t g(k) be the third derivative of k**7/840 - k**6/60 - 7*k**5/120 - 7*k**3/3 + 11*k**2. Let p(l) be the first derivative of g(l). Solve p(b) = 0 for b.
-1, 0, 7
Let n be (90/(-56))/((-186)/496). Solve -3/7*k**2 + n*k - 75/7 = 0.
5
Determine a so that -118/11*a**2 + 0 - 116/11*a - 2/11*a**3 = 0.
-58, -1, 0
Let o = -3 - -17. Suppose 5*p + 15 = 0, -4*l + o = -4*p - 10. Factor 9/2*y**2 - 3/2*y - l.
3*(y - 1)*(3*y + 2)/2
Let 28/3*k**2 + 12 - 76/3*k**3 + 16/3*k**4 + 52*k = 0. What is k?
-1, -1/4, 3
Suppose 35 = s + 5*b, -5*s + 28 = -3*b - 7. Let q(c) = -s + c + 9 + 1. Let t(v) = -3*v**3 + 14*v + 6. Let h(j) = -5*q(j) + t(j). Factor h(y).
-3*(y - 2)*(y + 1)**2
Let s(g) = -g**2 + 547*g - 4. Let k(h) = -5*h**2 + 2185*h - 15. Let y(x) = -4*k(x) + 15*s(x). Let y(d) = 0. What is d?
0, 107
Let h(g) be the second derivative of g**7/147 - 3*g**6/35 + 3*g**5/10 - 19*g**4/42 + 2*g**3/7 - 450*g. Factor h(y).
2*y*(y - 6)*(y - 1)**3/7
Let x(w) be the second derivative of 5*w**7/42 - 5*w**6/6 + w**5 - 64*w. Determine d, given that x(d) = 0.
0, 1, 4
Let h(t) be the first derivative of t**5/10 + 27*t**4/8 - t**3/6 - 27*t**2/4 + 39. Factor h(y).
y*(y - 1)*(y + 1)*(y + 27)/2
Let c(o) be the third derivative of -o**8/2688 - o**7/1680 + o**6/160 + o**5/20 + 6*o**2. Let y(p) be the third derivative of c(p). Factor y(x).
-3*(x + 1)*(5*x - 3)/2
Suppose 0 = 2*b - 2 + 6. Let t be (-5)/b*42/35. Find k such that 24 + 3*k**2 - 24 - 3*k**t = 0.
0, 1
Let c = -2231/4 + 6697/12. Factor 0 - c*u**2 - u**3 + 0*u.
-u**2*(3*u + 1)/3
Suppose 22/3*g + 52/3 - 2/3*g**2 = 0. Calculate g.
-2, 13
Let u(z) be the first derivative of z**6/1440 - z**5/240 - 16*z**3/3 + 17. Let c(k) be the third derivative of u(k). Factor c(x).
x*(x - 2)/4
Let q(v) = 197*v**2 - 5*v - 2. Let g be q(-1). Let c = -195 + g. Factor 3/4*u**c + 12*u - 21/4*u**4 - 3 - 75/4*u**2 + 57/4*u**3.
3*(u - 2)**2*(u - 1)**3/4
Let c(j) be the first derivative of j**6/33 - 8*j**5/5 + 22*j**4 + 113. Factor c(l).
2*l**3*(l - 22)**2/11
Suppose d - 3*d = -4*h - 12, 3*d + h - 4 = 0. Factor -u**4 + 4*u**d - 3 - 53*u**3 + 2*u - 57*u**3 + 108*u**3.
-(u - 1)**2*(u + 1)*(u + 3)
Let y = -180 - -183. Suppose 0 + 2 = -2*a, -3*f + y = 3*a. Let 4/5 - 6/5*r - 2/5*r**f - 2/5*r**4 + 6/5*r**3 = 0. Calculate r.
-1, 1, 2
Solve 12*w**2 - 4*w**4 - 45 + 165*w**3 - 141*w**3 - 54*w + 11 - 10*w - 14 = 0.
-1, 2, 6
Let p be (-129)/172 + (2 - 44/(-16)). Let 13/6*u**3 - 1/3 - 19/6*u**2 + 11/6*u - 1/2*u**p = 0. What is u?
1/3, 1, 2
Let u(h) be the first derivative of -2*h**5/65 - 7*h**4/26 - 22*h**3/39 - 5*h**2/13 - 105. Factor u(p).
-2*p*(p + 1)**2*(p + 5)/13
Let n(g) be the second derivative of g**6/15 + 7*g**5/5 + 53*g**4/6 + 76*g**3/3 + 36*g**2 + 552*g. Factor n(r).
2*(r + 1)*(r + 2)**2*(r + 9)
Let q be (182/35 - 4) + 38/10. Let v(t) be the third derivative of -1/80*t**q - 1/96*t**6 + 5/96*t**4 + 0 - 3*t**2 + 0*t + 1/210*t**7 - 1/24*t**3. Factor v(w).
(w - 1)**2*(w + 1)*(4*w - 1)/4
Let a be 2/12 + (-70)/(-12). Suppose 3 = -3*m + a*m. Factor -m + 5*i - 5*i - 3*i**2 + i**3 + 3*i.
(i - 1)**3
Let i(y) be the first derivative of y**6/180 + 31*y**5/270 + 5*y**4/54 - 41*y**2/2 - 40. Let h(t) be the second derivative of i(t). Factor h(o).
2*o*(o + 10)*(3*o + 1)/9
Let z = -23033/3 + 7746. Let i = z + -68. Factor i*q + 0 + q**2.
q*(3*q + 1)/3
Let l(b) be the third derivative of b**8/1848 + 2*b**7/1155 - b**5/165 - b**4/132 - 330*b**2. Suppose l(y) = 0. What is y?
-1, 0, 1
Let f(n) be the first derivative of -1/2*n**4 + 11 + 0*n**2 + 0*n + 2*n**3. Solve f(h) = 0.
0, 3
Let c(n) be the second derivative of -n**4/42 - 3*n**3/7 - 2*n**2 + 3*n - 12. Factor c(h).
-2*(h + 2)*(h + 7)/7
Let r be (-10)/(-3) + -1 + -1. Suppose 8*v = 4*v + 5*w + 8, -4*w = 0. Suppose -r*o - 2/3*o**v - 2/3 = 0. Calculate o.
-1
Let r(w) = 1915*w - 1912. Let l be r(1). Let 12/7*g**l + 0 + 3/7*g**4 + 0*g + 12/7*g**2 = 0. What is g?
-2, 0
Let a(n) be the second derivative of -n**4/16 + 67*n**3/4 - 13467*n**2/8 - 381*n - 1. Determine f, given that a(f) = 0.
67
Let s(n) be the second derivative of -1/102*n**4 - 4/17*n**2 - 4/51*n**3 + 12*n + 0. Factor s(v).
-2*(v + 2)**2/17
Find n, given that -84*n**4 + n**3 - n**3 - 3*n**2 + 87*n**4 = 0.
-1, 0, 1
Let y(i) be the second derivative of 0 + 1/147*i**7 + 0*i**4 + 0*i**2 + 2/105*i**6 + 1/70*i**5 - i + 0*i**3. Suppose y(k) = 0. What is k?
-1, 0
Let h(p) be the first derivative of -2/15*p**5 + 0*p + 2/9*p**3 - 1/9*p**6 + 5 + 1/6*p**4 + 0*p**2. Factor h(k).
-2*k**2*(k - 1)*(k + 1)**2/3
Let t be (-2)/(-2) + (-172)/12 + 15. Let -5*i**2 - t + 5/3*i**3 + 5*i = 0. Calculate i.
1
Suppose 2*r - p - 8 = -2, -2 = -5*r - 4*p. Let q(m) be the first derivative of 10 - m**r + 0*m + 2/3*m**3. Determine n, given that q(n) = 0.
0, 1
Let t = -4 + 7. Suppose t*v = -v + 8. Factor 0*g**3 + 5*g**3 - g**3 - v + 6*g**2.
2*(g + 1)**2*(2*g - 1)
Let o(d) = -5*d**2 - 20*d - 31. Let k = -14 - -17. Suppose 2*x = -k - 1. Let u(m) = m**2 + 4*m + 6. Let p(q) = x*o(q) - 11*u(q). Factor p(h).
-(h + 2)**2
Let q be (13 - 63/5) + -3 + 3. Factor -12/5 + 2/5*v + q*v**2.
2*(v - 2)*(v + 3)/5
Determine i so that 2*i**4 + 46 - 23*i + 338 - 44*i**3 - 440*i**2 + 57*i + 142*i + 336*i**2 = 0.
-2, 2, 24
Suppose v - 5 = -p, 10*v - 5*v + 2 = 4*p. Let y be (6 - 3)/(-18)*(-4)/v. Factor 1/3 - 1/3*n + y*n**3 - 1/3*n**2.
(n - 1)**2*(n + 1)/3
Suppose 0 + 11/4*j + 1/4*j**3 - 3*j**2 = 0. Calculate j.
0, 1, 11
Suppose -4*i + 4*q - 2*q = -30, q = -3. Let p be (-43)/(-129) - ((-7)/i + 1). Determine c, given that 0 + p*c + 0*c**2 - 1/2*c**3 = 0.
-1, 0, 1
Let y(u) be the first derivative of 4*u**3/3 + 52*u**2 + 276*u + 179. Determine q so that y(q) = 0.
-23, -3
Let a = -27 + 31. Factor 2*b + 2*b**3 - b**3 - a*b + b**3 + 4 - 4*b**2.
2*(b - 2)*(b - 1)*(b + 1)
Let z(w) be the first derivative of 5*w**3 - 3*w**2/2 - 18*w/5 - 139. Determine a so that z(a) = 0.
-2/5, 3/5
Let d(w) = 2*w**4 - 3*w**3 - 2*w**2 + 3*w - 3. Let u(s) = s**3 - s + 1. Suppose -5 = p + 3. Let k = p + 9. Let i(g) = k*d(g) + 3*u(g). Let i(q) = 0. What is q?
-1, 0, 1
Let f(i) be the first derivative of i**5/70 + i**4/14 + 2*i**3/21 + 5*i + 10. Let g(m) be the first derivative of f(m). Factor g(h).
2*h*(h + 1)*(h + 2)/7
Let t be ((-2)/4)/(7/2968) - -1. Let g = -207 - t. Factor 0 - 3/5*m**3 + 3/5*m**g - 3/5*m**2 + 0*m + 3/5*m**5.
3*m**2*(m - 1)*(m + 1)**2/5
Let w(v) be the second derivative of v**5/4 + 25*v**4/4 + 65*v**3/3 + 155*v - 1. Factor w(l).
5*l*(l + 2)*(l + 13)
Let k(m) = -3*m**3 + 8*m**2 + 11*m - 5. Let q(p) = 4*p + 10. Let b be q(0). Let f(y) = y**3 - 4*y**2 - 5*y + 2. Let u(l) = b*f(l) + 4*k(l). Factor u(n).
-2*n*(n + 1)*(n + 3)
Suppose 0 = -g - 2*g + f, 0 = -4*g + 5*f. Suppose g = -3*u - 3*u. Suppose u + 1/4*d**2 - 1/2*d = 0. Calculate d.
0, 2
Suppose 2*m = -2 + 8. Factor 1 - 36*c**m - 12*c**2 - 1 - 15*c**2 - 12*c**4.
-3*c**2*(2*c + 3)**2
Let u(k) be the second derivative of -1/20*k**5 + 0 + 1/40*k**6 + 0*k**3 - 1/4*k**4 - 3*k + 1/2*k**2. Let d(y) be the first derivative of u(y). Factor d(o).
3*o*(o - 2)*(o + 1)
Let d(w) be the second derivative of 2/5*w**6 - 13*w + 0 + 3/10*w**5 - 9/2*w**3 - 3*w**4 - 1/14*w**7 + 0*w**2. Let d(c) = 0. What is c?
-1, 0, 3
Let j = -15 - -17. Suppose j*m = -0*m + 10. Suppose 13 - 56*t**3 - 82*t**2 + 81*t**4 + 241*t**2 - 72*t - 1 - 15*t**m - 109*t**3 = 0. Calculate t.
2/5, 1, 2
Let h = -7 + 8. Let b(k) = 3*k**2 + 12*k. Let c(q) = -q. Let i(v) = h*b(v) + 12*c(v). Factor i(d).
3*d**2
Let a(v) = -3*v**2 - v - 11. Let k(s) = 2*s**2 - 2*s + 12. Let c(o) = -4*a(o) - 5*k(o). Factor c(n).
2*(n - 1)*(n + 8)
Let u = 46 + -44. Factor 3 + 3*t**u - 2*t**2 + 8*t + 13 + 0*t**2.
(t + 4)**2
Factor -5*v**2 - 17626 + 355*v - 24694 - 1275*v.
-5*(v + 92)**2
Let l(x) be the second derivative of 8*x + 0 + 2/15*x**3 + 0*x**2 + 1/60*x**4. Solve l(h) = 0.
-4, 0
Let m(d) be the second derivative of -d**7/42 + d**6/10 - d**5/10 - d**4/6 + d**3/2 - d**2/2 + 2*d - 85. What is j in m(j) = 0?
-1, 1
Let g be ((48/26)/2)/2. Let n = -31716/13 + 2440. Factor g - n*q - 2/13*q**2.
-2*(q - 1)*(q + 3)/13
Factor -4/3*z**3 + 6*z**2 - 20/3*z - 1/3*z**4 + 7/3.
-(z - 1)**3*(z + 7)/3
Let u(j) be the third derivative of j**8/504 - 8*j**7/315 + j**6/15 - 2*j**2 + 406*j. Solve u(q) = 0.
0, 2, 6
Let n(k) be the second derivative of k**7/84 - k**6/10 + k**5/10 + k**4/4