What is n in g(n) = 0?
0, 1
Let z(r) be the third derivative of -r**7/140 + r**6/40 - r**5/40 - 2*r**3/3 - 8*r**2. Let f(a) be the first derivative of z(a). Factor f(x).
-3*x*(x - 1)*(2*x - 1)
Suppose -h + 16 = 3*h. Suppose -x + h + 2 = 4*d, -x = 3*d - 4. Factor -w**4 + d*w**3 - 2*w - 1 + 2 + 0*w**4.
-(w - 1)**3*(w + 1)
Let b(g) be the first derivative of -g**5/10 + g**4/3 - g**3/3 - 2*g + 3. Let t(a) be the first derivative of b(a). Factor t(v).
-2*v*(v - 1)**2
Let n = 382/153 - -1/306. Determine r, given that n*r**3 + 9/2*r**2 + 1/2*r**4 + 1 + 7/2*r = 0.
-2, -1
Let y(k) be the third derivative of k**7/3780 - k**6/1080 - k**4/24 + k**2. Let o(s) be the second derivative of y(s). Factor o(n).
2*n*(n - 1)/3
Let t(w) be the second derivative of -w**4/10 - w**3/15 + 2*w**2/5 + 21*w. Factor t(m).
-2*(m + 1)*(3*m - 2)/5
Let b(u) = 3*u**3 + u. Let d be b(1). Let c = 15 + -11. Factor -p**3 - d*p**4 + 2*p - p**3 + 2*p**2 + 2*p**c.
-2*p*(p - 1)*(p + 1)**2
Let t = 3/278 + -2837/5282. Let b = t - -59/76. Find v, given that b*v**2 + 0 - 1/2*v - 1/4*v**4 - 1/4*v**5 + 3/4*v**3 = 0.
-2, -1, 0, 1
Let s(w) = 17*w**3 - 97*w**2 + 277*w - 277. Let j(v) = 9*v**3 - 49*v**2 + 139*v - 139. Let a(l) = 7*j(l) - 4*s(l). Let a(z) = 0. What is z?
3
Let x be ((-2)/8*0)/1. Suppose x = 2*z + 2*l - 0*l - 8, 16 = -z + 4*l. Find w, given that -1/3*w**4 + z*w + 0*w**2 - 2/3*w**3 + 0 = 0.
-2, 0
Let b(m) be the first derivative of m**4/6 - 2*m**3/9 - 4*m**2/3 + 8*m/3 + 1. Factor b(g).
2*(g - 2)*(g - 1)*(g + 2)/3
Suppose 0 = 3*p - p + p. Suppose 3*b = 4*b. Find k such that p*k + b + 2/7*k**2 = 0.
0
Let k = -122 + 54. Let b = k + 206/3. Solve 0 - b*f**2 + 0*f = 0 for f.
0
Let b be (-6)/(-10)*5435/(-7). Let g = b - -467. Determine r, given that -2/7 - 6/7*r + g*r**2 = 0.
-1/4, 1
Let y = -395 - -3557/9. Factor 0*x + y*x**3 - 2/9*x**4 + 0*x**2 + 0.
-2*x**3*(x - 1)/9
Let r be -3 + (-4)/5 - -4. Solve r*d**3 + 0*d**2 - 1/5*d + 0 = 0.
-1, 0, 1
Let c(a) be the second derivative of -a**6/105 + a**5/70 + a**4/21 + 15*a. Factor c(k).
-2*k**2*(k - 2)*(k + 1)/7
Let r = 2/541 + 511/8115. Let c(m) be the third derivative of -r*m**5 - 1/60*m**6 - 1/12*m**4 + 0*m**3 - m**2 + 0*m + 0. Suppose c(x) = 0. What is x?
-1, 0
Factor 5*p**2 - 6*p**2 + 5*p**2 + 8*p.
4*p*(p + 2)
Let a(n) be the third derivative of -n**9/30240 - n**8/1120 - 3*n**7/280 - 3*n**6/40 + n**5/30 - 6*n**2. Let q(i) be the third derivative of a(i). Factor q(l).
-2*(l + 3)**3
Factor 28*r**4 - r**4 - 3*r**5 + 34*r**2 - 81*r**3 + 32*r**2 + 15*r**2.
-3*r**2*(r - 3)**3
Let x = 358 - 1787/5. Factor -6/5*n**2 + x*n**3 + 3/5*n + 0.
3*n*(n - 1)**2/5
Let t(w) = w**3 + 6*w**2 + 7*w + 5. Let j be t(-5). Let c(x) = -x - 5. Let r be c(j). Let 4*l + 3*l**4 - 4*l**3 - 3*l**2 + r*l**2 + l**3 - l = 0. Calculate l.
-1, 0, 1
Let u(j) = -j**3 + j**2 - j - 1. Let q(r) = -2*r**4 + 14*r**3 + 46*r**2 + 18*r - 4. Let k(v) = -q(v) + 4*u(v). Suppose k(b) = 0. What is b?
-1, 0, 11
Let v(k) be the third derivative of 0*k - 1/40*k**6 + 0 - 2*k**3 - k**4 + 5*k**2 - 1/4*k**5. Factor v(u).
-3*(u + 1)*(u + 2)**2
Let k(g) = 135*g**2 - 215*g + 80. Let u(r) = -5*r**2 + 8*r - 3. Let b(l) = 2*k(l) + 55*u(l). Factor b(a).
-5*(a - 1)**2
Let z(b) = b**3 + 9*b**2 + 2. Let g be z(-9). Let y = -15 + 18. Suppose c**5 - 4*c**y + c**5 + 10*c**5 - g*c**2 + 10*c**4 = 0. Calculate c.
-1, -1/3, 0, 1/2
Find g such that -2/5*g**2 - 2/5*g + 0 + 2/5*g**4 + 2/5*g**3 = 0.
-1, 0, 1
Let h be (-46)/18 - (13 + -5 + -11). Determine b so that -h + 14/9*b + 2/3*b**3 - 16/9*b**2 = 0.
2/3, 1
Determine z so that 14/3*z**3 + 0*z + 4/3*z**2 - 8/3*z**4 + 0 = 0.
-1/4, 0, 2
Let c(r) = -7*r**2 - 8*r - 13. Let v(o) = 8*o**2 + 8*o + 14. Let f(g) = 6*c(g) + 5*v(g). Factor f(l).
-2*(l + 2)**2
Let a be (1 - -1)/((-21)/249). Let y = a + 24. Factor -8/7*j**2 - 4/7 - y*j**3 - 10/7*j.
-2*(j + 1)**2*(j + 2)/7
Let o(u) be the second derivative of -u**8/2240 + u**7/840 + u**6/120 - u**4/6 - 4*u. Let j(n) be the third derivative of o(n). Find b such that j(b) = 0.
-1, 0, 2
Let d(i) = -219*i**3 + 111*i**2 - 21*i + 4. Let z(x) = 220*x**3 - 112*x**2 + 22*x - 5. Let w(h) = 4*d(h) + 3*z(h). Suppose w(b) = 0. Calculate b.
1/6
Let s(f) be the first derivative of -2*f**5/5 + 4*f**3/3 - 2*f - 2. Factor s(m).
-2*(m - 1)**2*(m + 1)**2
Let z = 1/2 + -3/10. Find x such that -2/5*x**3 + z - 2/5*x**2 + 1/5*x + 1/5*x**5 + 1/5*x**4 = 0.
-1, 1
Let v = -48 + 195/4. Determine t, given that -v + 3/4*t**2 + 9/4*t**3 - 9/4*t = 0.
-1, -1/3, 1
Let g = 17 + -17. Let r(f) be the third derivative of -1/36*f**4 + 1/180*f**6 + 0*f**3 - 1/90*f**5 - 2*f**2 + g + 0*f + 1/315*f**7. Factor r(m).
2*m*(m - 1)*(m + 1)**2/3
Let i(o) be the third derivative of o**8/560 - 2*o**7/175 - 3*o**6/200 + 7*o**5/50 - o**4/5 - 33*o**2. Suppose i(n) = 0. Calculate n.
-2, 0, 1, 4
Let g(o) be the second derivative of o**10/90720 + o**9/22680 - o**7/3780 - o**6/2160 + o**4/4 + 4*o. Let k(h) be the third derivative of g(h). Factor k(l).
l*(l - 1)*(l + 1)**3/3
Let 4*c - 26*c**4 + 0*c**4 - 9*c**5 - 18*c**3 + 2*c**2 - c**5 = 0. Calculate c.
-1, 0, 2/5
Let f(c) be the first derivative of c**5/20 - 3*c**4/4 + 9*c**3/2 - 7*c**2/2 + 5. Let m(w) be the second derivative of f(w). Find u such that m(u) = 0.
3
Let c(v) = 2*v**3 - 3*v**2 + 2*v - 3. Let m be c(2). Determine p so that 2*p**m - 2 + 3*p**2 + p**2 - 2*p - 4*p**4 + 2 = 0.
-1, 0, 1
Suppose 0 = -4*z + 20 - 0. Suppose -z*s = -3*n - 30, -4*s - 2*n + 12 + 12 = 0. Determine r so that 4*r**5 - 3*r**3 + 4*r**4 + s*r**2 - r - 7*r**2 - 3*r**2 = 0.
-1, -1/2, 0, 1
Factor 1/3 - 2/9*q**2 + 5/9*q.
-(q - 3)*(2*q + 1)/9
Let p(k) = -3*k**2 - k + 2. Let x(l) = -3*l**2 - 2*l + 1. Suppose 2*v - 15 = 5*v. Let i(d) = v*x(d) + 4*p(d). Factor i(j).
3*(j + 1)**2
Let d(m) be the first derivative of 8*m**7/105 + m**6/10 - m**5/3 - m**4/2 + 2*m**3/3 + 7*m**2/2 - 6. Let v(r) be the second derivative of d(r). Solve v(j) = 0.
-1, 1/4, 1
Let t be 3/(4 - 7) - -5. Suppose -f + 2 = -0*f. Find o such that -5*o + 4*o**2 - t*o**2 + 5*o**f + 3*o = 0.
0, 2/5
Let q(i) be the second derivative of i**8/112 + i**7/35 + i**6/40 - 2*i**2 - 5*i. Let l(z) be the first derivative of q(z). Factor l(a).
3*a**3*(a + 1)**2
Let j = 4633/3 - 1500. Let m = j + -44. Determine o so that m - 2/3*o + 1/3*o**2 = 0.
1
Let l be ((-21)/(-80))/(6/4). Let p(g) be the second derivative of l*g**5 + 1/30*g**6 + 3/8*g**4 - g + 5/12*g**3 + 1/4*g**2 + 0. Factor p(v).
(v + 1)**3*(2*v + 1)/2
Let z = -35 - -37. Let k(b) be the second derivative of 0 - 1/4*b**3 - 1/24*b**4 - 1/2*b**z - 3*b. Suppose k(u) = 0. Calculate u.
-2, -1
Let i be ((-6)/15)/((-1)/5). Find y, given that 0 - y**3 - 1/3*y + 1/3*y**4 + y**i = 0.
0, 1
Find m such that -m**2 + 1799*m**4 - 6*m**3 - 1797*m**4 - 2*m + 7*m**2 = 0.
0, 1
Let n(p) = -11*p**2 - 5*p + 10. Let v(t) = 7*t**2 + 3*t - 7. Let c(j) = 5*n(j) + 8*v(j). Suppose c(g) = 0. Calculate g.
-2, 3
Let u(h) be the third derivative of 0 + 0*h + 2*h**2 + 0*h**4 - 1/60*h**6 + 0*h**3 + 1/30*h**5. Suppose u(b) = 0. What is b?
0, 1
Factor 2/11*v**2 + 2/11 - 4/11*v.
2*(v - 1)**2/11
Let d = -2282/13 + 723420/4121. Let p = 3184/2219 - d. Suppose 2/7 - 8/7*o**4 + 10/7*o + 6/7*o**2 - p*o**3 = 0. What is o?
-1, -1/4, 1
Let g be ((-4)/(-3))/(2/6). Let d = -96 - -100. Factor g*f**2 - 6*f**2 + 2*f**2 - 2*f**d + 2*f**3 + 2*f**2 - 2*f.
-2*f*(f - 1)**2*(f + 1)
Let y(w) be the first derivative of -3*w**6/2 - 6*w**5/5 + 21*w**4/4 - 2*w**3 + 4. Solve y(h) = 0.
-2, 0, 1/3, 1
Suppose 18*y = 16*y. Let u(h) be the third derivative of 0*h**4 + 1/9*h**3 - 3*h**2 - 1/90*h**5 + 0 + y*h. Factor u(p).
-2*(p - 1)*(p + 1)/3
Factor 0 + 30/7*d + 2/7*d**2.
2*d*(d + 15)/7
Let a(v) be the third derivative of v**8/1680 + v**7/420 - v**5/60 - v**4/24 + v**3/6 + 4*v**2. Let d(s) be the first derivative of a(s). Factor d(z).
(z - 1)*(z + 1)**3
Let g(l) = l**3 - l**2 - l + 1. Suppose 0*v = -3*v, 0 = -5*m - 3*v + 10. Let f(r) = 2*r**3 - r + 1. Let x(c) = m*g(c) - 2*f(c). Factor x(p).
-2*p**2*(p + 1)
Let d(o) be the third derivative of o**8/110880 - o**7/4620 + o**6/440 - o**5/20 + o**2. Let c(n) be the third derivative of d(n). Solve c(r) = 0.
3
Let m = 1/3 + 1/6. Let f(h) be the first derivative of h**2 - 2/3*h**3 - 3 - m*h**4 + 2*h. Factor f(d).
-2*(d - 1)*(d + 1)**2
Find h such that -h**3 + 4*h**5 + 0*h**5 - 55*h*