t f(i) = i**4 + 41*i**3 + 144*i**2 + 340*i + 191. Let y(k) = -2*k**3 + 2*k**2 + 1. Let j(u) = 2*f(u) + 18*y(u). Find v such that j(v) = 0.
-10, -2, -1
Let n(l) be the second derivative of -l**4/54 - l**3/9 + 2*l**2 - 214*l. Factor n(b).
-2*(b - 3)*(b + 6)/9
Let b be 2/11 + 870/55. Factor -4*i**3 - 13*i + b*i**2 - 4*i - 4*i + 5*i.
-4*i*(i - 2)**2
Let z = -56 + 57. Let i(r) = r**2 - r - 1. Let k(m) = 2*m**3 + 2*m**2 - 2. Let y(t) = z*k(t) + 2*i(t). Factor y(q).
2*(q - 1)*(q + 1)*(q + 2)
Suppose 225 + 211 = 109*m. Determine b, given that 4 + 1/2*b**3 + 1/2*b**m - 3*b**2 - 2*b = 0.
-2, 1, 2
Let r(y) be the third derivative of y**7/840 - y**6/480 - y**5/60 + y**4/24 - 29*y**2 + 2. Determine x so that r(x) = 0.
-2, 0, 1, 2
Let c be 1/((-9)/(-2)) - (-236)/(-9). Let m be (-1)/((-10)/54) - c/(-65). Determine d, given that 132/7*d**4 - 8/7*d + 46/7*d**3 + 10*d**m + 0 - 24/7*d**2 = 0.
-1, -2/7, 0, 2/5
Let n = 15 + -10. Suppose n*x + 0*x = 0. Factor 2/7*c - 2/7*c**2 + x.
-2*c*(c - 1)/7
Let x(c) be the second derivative of c**4/42 + 17*c**3/21 - 18*c**2/7 - 18*c + 1. Let x(n) = 0. What is n?
-18, 1
Let w(q) be the third derivative of -q**8/4704 - q**7/4410 + q**6/840 + 7*q**4/8 + q**3/3 + 29*q**2. Let c(m) be the second derivative of w(m). Factor c(d).
-2*d*(d + 1)*(5*d - 3)/7
Let k(c) = c**2 - 3*c + 1. Let d(f) = -2*f**3 + 4*f**2 + 14*f - 22. Let p(l) = d(l) + 6*k(l). Factor p(a).
-2*(a - 4)*(a - 2)*(a + 1)
Let l = -979 - -19581/20. Let f(k) be the second derivative of -l*k**5 + 0*k**2 - 2*k - 1/6*k**4 + 0*k**3 + 0. Factor f(y).
-y**2*(y + 2)
Factor 218/9*t**3 - 2/9 + 26/3*t - 74/3*t**2 - 8*t**4.
-2*(t - 1)**3*(36*t - 1)/9
Let x(l) be the third derivative of -1/9*l**3 - 10*l**2 - 5/108*l**4 - 1/270*l**5 + 0*l + 0 + 1/540*l**6. Factor x(i).
2*(i - 3)*(i + 1)**2/9
Find x such that 41*x**2 - 105*x**2 + 4*x**3 + 36*x**2 - 12*x + 36*x**2 = 0.
-3, 0, 1
Solve 2/9*i**3 + 154/9*i + 484/9 - 40/9*i**2 = 0 for i.
-2, 11
Let h be (18/81)/(67/36 + (-132)/176). Let s(i) = -2*i - 2. Let j be s(-2). Factor -h*z**j - 5 - 2*z.
-(z + 5)**2/5
Let j(o) be the third derivative of o**8/84 + 13*o**7/90 + 19*o**6/180 - 7*o**5/15 - 25*o**4/36 - 7*o**3/18 + 2*o**2 - 5. Solve j(x) = 0.
-7, -1, -1/3, -1/4, 1
Suppose 0 = -3*g + 7 - 1. Suppose -2*o - 5*n + 9 = 0, -2*o - 9*n + 14*n - 1 = 0. Find j, given that 3*j**o - 2*j**2 - 12*j + 5*j**2 + 6*j**g - 3*j**3 = 0.
0, 2
Factor -106/9 - 104/9*r + 2/9*r**2.
2*(r - 53)*(r + 1)/9
Factor 2*p + 3*p**2 + 15 + 17*p - p + 0*p.
3*(p + 1)*(p + 5)
Let z = -38 - -46. Suppose z*f = 22 - 6. Solve -81*o - 15*o**3 - 3/2*o**4 - 54*o**f - 81/2 = 0.
-3, -1
Suppose 0 = -2*y + 7*y - 80. Let h(f) = -f**3 + 17*f**2 - 17*f + 18. Let a be h(y). Let -5*i - 10*i - i**a - 3 + 11*i = 0. Calculate i.
-3, -1
Let o(k) be the third derivative of 1/60*k**5 + 1/4*k**4 - 10*k**2 + 0 + 3/2*k**3 + 0*k. Factor o(p).
(p + 3)**2
Let a = -4 - -6. Let s be (-65)/10 + (-18117)/(-2562). Factor s + 10/7*j**a - 2*j.
2*(j - 1)*(5*j - 2)/7
Solve 66*w**2 - 30/7*w**4 + 3/7*w**5 - 12/7*w**3 + 63*w + 0 = 0.
-3, -1, 0, 7
Let o(h) be the second derivative of -2/21*h**3 - 1/14*h**4 + 1/35*h**6 + 0*h**2 - 10*h + 1/70*h**5 + 1/147*h**7 + 0. Solve o(n) = 0.
-2, -1, 0, 1
Suppose 8*r - 11*r + 6 = 0. Factor 4*j**3 - 34*j + 2*j**r + 34*j - 5*j**3.
-j**2*(j - 2)
Let s(m) = 90*m**3 - 390*m**2 - 840*m - 360. Let h(g) = 9*g**3 - 39*g**2 - 84*g - 36. Let p(u) = -21*h(u) + 2*s(u). Factor p(a).
-3*(a - 6)*(a + 1)*(3*a + 2)
Let j(w) be the second derivative of -w**9/3024 + w**8/1680 + w**7/210 - w**6/90 + 7*w**3/2 - 26*w. Let p(z) be the second derivative of j(z). Factor p(r).
-r**2*(r - 2)*(r - 1)*(r + 2)
Let q(o) be the first derivative of o**6/72 - 5*o**4/6 - 34*o**3/3 + 52. Let g(j) be the third derivative of q(j). Solve g(l) = 0 for l.
-2, 2
Let 0 + 2/3*n**2 - 32/3*n = 0. What is n?
0, 16
Let x be (-18)/4*(-192)/216 + (2 - 6). Factor 4/7*b**2 - 2/7*b**3 + x + 16/7*b.
-2*b*(b - 4)*(b + 2)/7
Let z(d) be the second derivative of d**5/5 - 2*d**4/3 + 2*d**3/3 - 2*d + 267. Suppose z(w) = 0. Calculate w.
0, 1
Let t = -100838/55 - -9168/5. Find i, given that -t + 2/11*i**2 - 2/11*i + 2/11*i**3 = 0.
-1, 1
Let u = -22 + 25. Factor 10*h - 2*h**4 - 7*h**u + 2*h - 4*h**4 - 2*h**3 + 12*h**2 + 3*h**5.
3*h*(h - 2)**2*(h + 1)**2
Find q, given that -9*q**5 - 6*q**3 + 11*q**5 + 9*q**2 - 25*q**2 + 4*q**4 - 8*q = 0.
-2, -1, 0, 2
Let i(z) = z**5 - z**4 + 7*z**3 - 4*z**2 - 8*z + 5. Let l(q) = -q**4 + q**3 - q + 1. Let w(h) = -i(h) + 5*l(h). Factor w(o).
-o*(o - 1)*(o + 1)**2*(o + 3)
Let w be (-91)/3*(4 - -2)/(-2). Let x = 95 - w. Factor 11/5*s**2 + 1/5*s**5 - 3/5*s**x + 4/5 - 12/5*s - 1/5*s**3.
(s - 2)*(s - 1)**3*(s + 2)/5
Factor -27 + 51*g**3 - 181*g**3 - 204*g**2 - 25*g**4 - 124*g - 2*g.
-(g + 1)*(g + 3)*(5*g + 3)**2
Let j(x) be the second derivative of x**5/60 - 7*x**4/36 - 5*x**3/18 + 25*x**2/2 + 2*x + 21. Factor j(y).
(y - 5)**2*(y + 3)/3
Let i(s) = -2*s**3 - 9*s**2 + 3. Let o be (-2)/(-4) - 74/(-4). Let n(k) = 9*k**2 + 5*k**3 + 19*k**2 + k + 9 - o - 2*k. Let f(l) = -7*i(l) - 2*n(l). Factor f(z).
(z + 1)**2*(4*z - 1)
Let 3*q**3 - 8*q**2 - 5*q**2 - 2*q**2 - 1 - 8 + 21*q = 0. Calculate q.
1, 3
Factor 128/7 - 2/7*a**3 + 40/7*a**2 - 136/7*a.
-2*(a - 16)*(a - 2)**2/7
Suppose 5*g = -2*k + 17, 0*g = 5*k - g - 2. Let l(f) = -f + 1. Let t(c) = -c**2 + 19*c - 67. Let u(n) = k*t(n) + 3*l(n). Factor u(p).
-(p - 8)**2
Let q = -93 + 96. Let 12 + q*b**5 - 8*b**3 + 27*b**3 - 30*b**3 - 19*b**3 - 45*b + 60*b**2 = 0. Calculate b.
-4, 1
Let a(g) be the second derivative of g**5/10 + 7*g**4/6 + 2*g**3/3 - 40*g**2 + 302*g. Factor a(i).
2*(i - 2)*(i + 4)*(i + 5)
Let 154 + 88 + 448*t - 46 + 4*t**4 + 64*t**3 + 312*t**2 = 0. What is t?
-7, -1
Let j(y) = 5*y**2 + 5*y + 20. Let s(u) = -3*u - 23. Let i be s(-16). Let h(w) = w + 1. Let n(z) = i*h(z) + j(z). Factor n(g).
5*(g + 3)**2
Suppose -9*p - 5*p**5 + 51*p**4 + 30*p - p**3 + 18*p**3 - 80*p**3 - 3*p**2 - p**5 = 0. Calculate p.
-1/2, 0, 1, 7
Let w(j) = -j. Let t be w(-2). Let b be (6*(-4)/(-36))/t. Let 2/3 + c + b*c**2 = 0. Calculate c.
-2, -1
Let g(w) be the first derivative of 3*w**4/22 - 36*w**2/11 - 96*w/11 + 35. Suppose g(i) = 0. Calculate i.
-2, 4
Let l(q) = 2*q**4 + 11*q**3 + 5*q**2 - 13*q - 5. Let o(x) = 2*x**4 + 12*x**3 + 6*x**2 - 14*x - 6. Let m(i) = -6*l(i) + 5*o(i). Determine w, given that m(w) = 0.
-2, 0, 1
Let t(w) = 27*w**3 + 23*w**2 + 7*w + 11. Let o(x) = -14*x**3 - 12*x**2 - 4*x - 6. Let g(s) = 11*o(s) + 6*t(s). Solve g(b) = 0 for b.
-1, 0, 1/4
Let x(b) be the third derivative of b**5/15 + 11*b**4 + 726*b**3 - 15*b**2. Factor x(v).
4*(v + 33)**2
Factor 205*f - 32*f**2 + 27*f**2 - 3*f**3 - 2*f**3 - 38*f**2 + 285 - 42*f**2.
-5*(f - 3)*(f + 1)*(f + 19)
Let a be (-1 - (2 - (-32)/(-9)))*(-2202)/(-1835). Factor -4/3*t + a*t**2 + 0.
2*t*(t - 2)/3
Solve 5/3*t**2 + 0 - 1/6*t**3 - 3/2*t = 0 for t.
0, 1, 9
Let j(y) = 14*y**2 + 34*y + 44. Let m(o) = -9*o**2 - 23*o - 30. Let a(s) = -5*j(s) - 8*m(s). Solve a(n) = 0.
-5, -2
Let d(z) be the first derivative of -z**9/10584 - z**8/2940 + z**6/630 + z**5/420 + 4*z**3/3 - 11. Let b(i) be the third derivative of d(i). Factor b(v).
-2*v*(v - 1)*(v + 1)**3/7
Factor -1/6*b**4 + 0 + 1/2*b**3 - 2/3*b + 0*b**2.
-b*(b - 2)**2*(b + 1)/6
Let c(g) be the third derivative of -g**8/2184 + 4*g**7/455 - 11*g**6/390 - 14*g**5/65 - 49*g**4/156 + g**2 + 25. Factor c(z).
-2*z*(z - 7)**2*(z + 1)**2/13
Let k(w) = -w**4 + 2*w**3 + w**2 - 1. Let c(m) = m**4 - m**3 - 5*m**2 + m + 2. Let z(a) = c(a) + 2*k(a). Determine y, given that z(y) = 0.
0, 1
Solve 2/19*f**4 - 2/19*f**2 + 0*f + 0 + 2/19*f**5 - 2/19*f**3 = 0.
-1, 0, 1
Let v(r) be the second derivative of r**5/5 - r**4/2 + r**3 + r**2 + 9*r. Let m(u) = -9*u**3 + 12*u**2 - 13*u - 5. Let w(o) = 2*m(o) + 5*v(o). Factor w(i).
2*i*(i - 2)*(i - 1)
Let x(p) = -p**3 - 7*p**2 + p + 61. Let l be x(-5). Solve -3/2*f**4 + 0*f - l*f**3 - 6*f**2 + 0 = 0.
-2, 0
Let u(p) = 15*p**3 - 59*p**2 + 59*p - 9. Let x(f) = -f**2 + f - 1. Let q(y) = -u(y) - 6*x(y). Factor q(a).
-5*(a - 3)*(a - 1)*(3*a - 1)
Let 1/4*x**2 + 13/2*x + 0 = 0. Calculate x.
-26, 0
Let u be ((-2)/(-30))/((-12)/36) - (-110)/50. Let p be ((-6)/(-8))/(9/8). Find w, given that p*w - 2/3*w**u + 4/3 = 0.
-1, 2
Factor 1/4*b**5 + 0 - 9*b**4 + 81*b**3 + 0*b + 0*b**2.
b**3*(b - 18