**2 + 641. Solve b(t) = 0 for t.
0, 2, 24
Suppose 9 = -r + 4*r. Let n be (-403)/(-5) - (-42)/105. Factor -2 - 78*y**3 + 9*y + 9*y**2 + n*y**r + 5.
3*(y + 1)**3
Let b(h) = 7*h**3 + 25*h**2 + 180*h + 450. Let f(a) = -3*a**3 - a**2 - 2*a - 1. Let t(z) = -2*b(z) - 4*f(z). Factor t(m).
-2*(m + 7)*(m + 8)**2
Let q(t) = 9*t**3 - 24*t**2 + 73*t - 32. Let z(n) = -2*n**3 + 6*n**2 - 18*n + 8. Let o(w) = w - 2. Let l be o(8). Let x(h) = l*q(h) + 26*z(h). Factor x(v).
2*(v - 1)**2*(v + 8)
Let c(s) be the first derivative of -2*s**5/35 + s**4/14 + 6*s**3/7 + 11*s**2/7 + 8*s/7 + 54. Let c(n) = 0. What is n?
-1, 4
Let m(f) be the third derivative of -f**7/1050 + 17*f**6/600 - 3*f**5/20 + 43*f**4/120 - 7*f**3/15 + f**2 + 141*f. Find i, given that m(i) = 0.
1, 14
Factor 7/3*t + 6 - 1/3*t**2.
-(t - 9)*(t + 2)/3
Let b(s) = -7*s**2 - 20*s - 13. Let i(t) = -20*t**2 - 60*t - 40. Let r(h) = h**3 + 7*h**2 + 8*h + 9. Let q be r(-6). Let n(k) = q*i(k) + 8*b(k). Solve n(v) = 0.
-4, -1
Let p(w) be the third derivative of -1/240*w**5 + 0*w + 1/12*w**3 + 0 - 1/840*w**7 + 1/160*w**6 - 42*w**2 - 1/32*w**4. Factor p(f).
-(f - 2)*(f - 1)**2*(f + 1)/4
Let h(k) be the second derivative of k**7/98 - 4*k**6/35 + 9*k**5/35 - 778*k. Factor h(v).
3*v**3*(v - 6)*(v - 2)/7
Let d(u) = -u**2 + 7*u + 10. Let c be d(8). Suppose -5*w = 4*b + 3, -5*b - c*w = -5 - 4. Factor -b*j**3 - 8/3 + 20/3*j - 2*j**2.
-(j + 2)*(3*j - 2)**2/3
Let t = 104 + -128. Let x be ((-24)/t)/((-2 - -1)/(-2)). Factor 0*c + 2/7*c**x - 8/7.
2*(c - 2)*(c + 2)/7
Suppose 1 + 0 = q, q - 5 = -z. Suppose -r - 4*w - 8 = 0, r = z*w - 3*w + 2. Find o such that -2/3*o**2 + 2/3*o + r = 0.
0, 1
Let p(o) be the second derivative of o**7/21 - 4*o**6/15 - 9*o**5/5 - 10*o**4/3 - 7*o**3/3 - 72*o. Factor p(s).
2*s*(s - 7)*(s + 1)**3
Let m(w) be the first derivative of w**4/4 + 4*w**3/9 - 14*w**2/3 + 16*w/3 + 326. Factor m(c).
(c - 2)*(c + 4)*(3*c - 2)/3
Let i be (-4)/14 - ((-548)/1036)/1. Let m = i + 963/148. Factor m*u**2 - 3/2 - 21/4*u.
3*(u - 1)*(9*u + 2)/4
Let a(g) be the third derivative of -g**2 + 2/315*g**7 + 0*g**3 + 0 + 0*g + 1/45*g**5 + 1/72*g**4 + 1/1008*g**8 + 1/60*g**6. Find b, given that a(b) = 0.
-1, 0
Suppose 0 = -2*m - 5*a + 33, 0 = 2*m - 6*m - 5*a + 41. Let b be (6/11)/(920/1265). Suppose b*k**m + 3/4*k**3 - 3/2 - 15/4*k - 9/4*k**2 = 0. What is k?
-1, 2
Let l(a) be the third derivative of a**8/3360 + a**7/1260 - a**6/360 - a**5/60 - 23*a**4/24 - 2*a**2. Let c(f) be the second derivative of l(f). Factor c(z).
2*(z - 1)*(z + 1)**2
Let w(y) be the second derivative of 147*y**5/10 - 7*y**4/3 + y**3/9 - 316*y. Factor w(c).
2*c*(21*c - 1)**2/3
Let u(c) = -4*c**5 + 32*c**4 + 288*c**3 + 428*c**2 + 284*c + 84. Let m(j) = 2*j**4 - 2*j**3 - j**2 - 1. Let r(b) = -12*m(b) - u(b). Factor r(i).
4*(i - 18)*(i + 1)**4
Factor -5/4*k**2 + 0 + 185/4*k.
-5*k*(k - 37)/4
Suppose -9 - 5 = -7*v. Factor -2*y + 8*y**2 - v*y + 3*y**2 - 10*y**2.
y*(y - 4)
Factor -2*v**2 - 7 + v**2 + 11 + 20 + 55*v - 60*v.
-(v - 3)*(v + 8)
Let n(f) be the first derivative of -f**7/420 + f**6/180 + f**5/30 + 6*f**3 + 7. Let b(z) be the third derivative of n(z). Solve b(k) = 0 for k.
-1, 0, 2
Let j(u) be the first derivative of -u**5 - 75*u**4 + 305*u**3/3 - 315. Let j(k) = 0. Calculate k.
-61, 0, 1
Let b(l) be the first derivative of 5*l**4/8 + 25*l**3/6 + 26. What is o in b(o) = 0?
-5, 0
Determine l, given that -70*l**3 + 1381 + 269*l - 49*l - 2*l**4 - 85 - 572*l**2 + 366*l + 206*l = 0.
-18, -1, 2
Solve 4/9*j**4 - 155/9*j + 52/9 - 1/3*j**2 + 208/9*j**3 = 0.
-52, -1, 1/2
Let p(f) be the first derivative of 31*f**4/7 - 380*f**3/21 + 12*f**2/7 - 80. What is b in p(b) = 0?
0, 2/31, 3
Let n be (3 - 10/3)/(73/12). Let r = 644/1095 + n. Let 6/5*j**3 - r*j + 8/5*j**2 + 0 - 14/15*j**4 = 0. What is j?
-1, 0, 2/7, 2
Let p(i) = -i**3 + 6*i**2 + 8*i - 5. Let y be p(7). Suppose -239*d**4 + 3*d**2 + d**y - 2*d**3 + 237*d**4 = 0. Calculate d.
-2, 0, 1
Let l(w) be the first derivative of -w**6/12 - 11*w**5/5 - 17*w**4 - 56*w**3/3 + 140*w**2 + 400*w + 91. Find m such that l(m) = 0.
-10, -2, 2
Suppose -112*u + 6*u**4 + 76/3*u**3 - 24 - 38/3*u**2 = 0. Calculate u.
-3, -2/9, 2
Let m = 12492 + -12487. Let 6/7*c**2 - 6/7*c**4 + 3/7*c**m + 0*c**3 - 3/7*c + 0 = 0. Calculate c.
-1, 0, 1
Find g, given that -g + 0 + 13/6*g**2 + 1/6*g**4 - 4/3*g**3 = 0.
0, 1, 6
Let u(g) be the first derivative of g**8/1008 - 4*g**7/315 + 2*g**6/45 - 12*g**2 + 22. Let s(y) be the second derivative of u(y). Let s(n) = 0. What is n?
0, 4
Let a = 102455/7 - 14635. Solve a + 2/7*i**2 - 12/7*i = 0.
1, 5
Let k(w) be the first derivative of 0*w**2 + 0*w - 2/35*w**5 + 1/21*w**6 - 1/14*w**4 + 4 + 2/21*w**3. Factor k(r).
2*r**2*(r - 1)**2*(r + 1)/7
Find b such that -3/7*b + 4/7*b**2 + 0 + 2/7*b**3 - 4/7*b**4 + 1/7*b**5 = 0.
-1, 0, 1, 3
Let p(f) be the first derivative of 0*f + 1/42*f**4 + 1/7*f**2 - 8/63*f**3 - 8. Solve p(v) = 0.
0, 1, 3
Let o(c) be the third derivative of -1/10*c**5 - 4*c**2 + 0 + 0*c**3 + 0*c**4 + 23/40*c**6 + 0*c. Find w such that o(w) = 0.
0, 2/23
Let j(n) = 4*n**2 + 56*n - 44. Let z(x) = 2*x**2 + x + 1. Let v(s) = -j(s) + 4*z(s). Let v(m) = 0. What is m?
1, 12
Let w(f) = 2*f**2 + 319*f + 1548. Let g be w(-5). Factor -8/21 - 16/21*t - 2/21*t**g - 10/21*t**2.
-2*(t + 1)*(t + 2)**2/21
Let u(t) be the third derivative of t**6/420 + t**5/70 + t**4/42 + 18*t**2 + 5*t. Let u(c) = 0. Calculate c.
-2, -1, 0
Let l = 2 + 1. Let s(j) = 5*j**3 - 2*j**2 + 1. Let w be s(1). Factor n**l - 3*n**2 + w*n**2 - 1 + 0*n**2 - n.
(n - 1)*(n + 1)**2
Factor -25/4 - 1/4*h**2 - 5/2*h.
-(h + 5)**2/4
Let r = 898 - 9890/11. Let v = 83/66 + r. Factor 1/2*z**2 - 1/2*z**3 + 0 + 1/6*z**4 - v*z.
z*(z - 1)**3/6
Let t(j) = 2 + 5 - 5 - 3 - j**2. Let a(f) = 7*f**2 + 4*f**2 + f**2 + 0*f + 12 + 4*f. Let b(r) = a(r) + 10*t(r). Factor b(d).
2*(d + 1)**2
Let f(v) be the second derivative of v**5/30 - v**4/6 - 117*v. Factor f(k).
2*k**2*(k - 3)/3
Let n(o) be the first derivative of 5*o**4/4 - 10*o**3 + 20*o**2 + 181. Factor n(t).
5*t*(t - 4)*(t - 2)
Let r(u) be the second derivative of 5*u**7/42 - 4*u**6/3 + 15*u**5/4 + 10*u**4/3 - 40*u**3/3 - 493*u. Factor r(m).
5*m*(m - 4)**2*(m - 1)*(m + 1)
Find d such that 9*d**3 + 8*d**3 + 528*d**2 + 44510*d + 1362944 + 1954*d - 15*d**3 = 0.
-88
Suppose -i + 42 = -5*g, 8*i + 33*g = 35*g + 32. Factor -44/7*c + 242/7 + 2/7*c**i.
2*(c - 11)**2/7
Suppose -4*z + 0*z - 18 = -26. Factor 9/5 - 3/5*p**z - 6/5*p.
-3*(p - 1)*(p + 3)/5
Let x be (-10 - -10) + 3*1. Let f be 0*(6 - x)/(-3). Determine n, given that 4 + 6*n**5 - 8*n**4 + 4*n**2 - 22*n**3 + 14*n + f*n**5 + 4*n**5 - 2*n**5 = 0.
-1, -1/2, 1, 2
Let b(l) be the third derivative of -1/600*l**6 + 12*l**2 - 1/300*l**5 + 0*l**3 + 0*l + 0*l**4 + 0. Solve b(w) = 0 for w.
-1, 0
Factor 16/3*j**2 + 2/3*j**3 + 512/3 - 224/3*j.
2*(j - 4)**2*(j + 16)/3
Let u(w) = -w**3 - w**2. Let s(j) be the second derivative of 1/5*j**5 + 1/12*j**4 - j**2 - 5/6*j**3 + 0 + 4*j. Let b(i) = 3*s(i) + 15*u(i). Factor b(d).
-3*(d + 1)**2*(d + 2)
Suppose -14 + 16 = s. Factor 0*z**2 - 19*z + 3*z**3 + 49*z - 33*z**s.
3*z*(z - 10)*(z - 1)
Let i(w) = -w - 4. Let d be i(-8). Suppose d*g + 2*z = 5*z - 4, 5*g - 2 = 2*z. Find c such that 3*c - 1/4*c**4 - 13/4*c**g + 3/2*c**3 - 1 = 0.
1, 2
Let y(c) be the third derivative of -c**8/840 + c**6/75 - 336*c**2. Factor y(n).
-2*n**3*(n - 2)*(n + 2)/5
Let t(c) be the third derivative of -c**5/100 + c**4/5 + 24*c**3/5 + 73*c**2 + 3. Factor t(l).
-3*(l - 