et g(b) be the second derivative of b**5/60 - 5*b**4/9 - 23*b**3/2 + 81*b**2 - 286*b - 2. Find h, given that g(h) = 0.
-9, 2, 27
Let h = -2/9005 + 216146/117065. Factor 2/13*i**2 + 0 - h*i.
2*i*(i - 12)/13
Let s = -235548 + 235552. Factor 0 - 4/13*x - 10/13*x**2 + 2/13*x**5 + 2/13*x**s - 6/13*x**3.
2*x*(x - 2)*(x + 1)**3/13
Let n(y) be the second derivative of -y**5/160 - 7*y**4/48 - 3*y**3/16 + 45*y**2/4 + 7642*y. Let n(z) = 0. Calculate z.
-12, -5, 3
Let c(a) = -5 + 0*a - 3*a + 6 + 6 + a**2. Let y be c(5). Factor v**4 + 11*v**3 - 4*v**4 + 6*v - y*v**3 + 3.
-3*(v - 1)*(v + 1)**3
Let f(a) be the first derivative of -5/13*a**2 - 112 - 2/39*a**3 + 0*a. Solve f(r) = 0 for r.
-5, 0
Let f(s) = 2*s**2 - 15*s - 149. Let j be f(13). Let q(b) = -9*b**2. Let a(n) = 4*n**2. Suppose u + u = -26. Let r(m) = j*q(m) + u*a(m). Factor r(z).
2*z**2
Let g = 5132/149 - 24617/745. What is s in -13/5*s**2 + 0 + g*s + 6/5*s**3 = 0?
0, 1, 7/6
Let x be (-1*(-2)/(-2))/((-229)/((-130530)/(-380))). Find a, given that x + 3*a**3 - 2*a**4 - 13/4*a + 1/2*a**2 + 1/4*a**5 = 0.
-1, 1, 6
Let f(k) = -k**3 + 34*k**2 - k + 74. Let q be f(34). Solve -50 - 32*o - q*o**2 + 28*o**3 + 5*o**4 - 3*o**3 - 53*o + 25*o**2 = 0.
-5, -1, 2
Let n(m) be the third derivative of -m**6/480 + m**5/60 - 5*m**4/96 + m**3/12 - 796*m**2. Suppose n(b) = 0. Calculate b.
1, 2
Let s(v) be the second derivative of v**4/14 + 67*v**3/21 + 12*v**2 - 130*v + 2. Factor s(t).
2*(t + 21)*(3*t + 4)/7
Suppose 0 = -3*y + 3*d + 39, 3*y + 30*d = 32*d + 32. Find n such that 0 - y*n - 9*n**4 - 18*n**2 - 3/2*n**5 - 39/2*n**3 = 0.
-2, -1, 0
Let t(c) be the third derivative of -c**6/30 - 234*c**5/5 - 20650*c**4 - 490000*c**3/3 + 35*c**2 + c - 3. Factor t(y).
-4*(y + 2)*(y + 350)**2
Let f(y) be the second derivative of -3*y**5/5 + 3863*y**4/4 - 466095*y**3 - 699867*y**2/2 + 12647*y. Factor f(t).
-3*(t - 483)**2*(4*t + 1)
Let x(q) be the first derivative of 3*q**4/20 - q**3/5 - 431. Factor x(j).
3*j**2*(j - 1)/5
Let s(o) = 4*o**2 - 56*o + 164. Let q be s(11). Let k(z) be the second derivative of -z**2 + 0 + 1/6*z**3 - q*z + 1/12*z**4. Let k(u) = 0. What is u?
-2, 1
Let i(z) be the first derivative of 0*z - 21 - 4/9*z**3 + 7/18*z**4 - 2/45*z**5 + 0*z**2. What is y in i(y) = 0?
0, 1, 6
Factor -3319*r + 292820*r**2 - 617*r - 3324*r + 45.
5*(242*r - 3)**2
Factor -412/9*o**2 - 404/3 + 2/9*o**3 + 1622/9*o.
2*(o - 202)*(o - 3)*(o - 1)/9
Let -85/2 - 1/6*t**2 + 128/3*t = 0. What is t?
1, 255
Let a(s) be the third derivative of 0*s**3 + 2*s**2 + 1/24*s**4 + 0*s + 13 - 1/180*s**5. Factor a(m).
-m*(m - 3)/3
Let z(k) be the first derivative of -1/5*k**4 + 0*k**2 - 16/45*k**3 - 2/75*k**5 + 47 + 0*k. Let z(a) = 0. What is a?
-4, -2, 0
Suppose 3*w - 280 = -17*w. Suppose -5*z = -f - w, 5*f + 8 = 2*z + 7. Let 85*p**2 - 57*p - 4*p**z - 45*p**2 + 21*p = 0. What is p?
0, 1, 9
Let w = -26957 - -26961. Let 1/2*j**3 - 2/3*j + 0*j**2 + 1/6*j**w + 0 = 0. Calculate j.
-2, 0, 1
Let i(s) = -17*s - 250. Let f be i(-15). Let o be (f/(45/18))/6. Find j, given that -o*j**2 + 1/3*j + 2/3 = 0.
-1, 2
Let q(f) be the first derivative of -4*f**3/3 - 5156*f**2 - 437. Suppose q(s) = 0. What is s?
-2578, 0
Suppose -31 + 46 = 5*l. Suppose 0 = 4*w + 5*a + 7, -3*a - 1 = 7*w - l*w. Let -18*z + 5*z**w + 28*z - 13*z**2 - 2 = 0. What is z?
1/4, 1
Suppose -128 = -9*d - 101. Suppose 2*q**4 - 18*q**d - q**4 - 5*q + 6*q**2 + 9*q**3 + 21*q = 0. What is q?
-1, 0, 2, 8
Factor 25/4*x + 1/4*x**3 + 0 + 5/2*x**2.
x*(x + 5)**2/4
Let y(h) = 22*h**4 - 36*h**3 + 162*h**2 + 540*h + 290. Let c(r) = 2*r**4 + 3*r**3 + r - 1. Let n(a) = 20*c(a) - 2*y(a). Solve n(g) = 0 for g.
-1, 5, 30
Let j(d) = -2*d**2 + 2*d + 40. Let o be j(5). Suppose 14*r = -n + 9*r - 15, o = 5*r + 15. Factor 5/6*u**3 - 5/6*u**2 + n - 5/3*u.
5*u*(u - 2)*(u + 1)/6
Let y(k) = -k**3 + 19*k**2 + 2*k - 14. Let v be y(8). Let p = -2116/3 + v. Solve -4/3*a**2 + 0 - p*a**3 + 2*a = 0.
-3, 0, 1
Let a(q) be the third derivative of -q**6/600 + 13*q**5/15 - 2176*q**4/15 + 32768*q**3/15 + 1546*q**2 - 2. Suppose a(r) = 0. What is r?
4, 128
Let v(n) = 12*n**2 - 4550*n + 433560. Let l(z) = 4*z**2 - 1517*z + 144508. Let u(a) = -10*l(a) + 3*v(a). Factor u(w).
-4*(w - 190)**2
Let k(d) be the third derivative of 3*d**8/112 - d**7/7 - 23*d**6/40 + 49*d**5/10 - 9*d**4/2 - 36*d**3 - 85*d**2. Determine u so that k(u) = 0.
-3, -2/3, 2, 3
Let m = 2111 - 1045. Suppose 106 - 10 - 1026*i + m*i - 4*i**2 = 0. Calculate i.
-2, 12
Let t be -8 + (-1044)/(-132) - 4304/(-880). Find f such that 1/5*f**4 - 8/5*f**3 - t*f + 9/5 + 22/5*f**2 = 0.
1, 3
Solve 5/6*x**4 + 1/2*x**3 - 5/6*x**2 - 2/3*x + 0 + 1/6*x**5 = 0 for x.
-4, -1, 0, 1
Let j(c) be the third derivative of -c**6/150 - c**5/75 + 87*c**4/10 - 1026*c**3/5 - 424*c**2. Let j(s) = 0. What is s?
-19, 9
Factor 3*d**2 - 351*d + 26*d**2 - 6*d**2 + d**3 + 43*d**2 + 284.
(d - 4)*(d - 1)*(d + 71)
Let v(g) be the first derivative of 4 - 57*g**2 - 3267*g - 5*g**2 + 13 - 39*g**2 - g**3 + 2*g**2. Solve v(a) = 0 for a.
-33
Suppose -5*r = a - 20, 440*a - 442*a + 5*r - 5 = 0. Let o(l) be the second derivative of 1/22*l**4 - 5*l + 0*l**2 + 0 + 2/33*l**3 + 1/110*l**a. Factor o(p).
2*p*(p + 1)*(p + 2)/11
Let f(c) be the second derivative of -7 - 1/4*c**5 - 2535/2*c**3 + 0*c**2 + 65/2*c**4 + 3*c. Suppose f(d) = 0. Calculate d.
0, 39
Let x(k) = 3*k**2 + 1350*k - 1191. Let l(h) = -10*h**2 - 4133*h + 3576. Let r(n) = 6*l(n) + 21*x(n). Factor r(t).
3*(t - 1)*(t + 1185)
Let m(f) = f**3 + 7*f**2 - 10*f - 13. Let j be m(-8). Determine c, given that -c**5 + 8*c**2 - 16*c**3 - 4*c**2 + 2*c**4 + 17*c**j - 6*c**2 = 0.
-1, 0, 1, 2
Determine v, given that -129/2*v**4 - 123*v**3 + 123/2 + 3*v**2 + 249/2*v - 3/2*v**5 = 0.
-41, -1, 1
Let x(w) be the third derivative of w**5/30 - 1115*w**4/12 - w**2 + 25*w + 2. Factor x(n).
2*n*(n - 1115)
Let r be (-2 - 30)/(1 + -3). Suppose 14 + r = 6*t. Factor -8/3*i**2 - 4/3*i**t + 4/3 + 8/3*i**3 + 4/3*i**4 - 4/3*i.
-4*(i - 1)**3*(i + 1)**2/3
Find x such that 219682 + 145*x + 14*x - x**2 - 219840 = 0.
1, 158
Let d(s) be the second derivative of -s**4/102 + 8*s**3/17 + 52*s**2/17 + 8190*s. Let d(p) = 0. What is p?
-2, 26
Let o(v) be the first derivative of 33 + 0*v**3 - 5/2*v**2 + 0*v + 1/12*v**5 + 5/24*v**4. Let u(r) be the second derivative of o(r). Factor u(q).
5*q*(q + 1)
Let p(m) be the second derivative of m**5/60 - m**4/12 - 4*m**3/3 + 74*m**2 + m + 5. Let o(j) be the first derivative of p(j). Solve o(f) = 0.
-2, 4
Let m = 1491/8 + -13387/72. Let u(j) be the first derivative of 29 - m*j + 2/27*j**3 + 1/9*j**2. Factor u(v).
2*(v - 1)*(v + 2)/9
Suppose 0 = -6*i + 144 - 24. Let v be 11/i + 18/72. Let 4/5 - v*j**2 - 6/5*j + 6/5*j**3 = 0. Calculate j.
-1, 2/3, 1
Let r be 3 + (-6)/3 - 0. Let l = r + 23. Let -a**3 + 7*a**4 - 20*a**4 + 13*a**3 + 11*a**4 - l*a**2 + 16*a = 0. What is a?
0, 2
Let v be (3150/1120)/((-6)/(168/(-35))). Let 25/4*x - v*x**3 + 15/4*x**2 + 1/4*x**4 + 0 = 0. What is x?
-1, 0, 5
Suppose -2*a = -5*q + 20, -1 = -q + 5*a - 4*a. What is h in 6 + 24*h**2 + 5 + 6*h**4 - 6*h - 20*h**3 - q*h - 9 = 0?
1/3, 1
Factor 341*t**4 + 4*t**5 - 124430*t - 156050*t**2 - 9*t**5 - 1366*t**4 - 54050*t**3 - 26646*t - 51005 - 2949*t.
-5*(t + 1)**3*(t + 101)**2
Suppose 89 = 8*b - 239. Let b*g + 4*g**2 - 21*g + 22*g - g**2 = 0. Calculate g.
-14, 0
Suppose -5*w - 17 = 4*v - 20, -15 = 5*v. Let c(h) be the second derivative of 21*h + 0 - 1/3*h**2 + 1/60*h**5 - 1/9*h**4 + 5/18*h**w. Solve c(r) = 0.
1, 2
Factor -1200 + 812*x - 196*x + 444*x - 3*x**2 - 2*x**2 + 145*x.
-5*(x - 240)*(x - 1)
Suppose 22/5*x + 18/5*x**3 - 42/5*x**2 + 2/5*x**4 + 0 = 0. What is x?
-11, 0, 1
Let d(w) be the third derivative of 0 - 1/6*w**5 + 1/80*w**6 + 9/16*w**4 - 5/6*w**3 + 192*w**2 + 0*w. Determine i so that d(i) = 0.
2/3, 1, 5
Factor 9/5*f**2 + 0 - 1/5*f**4 + 9/5*f - 1/5*f**3.
-f*(f - 3)*(f + 1)*(f + 3)/5
Let l(d) = -d**2 + 20*d + 60. Let g be l(21). Let y be (4/10)/(1 - g/45). Factor 0 - 3/2*c - 2*c**2 - 1/2*c**y.
-c*(c + 1)*(c + 3)/2
Let -200*f - 279*f - 211*f + 2*f**2 + 806*f = 0. Calculate f.
-58, 0
Let v = 111/454 - -22609/4086. Factor 0 + 16/3*x + v*x**2 + 4/9*x**3.
4*x*(x + 1)*(x + 12)/9
Let x = 677 - 623. Suppose -33*a = -x*a + 26*a. Factor 2/7*u + a*u**2 - 2/7*u**3 + 0.
-2*u*(u - 1)*(u + 1)/7
Let k(j) be the third derivativ