/5
Let v(w) = w**4 - w**3 + w**2 - w - 1. Let c(o) = -9*o**4 - 186*o**3 + 1005*o**2 - 1638*o + 834. Let b(j) = c(j) + 6*v(j). Find k, given that b(k) = 0.
-69, 1, 2
Let -178 + 13*p - 4*p**4 + 3*p - 186 - 178 + 12*p**2 + 526 - 8*p**3 = 0. What is p?
-2, 1
Suppose -t + o - 1 = 0, -5*t + 40 = 5*o + 15. Let c(p) = -25*p**2 + 103*p + 139. Let x(v) = -5*v**2 + 21*v + 28. Let s(a) = t*c(a) - 11*x(a). Factor s(h).
5*(h - 6)*(h + 1)
Find s such that 11*s**4 + 64*s**2 + 76*s**3 - 766*s + 622*s - 7*s**4 = 0.
-18, -2, 0, 1
Let s(a) = a**3 - 4*a**2 + 6*a - 1. Let q be s(3). Suppose -q = 7*i - 11*i. Factor 8*v**2 - 18*v**2 + 1 + 9*v**i.
-(v - 1)*(v + 1)
Let k(h) be the second derivative of -7*h**6/90 - 172*h**5/15 - 21*h**4/4 + 344*h**3/9 + 98*h**2/3 + 4278*h. Suppose k(c) = 0. What is c?
-98, -1, -2/7, 1
Let v(b) be the third derivative of -b**6/80 - 9*b**5/20 - 41*b**4/16 + 15*b**3 + 944*b**2. Factor v(j).
-3*(j - 1)*(j + 4)*(j + 15)/2
Let d = -356 + 363. Let v be -1*((-35)/d - -2). What is b in 2/3 - 1/3*b**4 + b - 1/3*b**2 - b**v = 0?
-2, -1, 1
Let g = -430735 + 1722961/4. Determine y so that 0 - 3/2*y**4 - 21/4*y**3 + 3/2*y**2 + 0*y + g*y**5 = 0.
-1, 0, 2/7, 1
Let k(i) be the third derivative of 0 + 1/140*i**5 - 40*i - 2/7*i**3 + 0*i**4 + 2*i**2. Determine r, given that k(r) = 0.
-2, 2
Let r(x) = -6*x**2 + 2. Let d(j) = 5*j**2 + 363*j - 2. Let k(q) = -d(q) - r(q). Let k(n) = 0. What is n?
0, 363
Determine x so that -6592 + 23971*x + 2*x**3 - 4222*x - 2079*x + 378*x**2 - 11458 = 0.
-95, 1
Solve 0 - 3/8*n**3 + 177/4*n**2 - 10443/8*n = 0 for n.
0, 59
Factor -90000/7 - 88*n**2 - 4/7*n**3 - 24900/7*n.
-4*(n + 4)*(n + 75)**2/7
Let m(i) be the first derivative of 5*i**6/6 - 95*i**4/4 + 170*i**3/3 + 30*i**2 - 200*i + 4380. Factor m(a).
5*(a - 2)**3*(a + 1)*(a + 5)
Let h = -397 - -401. Solve 12*i - 3*i**2 - h - 2 - 6 = 0 for i.
2
Let p(w) = -35 - 7 - 8*w + 5*w. Let n be p(-17). Find z such that -7*z**5 + n*z**5 - 4*z**2 - 5*z**3 - z**3 = 0.
-1, 0, 2
Determine z so that -418/9 - 2/9*z**2 - 20/3*z = 0.
-19, -11
Let q be 2/(-8) - (-175)/28. Suppose 0*t + 24 = q*t. Solve -5*w - 9*w**t - 2*w - 37*w**2 + 30*w**3 - 4 + 27*w = 0.
2/3, 1
Let w(p) be the third derivative of p**5/120 + 93*p**4/8 - 559*p**3/12 - 11937*p**2. Factor w(t).
(t - 1)*(t + 559)/2
Let l(i) = 22*i**2 + 12*i + 53. Let u(o) = 22*o**2 - 4*o + 52. Let d(k) = 4*l(k) - 5*u(k). Factor d(w).
-2*(w - 2)*(11*w - 12)
Let d(o) be the second derivative of -5*o**4/24 - 155*o**3/12 - 210*o**2 - 10*o - 36. Solve d(k) = 0 for k.
-24, -7
Find w, given that -5714 - 3404*w - 5370 + 7676 + 4*w**2 = 0.
-1, 852
Let g(h) be the first derivative of -h**6/8 + 3*h**5/20 + 231*h**4/16 - 177*h**3/4 - 216*h**2 - 243*h + 2935. What is s in g(s) = 0?
-9, -1, 6
Suppose -291 = -26*a + 333. Suppose -2*q = -5*f - a, 0 = 4*q + 5*f + 49 - 37. Find i, given that 0 - 5/3*i**q - 10/3*i = 0.
-2, 0
Let x(k) be the third derivative of k**7/1365 - k**6/52 + 59*k**5/390 - 15*k**4/52 - 2*k**2 - 765*k. Factor x(i).
2*i*(i - 9)*(i - 5)*(i - 1)/13
Let b(o) = -5*o**2 + o + 15. Let k be b(3). Let p be k/(-15)*(-150)/(-90). Factor 5/7*v + 2/7 + 1/7*v**p + 4/7*v**2.
(v + 1)**2*(v + 2)/7
Suppose 2*c = 3*c - 320. Let h = c + -318. Solve 42*o**h - 236/5*o**3 - 72/5*o + 18*o**4 + 8/5 = 0 for o.
2/9, 2/5, 1
Suppose -1389 = 6*f + 447. Let s be 85/f*(-4)/1. Find d, given that 8/3*d + s*d**5 - 8/9 - 34/9*d**3 + 2/3*d**4 + 2/9*d**2 = 0.
-2, -1, 2/5, 1
Let r(y) be the third derivative of y**5/10 - 17*y**4/8 - 185*y**3 - 1687*y**2. Factor r(j).
3*(j + 10)*(2*j - 37)
Let y = -598725/7 + 85015. Let x = y + 518. Suppose -10/7*a**2 + 2/7*a**3 - x + 2*a = 0. What is a?
1, 3
Let x(o) be the second derivative of o**7/525 + 3*o**6/100 + 4*o**5/75 - 45*o**2/2 + 37*o. Let r(z) be the first derivative of x(z). Let r(u) = 0. Calculate u.
-8, -1, 0
Suppose -50 = -14*n - 8. Find u, given that -4 - 12*u**2 + 72*u + 5 + 15*u**n - 1 + 114*u**2 = 0.
-6, -4/5, 0
Suppose 0 = i - 5*i - 2*u, 0 = -4*i - 4*u - 8. Find g, given that 25*g**3 + 5*g**2 + 100*g**i + 15*g**3 + 18*g + 72*g + 5*g**4 = 0.
-3, -2, 0
Suppose 53*g + 22 = 64*g. Let a(b) be the second derivative of 1/14*b**4 + 10*b - 6/7*b**3 + 0 + 15/7*b**g. Factor a(p).
6*(p - 5)*(p - 1)/7
Let c(o) = 2*o**2 - 6*o - 15. Let u = 290 + -285. Let b be c(u). Solve 2/17*w**2 - 2/17*w**3 + 0*w + 2/17*w**b - 2/17*w**4 + 0 = 0 for w.
-1, 0, 1
Let f(w) be the first derivative of -w**8/168 + w**7/210 + w**6/120 + 55*w**2 + 202. Let r(v) be the second derivative of f(v). Factor r(c).
-c**3*(c - 1)*(2*c + 1)
Let l(k) = -4*k**3 - 176*k**2 - 4370*k - 17638. Let y(i) = -21*i**3 - 879*i**2 - 21851*i - 88189. Let j(g) = 11*l(g) - 2*y(g). Factor j(d).
-2*(d + 5)*(d + 42)**2
Suppose -4 = -34*c + 32*c. Solve 621*s - 15*s**3 + 91*s**c - 1746*s + 405 - 356*s**2 = 0 for s.
-9, 1/3
Suppose 2*m = -194 + 254. Suppose 35*k - m*k = 0. Factor -3/4*y - 1/4*y**3 + k - y**2.
-y*(y + 1)*(y + 3)/4
Let m be (-1006572)/(-75900) + (-4)/50 - 5. Factor -2/11*f**4 - m*f**2 + 24/11*f**3 + 100/11*f + 0.
-2*f*(f - 5)**2*(f - 2)/11
Let c(j) be the first derivative of -2*j**6/27 - 14*j**5/45 + 14*j**4/9 - 8*j**3/9 - 5465. Solve c(s) = 0.
-6, 0, 1/2, 2
Let l = 142678/154427 - 10/11879. Solve -10/13*f + l + 2/13*f**2 = 0.
2, 3
Let x(p) be the second derivative of -p**4/3 + p**3 + 2*p**2 + 4*p + 6. Let t(u) = -u**2 - 1. Let r(n) = -3*t(n) + x(n). Suppose r(j) = 0. What is j?
-1, 7
Let m(f) be the second derivative of 3/2*f**2 + 4/3*f**3 + 11 - f + 5/48*f**4. Suppose m(k) = 0. Calculate k.
-6, -2/5
Suppose -1062*q - 52 + 1267 + 270 = -639. What is k in -32/3 - 16/3*k**q - 2/3*k**3 - 40/3*k = 0?
-4, -2
Let v(f) be the third derivative of 0*f + 0*f**4 + 1/42*f**7 - 192*f**2 + 0*f**3 + 1/24*f**6 + 0 - 1/6*f**5. Factor v(r).
5*r**2*(r - 1)*(r + 2)
Let s(x) be the second derivative of x**7/630 + x**6/180 - x**5/15 + 17*x**4/12 + 3*x**2 + 56*x. Let k(r) be the third derivative of s(r). Factor k(i).
4*(i - 1)*(i + 2)
Let a(m) = 9*m**3 - 57*m**2 - 312*m - 426. Let x(k) = k**3 + 5*k + 1. Let g(l) = a(l) - 6*x(l). Factor g(o).
3*(o - 24)*(o + 2)*(o + 3)
Let a be ((-1)/(-1 + 3 - (-184)/(-69)))/((-9)/(-4)). Let -7/3*h**4 + 2/3 - a*h**5 - 5/3*h**3 + 7/3*h + 5/3*h**2 = 0. What is h?
-2, -1, -1/2, 1
Let y = 407/244 + -56/61. Let o(a) be the second derivative of 0*a**2 - 1/10*a**6 + 0*a**5 + 0 + y*a**4 + 5*a + a**3. Factor o(k).
-3*k*(k - 2)*(k + 1)**2
Suppose -3*a + 8 = -5*a, -4*a = 5*y + 6. Solve -3*u**4 - 17*u**2 - 52*u**y - 6*u + 33*u**3 + 72 + 18*u - 45*u = 0 for u.
-1, 1, 3, 8
Suppose 5670 = -3*u + 17*u + 2837 + 2833. Determine x so that 21/2*x - 3/4*x**2 + u = 0.
0, 14
Suppose -t = -31 + 25. Let b be -6 + 854/63 - t. Factor 0*j**2 + 0*j - 4/9*j**4 + 0 + 0*j**3 - b*j**5.
-2*j**4*(7*j + 2)/9
Find t such that 1/4*t**4 + 26896 + 108897/4*t**2 + 53956*t + 329/2*t**3 = 0.
-328, -1
Suppose -5*c = 4*u - 474, -2*u = -c + u + 110. Suppose c - 440*y + 50*y**3 - 18*y**3 - 340 - 2*y**4 - 156*y**2 + 8*y**3 = 0. Calculate y.
-1, 11
Let f(r) = -49*r**3 - 61*r**2 - 575*r + 625. Let j(s) = 90*s**3 + 120*s**2 + 1150*s - 1250. Let o(x) = 11*f(x) + 6*j(x). Factor o(m).
(m - 1)*(m + 25)**2
Suppose -4*t = 4*n - 8, -5*n - t = t - 13. Let r(w) = -w**2 + 27*w + 1078. Let f be r(49). Solve -2/9*v**n + 4/9 + 2/3*v + f*v**2 = 0 for v.
-1, 2
Suppose 0*b - 4*b + 3*r - 7151 = 0, -2*r - 7146 = 4*b. Let i = -1785 - b. Solve -i - 2*s**3 - 17/2*s**2 - 10*s = 0 for s.
-2, -1/4
Let o(f) be the second derivative of 20/3*f**3 - 4/21*f**7 - 8/5*f**5 + 19/3*f**4 - 22/15*f**6 + 102*f - 16*f**2 + 0. Solve o(v) = 0.
-4, -2, -1, 1/2, 1
Let v(z) be the third derivative of 0 + 1/2*z**4 + 1/20*z**5 + 0*z**3 + 0*z - 16*z**2. Factor v(b).
3*b*(b + 4)
Let w(o) be the third derivative of -5*o**3 + 4 - 12*o**2 + 2/3*o**5 + 0*o + 65/24*o**4. Factor w(r).
5*(r + 2)*(8*r - 3)
Let l(q) = -46*q**3 - 3*q**2 + q + 10. Let k be l(0). Let h(c) be the second derivative of -k*c**2 + 32*c + 0 + 1/50*c**5 - 2/5*c**4 + 3*c**3. Factor h(m).
2*(m - 5)**2*(m - 2)/5
Factor 1966*i**3 + 1970*i**2 - 3873*i**3 + 1902*i**3 - 194045*i.
-5*i*(i - 197)**2
Factor -19150/3 + 2/3*d**3 - 7610/3*d - 746/3*d**2.
2*(d - 383)*(d + 5)**2/3
Let w(l) = -8*l + 44. Let u be w(13). Let v = u + 65. Find h, given that 0*h + h**2 - 5 + h - v*h = 0.
-1, 5
Let w(x) be the second d