m) - w(m). Let r be n(-5). Solve -r*f**2 + 4*f**2 + 60 + 16*f + 45 - 41 = 0 for f.
-8
Let n = 19 - 16. Suppose -8*p = n*p - 11. Factor 0*d - p + 9 - 6*d - 2*d**2.
-2*(d - 1)*(d + 4)
Let t(v) = -v**3 + 42*v**2 - 203*v + 206. Let w be t(4). Let 3/8*f**w - 3/2*f - 15/8 = 0. Calculate f.
-1, 5
Suppose -4*i - 8 = 0, -3*i - i - 808 = -2*x. Let q be (x/(-450))/(52/(-18)). Let -q*w + 0 - 6/13*w**2 = 0. Calculate w.
-2/3, 0
Let j(h) be the second derivative of -h**4/48 + 69*h**3/8 - 2905*h. Factor j(i).
-i*(i - 207)/4
Let t(o) be the first derivative of -7*o**6/900 - o**5/450 - 34*o**2 + 169. Let p(k) be the second derivative of t(k). Solve p(j) = 0 for j.
-1/7, 0
Suppose -46*f + 74 = 2*f - 11*f. Let a(q) be the second derivative of 31/3*q**4 + 0 - 4*q**3 - 15*q + 2/3*q**7 + 2/3*q**6 - 37/5*q**5 + 0*q**f. Solve a(v) = 0.
-3, 0, 2/7, 1
Let f(v) be the second derivative of v**5/15 + 79*v**4/24 - 10*v**3/3 + 157*v**2 - 6*v + 24. Let y(g) be the first derivative of f(g). Solve y(j) = 0.
-20, 1/4
Let s(i) = i**3 - i**2. Let d(m) = 5*m**4 - 23*m**3 + 18*m**2. Suppose 2*w + 16 = 20. Suppose w*h + 38 = 36. Let f(y) = h*d(y) - 3*s(y). Factor f(u).
-5*u**2*(u - 3)*(u - 1)
Let g(f) be the first derivative of f**6/150 + f**5/30 - f**4/15 - 4*f**3/3 + 72. Let l(v) be the third derivative of g(v). Solve l(x) = 0.
-2, 1/3
Suppose 0 = 5*f + 15, 2*v = -4*f + 5*f + 101. Factor -v*d**2 + 22*d**3 + 4*d**2 + 26*d**3 + 11*d - 4*d**4.
-d*(d - 11)*(2*d - 1)**2
Let x(m) be the third derivative of -10*m**2 + 13/18*m**4 + 0*m**3 + 3*m + 1/90*m**5 + 0. Find n, given that x(n) = 0.
-26, 0
Suppose -2*w + 3740 = -3*r, -3*r = 5*w + 1694 + 2060. Let f be (-3)/4*r/1287. Factor 2/11*m**2 + f + 10/11*m.
2*(m + 1)*(m + 4)/11
Suppose -16*o**4 + 60*o**3 + 215*o - 2*o**5 - 23*o**2 - 193*o - 41*o**2 = 0. Calculate o.
-11, 0, 1
Solve 12 - 3/2*t**2 - 3*t = 0 for t.
-4, 2
Factor 0*j - 2240/3*j**3 - 2/9*j**5 + 76/3*j**4 + 0 + 12544/9*j**2.
-2*j**2*(j - 56)**2*(j - 2)/9
Suppose 3*u = 9, 3*f = 3*u - 1 - 8. Let l(o) be the second derivative of 1/14*o**4 + 0 - 12*o - 3/14*o**2 + f*o**3 + 0*o**5 - 1/70*o**6. Solve l(q) = 0 for q.
-1, 1
Factor -3*z**2 + 15*z**4 + 7*z**2 - 4*z**2 - 2*z**3 - 2277*z**5 + 2285*z**5.
z**3*(z + 2)*(8*z - 1)
Let t(n) be the second derivative of n**7/21 + 10*n**6/3 + 179*n**5/5 + 158*n**4 + 339*n**3 + 378*n**2 + 1448*n. Determine y, given that t(y) = 0.
-42, -3, -1
Let b be (-2)/(-7) + (-665)/(-245). Factor 110*v - 96*v**3 + 65*v**3 - 285*v**2 - 107*v**3 + 35*v**4 - 222*v**b.
5*v*(v - 11)*(v + 1)*(7*v - 2)
Let d be (68 - 54) + (5 - -6). Let k(m) be the first derivative of d + 0*m + 6*m**2 - 4/5*m**5 + 4/3*m**3 - 3*m**4. Factor k(l).
-4*l*(l - 1)*(l + 1)*(l + 3)
Let m = -30380 + 30380. Let k(d) be the second derivative of -1/4*d**4 + 9/2*d**2 + m + 42*d - d**3. Factor k(o).
-3*(o - 1)*(o + 3)
Suppose -2*k = 5*h - 4*h + 6, -2*k = 4*h. Suppose 22*a = -h*a + 72. Factor 3/2*c + 0 + a*c**2 + 3/2*c**3.
3*c*(c + 1)**2/2
Factor 0 - 15*v + 685/4*v**3 + 175/4*v**4 + 160*v**2.
5*v*(v + 2)**2*(35*v - 3)/4
Let s = 204904/61471 + -2/184413. Determine q so that -s*q**2 - 7/3*q + 6 - 1/3*q**3 = 0.
-9, -2, 1
Let h(k) be the first derivative of 5*k**4/4 - 130*k**3 + 765*k**2/2 - 380*k - 1268. Factor h(y).
5*(y - 76)*(y - 1)**2
Let x(g) be the second derivative of -g**5/5 - 690*g**4 - 952200*g**3 - 657018000*g**2 - 13*g - 57. Let x(n) = 0. Calculate n.
-690
Factor 2*s**3 + 0 + 0*s + 1/3*s**4 + 8/3*s**2.
s**2*(s + 2)*(s + 4)/3
Let z(w) be the second derivative of 2*w**6/15 - 9*w**5/10 + 5*w**4/2 - 11*w**3/3 + 3*w**2 - 34*w - 4. Find f such that z(f) = 0.
1, 3/2
Find n, given that -2/9 + 1/9*n**4 + 1/9*n**2 - 1/3*n + 1/3*n**3 = 0.
-2, -1, 1
Let t(m) be the first derivative of -3*m**4/8 - m**3 + 3*m**2 + 12*m + 532. Let t(d) = 0. Calculate d.
-2, 2
Let i(r) be the first derivative of 1/3*r**3 + 26*r - 229 + 15/2*r**2. Determine u, given that i(u) = 0.
-13, -2
Suppose 0 = -373*p + 4*p + 1476. Let k(y) be the first derivative of 0*y - 2*y**2 + 16 - 14/3*y**3 - 4*y**p - 6/5*y**5. Find d such that k(d) = 0.
-1, -2/3, 0
Let u(s) = 7*s**3 - 20*s**2 - 7*s + 12. Let h(z) = -z**3 + z**2 + z. Let k be (-6*2)/6 - 22. Let t(f) = k*h(f) - 3*u(f). Suppose t(o) = 0. Calculate o.
-12, -1, 1
Let k(c) be the second derivative of -c**4/3 + 10*c**3 - 52*c**2 - 159*c + 3. Determine r so that k(r) = 0.
2, 13
Let o(h) = 2*h**3 - 65*h**2 + 201*h + 65. Let t be o(29). Let d(i) be the second derivative of -2/3*i**3 - t*i + 0 + 1/12*i**4 + 0*i**2. Factor d(z).
z*(z - 4)
Let o = 1/135303 - -1894217/3382575. Let 56/25*q - 4/25*q**3 - 24/25 - o*q**2 = 0. Calculate q.
-6, 1/2, 2
Let u be -3 - -12 - (-3 + 8). Factor 6*f**2 - 9*f**2 - 20*f + u*f - 16 - f**2.
-4*(f + 2)**2
Let o(z) = 6*z**2 - 3. Let b be o(2). Suppose 0 = 19*y - b*y + 70. Factor 136*p**4 - y*p**3 - 28*p**3 - 45*p**5 - 31*p**4 + 13*p**3 - 30*p**2 + 15*p + 5.
-5*(p - 1)**3*(3*p + 1)**2
Let y(b) be the second derivative of 5/12*b**4 + 124*b + 0 + 12*b**3 + 14*b**2. Find h, given that y(h) = 0.
-14, -2/5
Let v(f) = f**3 - 85*f**2 + 8*f - 14. Let q(c) = 7*c**2 + 2*c + 1. Let j(t) = 14*q(t) + v(t). Find a, given that j(a) = 0.
-9, -4, 0
Let a(m) be the third derivative of -m**6/300 - m**5/10 + 37*m**4/60 + 17*m**3/5 - 2*m**2 - 19*m + 46. Factor a(j).
-2*(j - 3)*(j + 1)*(j + 17)/5
Let n(b) be the second derivative of -b**4/3 + 174*b**3 - b - 1041. Factor n(c).
-4*c*(c - 261)
Let k be (-15)/(-4) - (-12)/(-4). Let v = 747/1634 + 35/817. Factor -k*w + w**3 - v*w**2 + 0*w**4 - 1/4*w**5 + 1/2.
-(w - 1)**3*(w + 1)*(w + 2)/4
Factor 115216/5*v**2 - 224256/5*v + 396/5*v**4 - 2/5*v**5 - 4152*v**3 + 147456/5.
-2*(v - 96)**2*(v - 2)**3/5
Let q(n) = 42*n + 4. Let p be q(0). Solve 438*t**3 + t**2 + 3*t - 441*t**3 - 5*t**4 + 2*t**p + 2*t**4 = 0.
-3, -1, 0, 1
Suppose 31*f = 39*f - 640. Suppose -f*l = -82*l. Find u such that 4/13*u + 10/13*u**4 + 2/13*u**2 + l - 16/13*u**3 = 0.
-2/5, 0, 1
Let a = -111 + 113. Factor 16*d - 19520*d**a + 24*d + 19530*d**2 - 5*d**3.
-5*d*(d - 4)*(d + 2)
Factor -190*m - 1160/3 + 5/3*m**2.
5*(m - 116)*(m + 2)/3
Let l be ((-1648)/10)/((-24)/60). Let k = -815/2 + l. Factor 3/2*u**2 - k - 3*u.
3*(u - 3)*(u + 1)/2
Let k = -180/47 + 407/94. Suppose 0*x - 2*x = a + 2, 2*x - 6 = -3*a. Let k*s**a - 11/4*s**2 - 11/4*s - 3/4 - 1/4*s**3 = 0. What is s?
-1, -1/2, 3
Let c(m) be the second derivative of 6*m**3 - 120*m**2 - 2*m - 59. Let a be c(7). Factor 3/2*b**2 + 24 + a*b.
3*(b + 4)**2/2
Let i(a) be the third derivative of 0 + 1/3*a**3 - 5/24*a**4 - 1/120*a**6 - 34*a**2 + 1/15*a**5 + 0*a. Suppose i(b) = 0. What is b?
1, 2
Let c be 16/(1152/(-27))*-4. Let q(a) be the second derivative of 31/6*a**3 + 0 + 59/6*a**4 + c*a**2 + 16*a + 9/14*a**7 + 99/10*a**5 + 9/2*a**6. Factor q(i).
(i + 1)*(i + 3)*(3*i + 1)**3
Let g(u) = u**3 - 9*u**2 - 37*u + 17. Let a be g(12). Factor -33*l**2 + l**a - 13*l**5 + 7*l**5 + 25*l**4 + 400*l - 167*l**2 - 240.
-5*(l - 2)**4*(l + 3)
Suppose -4*u + 2*y = -74, -y + 165 - 117 = 3*u. Suppose -27*n = -u*n - 20. Solve 8/5*x**n - 6/5*x - 2/5*x**3 + 0 = 0 for x.
0, 1, 3
Let i be (-1)/2 + (-630)/(-28). Suppose -i = -15*s + 8. Determine z so that -8/3 - 4/3*z**s + 4*z = 0.
1, 2
Let i(l) be the third derivative of -l**6/720 + 17*l**5/120 - 275*l**4/144 + 25*l**3/4 + 6*l**2 - l - 120. Factor i(z).
-(z - 45)*(z - 5)*(z - 1)/6
Let j(l) = 70*l - 2. Let x = 10 + -8. Let s be j(x). Factor -153*t - 3 + 13 + 5*t**3 + s*t.
5*(t - 1)**2*(t + 2)
Let o(j) be the second derivative of -1/42*j**7 + 0*j**4 + 0*j**3 + 0 - 1/15*j**6 + 0*j**2 + 30*j + 0*j**5. Factor o(h).
-h**4*(h + 2)
Let l(b) be the third derivative of -b**6/60 + 131*b**5/30 + 271*b**4/4 + 411*b**3 + 67*b**2 + 6*b. Factor l(w).
-2*(w - 137)*(w + 3)**2
Suppose -5*p - 17 = -0*z + z, -5*p - 2*z - 14 = 0. Let h = p + 7. Factor -h*v**2 + 4*v + 6 + 4*v**2 + 3*v + 0*v.
(v + 1)*(v + 6)
Let o(j) be the second derivative of j**5/140 + 2*j**4/21 - j**3/42 - 4*j**2/7 + 2195*j. Factor o(w).
(w - 1)*(w + 1)*(w + 8)/7
Let c be (4*18/(-27))/(2/(-2) + 27/(-81)). Let j be 0 - 1 - (-78)/15. Factor 3/5 - j*i**c - 18/5*i.
-3*(i + 1)*(7*i - 1)/5
Let j(z) = 12*z - 715. Let w be j(73). Let y be w/23 - (1 + (-12)/(-4)). Factor -1/10*l**y + 1/5 + 1/10*l - 1/5*l**2.
-(l - 1)*(l + 1)*(l + 2)/10
Let k(i) = i**2 + 28*i + 199. Let o be 