?
1, 5
Let f(i) be the third derivative of -i**7/30 + i**6/10 - i**5/20 - i**4/12 + 83*i**2. Determine g, given that f(g) = 0.
-2/7, 0, 1
Factor -b - 4*b**3 + b**2 + 2*b**3 - 9*b + 5*b**3 - 2*b**3 + 8.
(b - 2)*(b - 1)*(b + 4)
Let p be (-2204)/(-399) + -4*16/(-56). Factor 2/3*w**2 + p*w + 50/3.
2*(w + 5)**2/3
Find u, given that 4/3 + 1/6*u**4 + 3*u**2 - 7/6*u**3 - 10/3*u = 0.
1, 2
Let x(y) be the second derivative of -1/4*y**4 + 10*y + 0*y**2 - 1/84*y**7 + 1/40*y**5 + 0 + 0*y**3 + 1/10*y**6. Find d such that x(d) = 0.
-1, 0, 1, 6
Suppose -20/7*a**4 - 4*a**2 + 4/7*a**5 + 0 + 8/7*a + 36/7*a**3 = 0. What is a?
0, 1, 2
Let q(t) be the third derivative of -8*t**2 + 0*t**3 + 1/180*t**5 - 1/72*t**4 + 1/360*t**6 - 1/630*t**7 + 0*t + 0. Factor q(u).
-u*(u - 1)**2*(u + 1)/3
Let c(a) be the first derivative of -a**3/21 + a**2/14 - 297. Factor c(o).
-o*(o - 1)/7
Let n(v) be the first derivative of -5*v**3/6 - 17*v**2 + 14*v - 138. Suppose n(k) = 0. Calculate k.
-14, 2/5
Let s(o) be the third derivative of -o**8/1176 - 2*o**7/735 + o**6/210 + 2*o**5/105 - o**4/84 - 2*o**3/21 + 83*o**2. Find g, given that s(g) = 0.
-2, -1, 1
Let l(f) be the second derivative of -f**5/20 - f**4/12 + f**3/3 - 126*f. Factor l(k).
-k*(k - 1)*(k + 2)
Let d(v) be the first derivative of v**6/840 + 13*v**5/140 + 169*v**4/56 - 34*v**3/3 - 13. Let c(l) be the third derivative of d(l). Factor c(r).
3*(r + 13)**2/7
Determine i so that 12*i**3 - 103*i**2 + 16*i + 4*i**4 - 23*i**2 + 15 + 41 + 54*i**2 + 40 = 0.
-6, -1, 2
Let l = 196 - 6467/33. Let f = l + 31/66. Factor f + 1/4*o**3 + 1/4*o**4 - 1/4*o - 3/4*o**2.
(o - 1)**2*(o + 1)*(o + 2)/4
Suppose 5 = 6*i - 7. Find o such that 10*o**2 - 44*o - 22*o**i - 12 - 12 = 0.
-3, -2/3
Let t(s) be the third derivative of s**6/24 - 5*s**5/12 - 65*s**4/24 - 35*s**3/6 - 5*s**2 - 3*s. Factor t(l).
5*(l - 7)*(l + 1)**2
Let w(q) = -2*q**3 - 4*q + 2. Let d(l) = -3*l**3 - 10*l + 5. Let s(f) = -2*d(f) + 5*w(f). Factor s(a).
-4*a**3
Suppose -2*g = 12 - 18. Factor -142*v**5 + 143*v**5 - v**3 + 7*v**2 - 3*v**4 + 3 - g - 4.
(v - 2)**2*(v - 1)*(v + 1)**2
Let a(i) = -i**4 + i**3 + i**2 + 2*i - 1. Let m(t) = -8*t**4 - 477*t**3 + 1473*t**2 - 1474*t + 492. Let k(h) = -3*a(h) + m(h). Factor k(x).
-5*(x - 1)**3*(x + 99)
Let b(i) = -i**3 + 8*i**2 - 1. Let o be b(8). Let v(g) = g + 3. Let q be v(o). Factor 0 + 0*y - 2/7*y**3 - 2/7*y**q.
-2*y**2*(y + 1)/7
Let p(b) be the second derivative of -14*b**6/75 - 53*b**5/50 + 7*b**4/10 + 38*b**3/15 + 8*b**2/5 - 6*b + 2. Determine j so that p(j) = 0.
-4, -1/2, -2/7, 1
Let o(x) be the first derivative of -x**6/33 - 4*x**5/55 + 4*x**3/33 + x**2/11 + 31. Factor o(l).
-2*l*(l - 1)*(l + 1)**3/11
Suppose 0 = -15*j + 6 + 24. Factor 22*t - 12 + 2*t**j + 29*t - 53*t.
2*(t - 3)*(t + 2)
Let b(v) = -v**3 - 5*v**2 - v. Let y be b(-6). Factor -3*a + y*a**3 + 24*a - 18*a**4 + 316*a**2 + 3*a**5 + 6*a - 364*a**2 - 6.
3*(a - 2)*(a - 1)**4
Factor -1 + 9 + 10*g - 23*g**2 - 67*g**3 + 72*g**3.
(g - 4)*(g - 1)*(5*g + 2)
Let a = -83 - -65. Let u = 20 + a. What is m in 1 + 1/3*m**u + 5/3*m - 1/3*m**3 = 0?
-1, 3
Factor -2/7*x**3 - 161376/7*x + 984/7*x**2 + 8821888/7.
-2*(x - 164)**3/7
Let 0*n + 0 - 15/2*n**2 - 3/2*n**3 = 0. Calculate n.
-5, 0
Let p(d) be the second derivative of -d**7/189 - 17*d**6/135 + 7*d**5/30 + 53*d**4/54 - 20*d**3/27 - 4*d**2 - 186*d. Determine q so that p(q) = 0.
-18, -1, 1, 2
Factor 30*g**2 - 12*g**3 + 10*g**3 + 69*g**2 + 56*g**2 + 242*g + 85*g**2.
-2*g*(g - 121)*(g + 1)
Let r(t) be the second derivative of -t**4/20 + 73*t**3/10 + 111*t**2/5 - 2*t - 46. Factor r(b).
-3*(b - 74)*(b + 1)/5
Let d = -26 + 28. Let i(s) = -s**2 - 5*s - 1. Let y be i(-4). Let d*j**4 + y*j**5 + 0*j**5 - 2*j**5 + j**3 = 0. Calculate j.
-1, 0
Let v(w) = -4*w**4 + 16*w**3 - 24*w**2 + 12*w + 4. Let l(a) = -a**2 + a + 1. Let f(y) = 4*l(y) - v(y). Solve f(z) = 0 for z.
0, 1, 2
Suppose -33*j + 30*j = 2*k - 9, 0 = 3*k + 5*j - 15. Factor -2/3*n**2 + 1/3*n**3 + 1/3*n + k.
n*(n - 1)**2/3
Suppose 94 = -3*w + 112. Factor -4*q**3 + q + q**3 - w*q**2 - 4*q + 0*q**3.
-3*q*(q + 1)**2
Let 166 - 91 + 3*m**3 + 15*m**2 - 75 + 15*m - 57*m = 0. What is m?
-7, 0, 2
Let o(s) be the second derivative of s**5/30 - 5*s**4/9 - s**3/9 + 10*s**2/3 + 23*s + 2. What is f in o(f) = 0?
-1, 1, 10
Let u = 29/76 - -7/380. Factor -2/5*c - 2/5*c**2 + 2/5*c**4 + 0 + u*c**3.
2*c*(c - 1)*(c + 1)**2/5
Let y(p) = 2. Let h(l) = 4*l**3 - 12*l**2 - 40*l + 12. Let d(a) = -h(a) + 6*y(a). Determine u, given that d(u) = 0.
-2, 0, 5
Let d = -8 + 1. Let t be 9/((-12)/4) - d. Determine q, given that -t*q**2 + 3*q**3 + q + 7*q**2 - q = 0.
-1, 0
Let m(r) be the first derivative of 1/10*r**5 + 9 - 1/4*r**2 + 1/4*r**4 + 1/2*r - 1/12*r**6 - 1/3*r**3. Find a such that m(a) = 0.
-1, 1
Let a(r) be the first derivative of -r**4/36 - r**3 - 28*r**2/3 + 196*r/9 - 39. Factor a(n).
-(n - 1)*(n + 14)**2/9
Suppose 4*x - 18 = 3*d, 4*x + x = -4*d + 7. Solve 9*m**3 - 2*m**4 - m + 2*m**2 - 4*m**3 - m - 3*m**x = 0 for m.
-1, 0, 1
Let o(f) be the third derivative of -f**8/20160 - f**7/1260 - f**6/240 + 3*f**5/20 - 15*f**2. Let q(j) be the third derivative of o(j). Factor q(n).
-(n + 1)*(n + 3)
Suppose 40*x + 33*x = 219. Suppose -4 = -7*j + 10. Factor -j + 1/4*d**x - d + 1/2*d**2.
(d - 2)*(d + 2)**2/4
Let z be (1 + -1 + 0)/(-2). Let x = 1278 - 1275. Let 2/9*v**2 - 4/9*v - 2/9*v**4 + z + 4/9*v**x = 0. What is v?
-1, 0, 1, 2
Let x(z) = 100*z**3 + 5750*z**2 + 249615*z + 3577815. Let q(a) = 11*a**3 + 639*a**2 + 27735*a + 397535. Let v(r) = -55*q(r) + 6*x(r). Factor v(w).
-5*(w + 43)**3
Let s(w) be the first derivative of 0*w**2 + 3/2*w**4 - 22 + 0*w - 8/3*w**3. Solve s(k) = 0.
0, 4/3
Let w = 196/19 + -550/57. Factor 20/3*c**3 - 2/3 + w*c**5 - 10/3*c**4 + 10/3*c - 20/3*c**2.
2*(c - 1)**5/3
Let f(g) be the second derivative of g**5/10 - 59*g**4/10 - 22*g**3/3 + 72*g**2/5 - 11*g - 8. Find u, given that f(u) = 0.
-1, 2/5, 36
Factor 0*o**3 + 2*o - 108 + 3*o**3 - 4*o - o + 27*o**2 + 81.
3*(o - 1)*(o + 1)*(o + 9)
Let m(p) be the second derivative of p**9/1512 - p**8/280 + p**7/210 + 5*p**3/6 - 13*p. Let u(l) be the second derivative of m(l). What is h in u(h) = 0?
0, 1, 2
Let m(p) be the second derivative of p**6/15 - 3*p**5/5 + 2*p**4 - 10*p**3/3 + 3*p**2 - 60*p. Factor m(l).
2*(l - 3)*(l - 1)**3
Suppose -2*l - 2*m = 3*l - 100, -100 = -5*l + 5*m. Suppose 20 = -10*q + l. Determine g so that 1/4*g - 1/4*g**5 + 0*g**3 + 1/2*g**2 + q - 1/2*g**4 = 0.
-1, 0, 1
Let q(i) = i**3 - i**2 + 2*i + 2. Let g be q(-1). Let o be 3/9 + -2 - g. Determine t, given that -2/3*t**3 + 0*t**2 + 1/3*t**4 + 2/3*t - o = 0.
-1, 1
Let u(q) be the second derivative of -q**7/336 + q**6/240 + q**5/160 - q**4/96 - 32*q. Solve u(n) = 0 for n.
-1, 0, 1
Let s(v) be the first derivative of 2*v**5/5 + v**4/8 - 8*v**3/3 - v**2 - 524. Factor s(n).
n*(n - 2)*(n + 2)*(4*n + 1)/2
Let p(h) = -h**2 - 4*h - 2. Let d(s) be the second derivative of s**3/6 + 3*s. Let x(q) = -d(q) - p(q). Factor x(v).
(v + 1)*(v + 2)
Factor -4/7*m**2 - 576/7*m - 20736/7.
-4*(m + 72)**2/7
Let x(h) = -h**3 + 3*h**2 + 3*h + 7. Let j be x(4). Find z such that 19*z**2 + 12*z**j + 18*z**2 + 8 - 12*z - 41*z**2 - 4*z**4 = 0.
-1, 1, 2
Let p(y) = -y**2 + 16*y - 10. Let t be p(15). Factor 191*d**3 - 187*d**3 - 8*d**4 + 2*d**t + 2*d**4.
2*d**3*(d - 2)*(d - 1)
Suppose 2*w = 3*s + 1112, w - s - 60 = 496. Factor 4*a**2 + w - 3*a**3 - 556 - a**4.
-a**2*(a - 1)*(a + 4)
Suppose 1473 = 2*f + 1473. Let y(d) be the first derivative of 1/3*d**4 - 1 + f*d - 4/3*d**2 + 4/9*d**3. Solve y(z) = 0.
-2, 0, 1
Factor 2/23*g**2 + 28/23 + 18/23*g.
2*(g + 2)*(g + 7)/23
Let y(v) be the third derivative of 0 - 1/57*v**5 + 0*v**3 + 0*v + 28*v**2 - 1/1140*v**6 - 25/228*v**4. Factor y(t).
-2*t*(t + 5)**2/19
Let q(l) = -8*l**2 + 4*l - 6. Let x be q(-5). Let n = -221 - x. Factor 4/5*s**3 - 2/5*s + 2/5*s**4 - 2/5*s**n + 2/5 - 4/5*s**2.
-2*(s - 1)**3*(s + 1)**2/5
What is d in -2*d**5 - 12*d**2 + 43*d**3 - 27*d**3 + 12 - 112*d + 98*d = 0?
-3, -1, 1, 2
Let h = -34 - -54. Factor -10*k**2 + 6*k + 15*k**4 - 15*k**3 - h*k**4 - 6*k.
-5*k**2*(k + 1)*(k + 2)
Let f be (-1 + -2)*(-10)/15. Suppose -f = -3*z + 10. Factor 10*m - 11*m**z + 5*m**3 - 9*m**2 - 2 - 3*m + 10*m**4.
-(m - 2)*(m - 1)**3
Let l(b) = b**3 + 75*b**2 - 43*b**2 - 33*b**2. Let j(d) = 9*d**3