Let a = -66 - -316. Let v = -1246/5 + a. Solve -2/5 - 2/5*s**4 + v*s**2 + 2*s**3 - s**5 - s = 0.
-1, -2/5, 1
Let a(f) be the first derivative of -f**5/140 + 13*f**4/84 - 153*f + 138. Let c(g) be the first derivative of a(g). Factor c(u).
-u**2*(u - 13)/7
Let l(t) = 2*t**2 + 1. Let w(k) = -3*k**4 + 2*k**3 + 9*k**2 + 4. Suppose 5*d + 1 - 6 = 0. Let h(v) = d*w(v) - 4*l(v). Factor h(x).
-x**2*(x - 1)*(3*x + 1)
Let y(k) be the third derivative of k**5/15 + 4*k**4/3 - 616*k**3/3 - k**2 + 2*k + 624. Factor y(o).
4*(o - 14)*(o + 22)
Suppose 16*v - 175 = 9*v. Factor -70*i**4 - 36*i**5 - 231*i**4 - 144*i**2 + v*i**4 + 416*i**3.
-4*i**2*(i + 9)*(3*i - 2)**2
Suppose -5*p + 125 = 115. Let b(f) be the third derivative of 0 + 1/450*f**5 + 2*f**p + 1/180*f**4 + 0*f**3 + 0*f. Suppose b(u) = 0. Calculate u.
-1, 0
Let k = 413 - 409. Suppose -15*z = -16*z - k*i + 7, 2*i = 5*z - 13. Suppose -2/11*m**4 - 4/11*m**z + 4/11*m + 0 + 2/11*m**2 = 0. What is m?
-2, -1, 0, 1
Let i(v) = -v**3 + 11*v**2 + 14*v - 23. Let k be i(12). Let 348*b**2 + k - 1 - 344*b**2 + 4*b**3 = 0. Calculate b.
-1, 0
Let p(n) be the second derivative of 17/2*n**2 + 0*n**3 + 30*n - 1/6*n**4 + 0 + 1/15*n**5. Let d(o) be the first derivative of p(o). Factor d(a).
4*a*(a - 1)
Let a(n) be the third derivative of n**6/480 + n**5/48 - n**4/96 - 5*n**3/24 - n**2 - 3*n + 751. Suppose a(p) = 0. Calculate p.
-5, -1, 1
Let p = 120 + -118. Let -9*d + 54 + 137*d**2 + 162*d**p + 57*d**3 - d**4 - 532*d**2 - 8*d**4 + 140*d**2 = 0. Calculate d.
-2/3, 1, 3
Let z be (75/(-60))/(28/16 + -2). Let f(j) be the third derivative of -1/36*j**4 + 0 + 0*j + 5*j**2 + 1/180*j**6 + 0*j**3 + 0*j**z. Solve f(a) = 0 for a.
-1, 0, 1
Let v(x) = -1 - 9*x - 8 + 21*x + 7. Let n be v(4). Factor 20*l + n*l**2 + 75 + 10*l - 43*l**2.
3*(l + 5)**2
Let i(v) be the third derivative of 0*v**3 + 0 - 2*v**2 + 1/126*v**7 - 11/12*v**5 - 201*v - 85/72*v**4 - 5/24*v**6. Let i(w) = 0. Calculate w.
-1, 0, 17
Let c(y) = -3*y**3 + 12*y**2 + 27*y - 13. Let m(l) = 2*l**3 - 13*l**2 - 29*l + 16. Let f(h) = -6*c(h) - 5*m(h). Factor f(o).
(o - 2)*(o + 1)*(8*o + 1)
Let d(c) be the third derivative of 2*c**7/105 - c**6/6 + 2*c**5/5 + 2*c**4/3 - 16*c**3/3 - 2108*c**2. Factor d(u).
4*(u - 2)**3*(u + 1)
Let o(u) be the first derivative of u**6/120 - 3*u**5/20 + u**4 - 8*u**3/3 + 3*u**2 + 7*u - 51. Let t(m) be the second derivative of o(m). Factor t(d).
(d - 4)**2*(d - 1)
Solve 10*l - 701*l**3 + 172*l**2 + 9*l + 339*l**4 - 23*l - 31*l**4 = 0.
0, 2/77, 1/4, 2
Let s = 17008 + -17005. Let z(b) be the first derivative of 0*b - 30*b**2 - 220/3*b**s - 35/4*b**4 + 19. Factor z(g).
-5*g*(g + 6)*(7*g + 2)
Let x(p) be the second derivative of p**9/22680 - p**8/2240 + p**7/756 - p**6/720 + 43*p**4/12 + p - 6. Let m(d) be the third derivative of x(d). Factor m(w).
w*(w - 3)*(w - 1)*(2*w - 1)/3
Let h be (-40520)/(-55) + -1*1/(7/(-224)*4). Find v, given that 256/11*v + 2/11*v**2 + h = 0.
-64
Let n be (-20240)/(-8)*(2 + (1 - 2)). Solve -4*l**5 - 48*l**3 + n*l - 44*l**4 - 2530*l - 8*l**5 - 16*l**2 = 0 for l.
-2, -1, -2/3, 0
Let a(t) = t**3 - 3*t + 5. Let l be a(0). Suppose 8 = -2*p - 2*r, p - 6*p = -l*r - 20. Factor 12*y**3 - 48 + 0*y + p*y**4 - 48*y + 3*y**4.
3*(y - 2)*(y + 2)**3
Let n(h) be the second derivative of 11*h + 3 + 2/5*h**6 + 0*h**3 - 10/21*h**7 + 4/3*h**4 + 12/5*h**5 + 0*h**2. Find f, given that n(f) = 0.
-1, -2/5, 0, 2
Let f(q) = q**3 + 4*q**2 - 15*q + 9. Let t be f(2). Suppose -11*w - 9*w = -t*w. Factor 0*d**3 - 1/4*d**5 + 1/2*d**2 + 1/4*d - 1/2*d**4 + w.
-d*(d - 1)*(d + 1)**3/4
Let j(i) be the second derivative of 2*i**6/15 + 23*i**5/5 - 50*i**4/3 + 3*i + 118. Factor j(t).
4*t**2*(t - 2)*(t + 25)
Let w = 101137/47145 + -16/6735. Suppose 1/7*f**3 - 1/7*f - w + 15/7*f**2 = 0. Calculate f.
-15, -1, 1
Let g be (34 + (-1386)/55)/((-4)/(-10)). Let a(f) be the first derivative of g + 6/5*f**2 + 36/5*f + 1/15*f**3. Factor a(t).
(t + 6)**2/5
Suppose 3*h = -2*u - 46, -5*h = 2*u - 7*h + 36. Let x be (-5)/u*(0 - -6). Let 9/4*c**3 + 3/4*c**2 + 3/4*c**4 - x - 9/4*c = 0. Calculate c.
-2, -1, 1
What is h in -4*h**3 - 8*h**2 - 48/13*h - 6/13*h**4 + 0 = 0?
-6, -2, -2/3, 0
Let -294/5 + 268/5*g**3 - 2/5*g**5 - 6*g**4 + 324/5*g**2 - 266/5*g = 0. What is g?
-21, -1, 1, 7
Let b = 60 - 593. Let y = b - -535. Suppose -1/2*t**y + 0 + 1/2*t**3 + 0*t = 0. What is t?
0, 1
Let o be (1 - 3)*1 - 138*-1. Let -o + 0*d + 128 + 4*d**3 - 12*d = 0. What is d?
-1, 2
Let y = 184 - 183. Let m(j) = -j. Let h(l) = 2*l**4 - 24*l**3 + 64*l**2 + 92*l - 288. Let w(c) = y*h(c) - 4*m(c). Let w(x) = 0. Calculate x.
-2, 2, 6
Let c(j) = 13*j - 230. Let w be c(18). Suppose -5*u - 2*n = -3*u, 0 = -w*u - n. Factor 0*z**3 - 2/5*z**4 - 2/5 + 4/5*z**2 + u*z.
-2*(z - 1)**2*(z + 1)**2/5
Let a(k) = -4*k**3 - 42*k**2 + 147*k - 77. Let i(l) = 35*l**3 + 335*l**2 - 1185*l + 615. Let b(v) = 25*a(v) + 3*i(v). Solve b(n) = 0 for n.
1, 4
Let j(q) be the second derivative of -q**5/15 - 7*q**4/9 + 952*q**3/9 - 312*q**2 - 15447*q. Factor j(k).
-4*(k - 18)*(k - 1)*(k + 26)/3
Let k be -4 - 2 - (33 + -51 + 9). What is s in -6/13*s**2 - 4/13*s + 6/13*s**k + 14/13*s**4 + 0 + 6/13*s**5 = 0?
-1, 0, 2/3
Let q(j) be the first derivative of j**6/30 - j**5/120 - j**4/24 + 38*j**3 - 208. Let u(f) be the third derivative of q(f). Factor u(i).
(3*i - 1)*(4*i + 1)
Let y(u) be the second derivative of u**4/3 + 218*u**3/3 - 381*u - 9. Solve y(s) = 0.
-109, 0
Let f = 293438/880359 - -5/293453. Factor 1/3*x + f*x**2 - 2/3.
(x - 1)*(x + 2)/3
Let w be ((650/(-7))/(-5))/((-3173)/(-133) + -10 - 13). Determine t, given that -320/3 - 740/3*t**2 - 320/3*t**3 - 5/3*t**5 - w*t**4 - 800/3*t = 0.
-4, -2, -1
Let 5/2*s**4 - 10 + 44*s + 19*s**3 - 111/2*s**2 = 0. Calculate s.
-10, 2/5, 1
Let b be (25 - 14)/(-2 - (-33)/15). Determine o, given that -11*o**2 - 5*o**3 + 76*o**2 - b*o**3 - 5*o**4 = 0.
-13, 0, 1
Let s be 45/(-10)*3/(-54)*5 + (1 - 2). Determine c, given that 1/4*c**3 + s*c**2 - 1/4*c + 0 - 1/4*c**4 = 0.
-1, 0, 1
Determine y, given that 195*y**4 + 0*y**5 - 4*y**5 + 2*y**5 + 5*y**5 - 3663*y**2 - 4770*y - 1764*y + 3063*y**3 = 0.
-33, -1, 0, 2
Let t = 715 - 120. Let r = 597 - t. Factor 0*x**2 + 2/3*x**4 + 0*x**3 - r*x**5 + 0*x + 0.
-2*x**4*(3*x - 1)/3
Factor -2/7*y**2 + 6/7*y + 20/7.
-2*(y - 5)*(y + 2)/7
Let a(l) = 2 + 23*l**3 + 1 + 23*l - 22*l**3 - 10*l**2 + 13 + 3. Let c(i) = -2*i**3 + 16*i**2 - 34*i - 28. Let w(z) = -8*a(z) - 5*c(z). What is t in w(t) = 0?
-2, -1, 3
Let a(z) be the first derivative of -z**3/3 + 491*z**2/2 - 1948*z + 11038. Suppose a(l) = 0. What is l?
4, 487
Let c(q) = -4*q**3 + 983*q**2 + 245*q + 248. Let h be c(246). Factor 2*v - 1/4*v**4 - h*v**3 - 3/2*v**2 + 7/4.
-(v - 1)*(v + 1)**2*(v + 7)/4
Let q be (-80)/320 + 153/68. Solve 92/3*d + 0 + 4/3*d**q = 0.
-23, 0
Suppose 2*w - 290 = 5*r, -7*r - 234 = -3*r - 2*w. Let z be (6/21)/((-2)/r). Factor -z + 2*o**3 - 18 - 16*o**2 - 4*o - 10 + 46*o.
2*(o - 3)**2*(o - 2)
Let h(k) be the first derivative of k**6/200 - 33*k**5/100 - 69*k**4/40 - 7*k**3/2 - 43*k**2/2 - k - 25. Let i(n) be the second derivative of h(n). Factor i(c).
3*(c - 35)*(c + 1)**2/5
Suppose -911 - 183 - 91 = -231*q - 30. Factor 1/12*h**q - 2/3*h**4 - 13/12*h + 1/2 + h**3 + 1/6*h**2.
(h - 6)*(h - 1)**3*(h + 1)/12
Let o be ((-530)/1749)/(24/(-66)). Let q(b) be the second derivative of 14*b + o*b**3 - 5/6*b**4 - 1/4*b**5 + 0 + 5*b**2. Factor q(w).
-5*(w - 1)*(w + 1)*(w + 2)
Let q(u) be the first derivative of u**5/20 + 23*u**4/36 + 5*u**3/18 + 3*u**2/2 + 7*u + 180. Let n(h) be the second derivative of q(h). Factor n(s).
(s + 5)*(9*s + 1)/3
Let v(d) = 3*d**2 + 12*d - 9. Let g be v(-5). Determine w, given that -g*w**5 - 2*w**2 + 5*w**2 - 1210*w**4 + 1207*w**4 + 9*w**3 - 3*w = 0.
-1, 0, 1/2, 1
Let -456/5*u + 84/5*u**2 + 114/5*u**3 - 432/5 + 6/5*u**4 = 0. What is u?
-18, -2, -1, 2
Let s(q) be the second derivative of 1/36*q**4 + 0*q**3 - 1/6*q**2 + 22*q + 0. Factor s(m).
(m - 1)*(m + 1)/3
Suppose 0 = 924*j - 995*j. Let d(i) be the third derivative of -25/6*i**3 + 1/6*i**5 + 0*i + 15/8*i**4 + j - 8*i**2. Let d(h) = 0. What is h?
-5, 1/2
Suppose 15*j - 13*j = 0. Suppose j*f + 30 = -6*f. Let d(k) = k**5 + 3*k**4 + 5*k**3 + k**2. Let c(h) = -h**4 - h**2. Let g(b) = f*c(b) + 5*d(b). Factor g(y).
5*y**2*(y + 1)**2*(y + 2)
Let x(v) = -2*v**2