e of -1/40*c**5 + 1/8*c**4 + 0 - 1/4*c**3 + 4*c + 1/4*c**2. What is n in r(n) = 0?
1
Let k = 6 + -4. Let p(n) be the second derivative of -1/2*n**5 + 2*n + 56/15*n**3 + 0 - 11/6*n**4 - 12/5*n**k. Factor p(f).
-2*(f + 3)*(5*f - 2)**2/5
Let k = -10852/7 + 53993/35. Let y = k - -59/7. Factor y*t - 2/5*t**2 + 0.
-2*t*(t - 2)/5
Let k be (-1)/((-2)/(-4)) - 222/(-21). Let o = k + -113/14. What is r in 3/2*r**2 + o*r + 0 - 1/2*r**3 - 3/2*r**4 = 0?
-1, -1/3, 0, 1
Let k(u) = 2*u**3. Let o(l) = 4*l**3. Suppose -21*g + 20*g = 11. Let f(z) = g*k(z) + 6*o(z). Suppose f(y) = 0. What is y?
0
Let c(j) be the third derivative of -1/12*j**4 + 18*j**2 + 0*j - 1/30*j**5 + 0 + 0*j**3. Factor c(z).
-2*z*(z + 1)
Factor -3/5*l**2 - 24/5 + 27/5*l.
-3*(l - 8)*(l - 1)/5
Let j(y) = 8*y**4 - 12*y**3 + 4*y**2 - 6*y + 6. Let n(a) = -a**4 + 2*a**2 + a - 1. Let v(r) = -j(r) - 6*n(r). Factor v(g).
-2*g**2*(g - 4)*(g - 2)
Let k(o) = o + 3. Let u be k(1). Let t(f) = 5*f**2 + 11*f - 12. Let x(c) = 11*c**2 + 23*c - 25. Let z(q) = u*x(q) - 9*t(q). Find r such that z(r) = 0.
-8, 1
Let w(d) = -3*d**2 - 39*d + 66. Let h(k) = 3*k + 1. Let v(s) = 6*h(s) - w(s). Solve v(x) = 0 for x.
-20, 1
Factor -32/3 + 8*y**4 + 20*y - 64/3*y**3 + 8/3*y**2 + 4/3*y**5.
4*(y - 1)**3*(y + 1)*(y + 8)/3
Let a be (4/(-3))/((-3)/(-447)*42). Let f = -40/9 - a. Find j, given that f*j**3 + 2/7 + 6/7*j**2 + 6/7*j = 0.
-1
Determine n, given that -128/11*n**5 - 12788/11*n + 51890/11*n**2 - 72152/11*n**3 + 544*n**4 + 1058/11 = 0.
1/4, 23
Let n(s) be the first derivative of s**6/3 - 4*s**5/5 - 2*s**4 + 16*s**3/3 + 154. Determine t, given that n(t) = 0.
-2, 0, 2
Let u(j) be the second derivative of -4*j**6/45 + 4*j**5/15 - 5*j**4/18 + j**3/9 + 49*j. Factor u(i).
-2*i*(i - 1)*(2*i - 1)**2/3
What is n in -16*n**4 - 4*n**4 - 220*n**2 + 315*n**3 - 43*n - 32*n = 0?
-1/4, 0, 1, 15
Let w(y) = y**2 + 3*y + 2. Let k be w(-4). Factor 3*b**2 + k*b**3 + 2*b**5 + 22*b**4 - 3*b**2 - 30*b**4.
2*b**3*(b - 3)*(b - 1)
Let o = 165 + -165. Suppose u - 2*b = 2*u - 76, 5*u - 356 = 2*b. Find j such that -6 - 36*j**5 + 112*j**3 + o*j**5 - 3 + u*j**2 + 1 - 12*j = 0.
-1, -1/3, 1/3, 2
Let x = 9 - 5. Let w = 2 + x. Let a(m) = m**2 - m + 1. Let s(c) = 3*c**3 - 18*c**2 + 21*c - 12. Let i(n) = w*a(n) + s(n). Factor i(k).
3*(k - 2)*(k - 1)**2
Let f(r) = -r - 17. Let u be f(-7). Let t be (2 + ((-18)/8)/1)*u. Solve 5/2*q**3 + 1/4*q**5 + 5/4*q**4 + 1/4 + t*q**2 + 5/4*q = 0.
-1
Suppose 204 = -l + 208. Let k(x) be the second derivative of 0 + 0*x**2 - 2*x + 0*x**l + 1/45*x**6 + 0*x**5 + 0*x**3. Suppose k(v) = 0. Calculate v.
0
Suppose -27*z + 22*z = -155. What is s in -z + 4*s**2 - 4*s**4 + 31 = 0?
-1, 0, 1
Find v such that v**2 + 1915 - 193*v + 3*v**2 + 1685 - 47*v = 0.
30
Suppose 0 = 5*f - 5*t - 0*t - 40, -3*t = 4*f + 3. Let c(n) = -n**3 - 8*n**2 - n - 5. Let i be c(-8). Factor -5*g**2 - i + f + 3*g**2 + 2.
-2*(g - 1)*(g + 1)
Let u(d) be the third derivative of -d**5/240 - d**4/96 + d**3/4 + 34*d**2. Let u(y) = 0. What is y?
-3, 2
Suppose -2*m = 65 - 69. Let a(b) be the second derivative of -1/27*b**3 + 0*b**4 - b + 0 + 1/90*b**5 + 0*b**m. Factor a(z).
2*z*(z - 1)*(z + 1)/9
Suppose 5*m - 18 = 3*k, 6*m = 10*m - 4*k - 16. Solve 9/2*r**2 - 3/2*r + 3/2*r**m - 3 - 3/2*r**4 = 0 for r.
-1, 1, 2
Let f(g) be the third derivative of -g**11/1330560 + g**9/120960 - g**7/20160 + 13*g**5/30 - 6*g**2. Let p(i) be the third derivative of f(i). Factor p(z).
-z*(z - 1)**2*(z + 1)**2/4
Suppose 0 = 4*o + 4*c - 152 + 144, 3*c = -5*o + 8. Factor -o + 1/3*r**4 + 4/3*r - 4/3*r**3 + 2/3*r**2.
(r - 3)*(r - 1)**2*(r + 1)/3
Let n(z) be the second derivative of -z**5/15 - z**4/9 + 20*z**3/9 - 16*z**2/3 - 29*z. Factor n(v).
-4*(v - 2)*(v - 1)*(v + 4)/3
Let k(o) = -o**2 + 4*o + 6. Let s be k(5). Suppose -2*f + 5 = s. Suppose 1/4*u**f + 0*u + 0 + 1/4*u**4 - 1/2*u**3 = 0. What is u?
0, 1
Let x(o) be the first derivative of -3*o**4/8 + 3*o**3 - 33*o**2/4 + 9*o + 206. Factor x(h).
-3*(h - 3)*(h - 2)*(h - 1)/2
Let s(p) be the second derivative of -3*p**5/100 - 13*p**4/20 - 19*p**3/10 + 99*p**2/10 - 287*p + 2. Factor s(i).
-3*(i - 1)*(i + 3)*(i + 11)/5
Determine u, given that -4/11*u**3 + 2/11*u**4 + 16/11*u - 6/11*u**2 - 8/11 = 0.
-2, 1, 2
Let a be (1/3 - 0)/((-7)/(-84)). Suppose 3*k = a + 2. Factor 2*n**4 + 0 - 7/6*n**5 - 1/2*n**3 + 0*n - 1/3*n**k.
-n**2*(n - 1)**2*(7*n + 2)/6
Let o = 54142/3 - 18046. Factor 0*z + 0 + o*z**4 - 2/3*z**2 + 1/3*z**3 - z**5.
-z**2*(z - 1)**2*(3*z + 2)/3
Let q(d) = -6*d - 2. Let r(k) = 2*k + 1. Let f(o) = -3*q(o) - 10*r(o). Let i be f(-3). Factor 4/5 + 2/5*w**i - 6/5*w.
2*(w - 2)*(w - 1)/5
Let l(o) be the second derivative of -2*o**7/147 + 2*o**6/35 + 8*o**5/35 - 8*o**4/7 - 32*o**3/21 + 96*o**2/7 - 20*o - 1. Solve l(h) = 0 for h.
-2, 2, 3
Let j be 22960/(-3936)*(2/(-7) - 0). Let c be 1*(0 + 1 + 2). Factor 0 - 10*u**2 - j*u**c - 15*u.
-5*u*(u + 3)**2/3
Let x(i) be the first derivative of -4*i**4 + 28*i**3 - 42*i**2 + 16*i - 72. Solve x(g) = 0 for g.
1/4, 1, 4
Let z(k) = 34*k - 28. Let f be z(7). Let s = -198 + f. Suppose s + 8*g + 4/3*g**2 = 0. What is g?
-3
Solve 16/5*l**2 + 12/5*l - 8/5*l**5 + 2/5 - 18/5*l**4 - 4/5*l**3 = 0.
-1, -1/4, 1
Suppose 41*v - 200 = 46. Let n(w) be the first derivative of v + 0*w**3 - 1/10*w**5 - 5/16*w**4 + 1/2*w + 5/8*w**2. Find f such that n(f) = 0.
-2, -1, -1/2, 1
Let c(n) = -3 - n + 1 + 21. Let u be c(17). Factor 5/2*j**4 + 5*j - 5/2 + 0*j**u - 5*j**3.
5*(j - 1)**3*(j + 1)/2
Let y(o) be the second derivative of 0 + 1/84*o**4 - 2*o + 2/7*o**2 - 5/42*o**3. Factor y(d).
(d - 4)*(d - 1)/7
Let h = -25 + 25. Let i(p) be the first derivative of -3/4*p**4 + 3 + 0*p**3 + h*p + 0*p**2 - 3/5*p**5. Factor i(f).
-3*f**3*(f + 1)
Solve 27/2 - 650*a**3 + 1089*a**2 - 234*a + 625/6*a**4 = 0 for a.
3/25, 3
Let i(a) be the first derivative of 3*a**5/10 + 9*a**4/8 + 3*a**3/2 + 3*a**2/4 + 413. What is x in i(x) = 0?
-1, 0
Let s be (0 + (-2)/4)/(-34 + (-1800)/(-54)). Factor 0 + 3/4*q**2 - s*q.
3*q*(q - 1)/4
Let -10*r**3 + 5*r**5 + 0*r**5 + r - 3*r + 5*r**4 + 2*r = 0. Calculate r.
-2, 0, 1
Let a(d) be the first derivative of -50*d**6/3 - 112*d**5 - 261*d**4 - 216*d**3 + 97. Factor a(s).
-4*s**2*(s + 2)*(5*s + 9)**2
Let i(t) be the second derivative of t**5/60 - t**3/6 - t**2/3 - 10*t + 2. Factor i(p).
(p - 2)*(p + 1)**2/3
Let p = 56487359/517 + -109260. Let o = 3/47 - p. Factor o*n**2 + 4/11*n - 2/11*n**3 + 0.
-2*n*(n - 2)*(n + 1)/11
Find a such that -28/9 + 2*a - 2/9*a**2 = 0.
2, 7
Let c(w) be the third derivative of w**7/490 - 9*w**6/280 + w**5/5 - 9*w**4/14 + 8*w**3/7 + 7*w**2 - 5*w. Solve c(m) = 0.
1, 2, 4
Suppose -8*q = -211 + 19. Let y be ((q/14)/(-3))/(4/(-6)). Factor 0 + y*d - 2/7*d**2.
-2*d*(d - 3)/7
Let f be -5*(12/(-10) - -2). Let l be f/(-10) + (0 - (-4)/(-10)). Find s such that -1/3*s**5 + l + 0*s + s**3 - 2/3*s**2 + 0*s**4 = 0.
-2, 0, 1
Suppose 0 = 5*t - 2*h - 6, 3*t + 9*h - 4*h = -15. Determine y so that 2/11*y**4 - 6/11*y**2 + t*y**3 + 4/11*y + 0 = 0.
-2, 0, 1
Let w(l) be the second derivative of 4/15*l**4 + 2*l**3 - 1 + 22*l - 8/5*l**2. Let w(a) = 0. What is a?
-4, 1/4
Suppose 2*n - 14 = x - 4, x + n = 5. Factor 0*s**3 + 2/3*s**4 - 1/3*s**5 + 1/3*s - 2/3*s**2 + x.
-s*(s - 1)**3*(s + 1)/3
Let -25/2*z**3 + 0 + 5/2*z**2 + 25/2*z - 5/2*z**4 = 0. Calculate z.
-5, -1, 0, 1
Let y(c) be the first derivative of -c**4/6 - 4*c**3/9 + c**2/3 + 4*c/3 + 409. Determine s so that y(s) = 0.
-2, -1, 1
Let n(k) = -4*k**3 + 31*k**2 + 17*k - 300. Let g(p) = -8*p**3 + 63*p**2 + 33*p - 600. Let j(l) = 3*g(l) - 7*n(l). Factor j(m).
4*(m - 5)**2*(m + 3)
Suppose 0 = 3*a - 0*a - 201. Suppose a + 2*h + 2*h - h**2 - 55 = 0. Calculate h.
-2, 6
Factor -5*h**3 + 0*h**2 - 29694*h**4 + 2*h**5 + 29695*h**4 + 2*h**2.
h**2*(h - 1)*(h + 2)*(2*h - 1)
Let t be 21/294*(-2)/35. Let o = t + 99/245. Let 2/5*v**4 - 2/5*v**2 + o*v**5 + 0*v + 0 - 2/5*v**3 = 0. Calculate v.
-1, 0, 1
Let j(h) be the first derivative of h**4/7 + 64*h**3/21 - 38*h**2/7 - 136*h/7 + 348. Determine g, given that j(g) = 0.
-17, -1, 2
Let s(h) be the second derivative of -4*h**6/165 - h**5/10 - 3*h**4/22 - h**3/33 + h**2/11 + 20*h. Factor s(y).
-2*(y + 1)**3*(4*y - 1)/11
Let p(b) be the second derivative of 0 - 10*b - 1/3*b**4 + 0*b**2 - 1/42*b**7 + 2/3*b**3 - 3/20*b**5 + 2/15*b**6. Factor p(k).
-k*(k 