**3 + 83*o**2 - 113*o**2.
-2*(o + 1)**3*(o + 4)
Let u(k) be the third derivative of -k**6/180 - 11*k**5/18 - 52*k**4/9 - 68*k**3/3 - 64*k**2 + 4. Suppose u(f) = 0. Calculate f.
-51, -2
Let i(y) = -52*y**3 - 3*y**2 - 4*y - 1. Let k be i(-1). Factor 235*a**2 - 1800*a - 651 - 14*a**4 + k*a**3 + 9*a**4 - 2*a**3 - 5829.
-5*(a - 9)**2*(a + 4)**2
Let w(t) = 58695*t**2 - 2*t - 1. Let r be w(-1). Suppose -4*d + r = 22268. Determine j, given that 2*j**4 + 2*j**3 - 4*j**2 - 9107*j + d*j = 0.
-2, 0, 1
Let h(y) be the second derivative of y**6/900 - y**5/30 - 11*y**4/60 + 14*y**3 - 10*y - 2. Let b(z) be the second derivative of h(z). Factor b(c).
2*(c - 11)*(c + 1)/5
Let c be (12/8)/(153/1088) - 8. Let y(q) be the second derivative of -q**5 + c*q**4 + 12*q**2 - 14*q + 38/3*q**3 + 0. Factor y(v).
-4*(v - 3)*(v + 1)*(5*v + 2)
Let w(g) = -g**2 + 79*g. Suppose 11*c - 58 + 3 = 0. Let p(j) = -42*j. Let v(d) = c*p(d) + 3*w(d). Determine l, given that v(l) = 0.
0, 9
Let q be (-11)/(583/(-530)) - (-78)/(-8). Factor 3/8*j**2 + 5/8*j + q.
(j + 1)*(3*j + 2)/8
Suppose 33 = 238*h + 33. Let k(r) be the second derivative of 0*r**5 - 7*r - 1/70*r**7 + 0 + h*r**2 + 1/50*r**6 + 0*r**3 + 0*r**4. Find a, given that k(a) = 0.
0, 1
Let w(n) be the third derivative of n**6/480 + n**5/60 - 7*n**4/24 + 4*n**3/3 - 622*n**2. Factor w(j).
(j - 2)**2*(j + 8)/4
Let g(f) be the third derivative of 1/20*f**5 - 199*f**2 + 8*f**3 + 0 + 0*f + f**4. Factor g(m).
3*(m + 4)**2
Let f = -12037187/7 - -1719601. Factor 2/7*u**3 + f + 4/7*u**2 - 26/7*u.
2*(u - 2)*(u - 1)*(u + 5)/7
Let l(p) = -p**3 - 2*p**2 + 25*p - 2. Let y be l(4). Factor -18 + 6 + 15 + 13 - d - 2*d**y + 5*d.
-2*(d - 4)*(d + 2)
Let p be 5/(-3) - ((-24750)/1080 - (-4 - 17)). Find d, given that -5/4*d**2 + p*d**3 - 3/2*d + 0 = 0.
-1, 0, 6
Let k(p) = 9*p**2 - 4*p + 2. Let g be 1/((-1)/((-8)/(-4) + -4)). Let m be k(g). Factor -3*h - 29*h**2 + m*h**2 - h + 2 + h.
(h - 2)*(h - 1)
Let y(f) be the third derivative of -8/9*f**3 + 0 + 210*f**2 - 1/45*f**5 + 0*f + 5/18*f**4. Determine u, given that y(u) = 0.
1, 4
Let f(o) = -7*o**3 + 111*o**2 + 254*o + 4. Let l(p) = -15*p**3 + 220*p**2 + 510*p + 10. Let c(m) = 5*f(m) - 2*l(m). Factor c(u).
-5*u*(u - 25)*(u + 2)
Let x be -8 - (-748)/51 - (-65)/78. Let k = 0 + 0. Factor k*w - x*w**2 - 6*w**3 + 3/2*w**4 + 0.
3*w**2*(w - 5)*(w + 1)/2
Factor -1595/2*q + 2544025/4 + 1/4*q**2.
(q - 1595)**2/4
Let n(m) be the first derivative of -11/20*m**5 + 3/20*m**6 - 1/2*m**2 + 3/4*m**4 - 1/2*m**3 + 18 + 0*m. Let k(c) be the second derivative of n(c). Factor k(d).
3*(d - 1)*(2*d - 1)*(3*d - 1)
Let i(v) be the second derivative of v**4/78 + 341*v**3/39 - 1389*v. Factor i(d).
2*d*(d + 341)/13
Suppose -5*c = -5*y - 1397 - 823, 0 = y - 5*c + 456. Let q = -4409/10 - y. Determine r so that -1/10*r**2 + 2/5 - 2/5*r + q*r**3 = 0.
-2, 1, 2
Let b(h) be the third derivative of 2/95*h**5 - 1/1995*h**7 + 7/114*h**4 + 0*h + 1/570*h**6 - 171*h**2 + 5/57*h**3 + 0. Determine l so that b(l) = 0.
-1, 5
Let r = 2167 + -2162. Let j(s) be the second derivative of -1/48*s**4 + 0*s**3 + 0 + 1/2*s**2 + r*s. Find d such that j(d) = 0.
-2, 2
Let i(t) be the first derivative of -t**5/120 + 11*t**4/24 - 12*t**2 + t + 12. Let a(l) be the second derivative of i(l). Factor a(g).
-g*(g - 22)/2
Let x(p) be the third derivative of -p**5/180 + 11*p**4/72 + 7*p**3 + 914*p**2. Factor x(y).
-(y - 18)*(y + 7)/3
Factor -8 - 36/5*t + 28/5*t**2.
4*(t - 2)*(7*t + 5)/5
Let t(h) = 4*h**4 - 24*h**3 - 14*h**2 + 29*h - 20. Let y(i) = 12*i**4 - 72*i**3 - 44*i**2 + 88*i - 64. Let r(n) = -16*t(n) + 5*y(n). Factor r(g).
-4*g*(g - 6)*(g - 1)*(g + 1)
Let k(z) be the first derivative of 0*z - 27/14*z**2 + 6/7*z**4 + 27 + 1/14*z**6 - 18/35*z**5 + 6/7*z**3. Solve k(g) = 0.
-1, 0, 1, 3
Let q(w) be the first derivative of 405*w**4/4 - 1560*w**3 - 1070*w**2 - 240*w + 2218. Suppose q(f) = 0. What is f?
-2/9, 12
Let f = -444926/5 + 88986. Suppose f*n**2 + 4*n + 16/5 = 0. What is n?
-4, -1
Let j(s) = -4*s**2 - 50*s + 46. Let l(i) = -13*i**2 - 106*i - 79*i - 32*i + 138 + 64*i. Let f(x) = -7*j(x) + 2*l(x). Factor f(g).
2*(g - 1)*(g + 23)
Let w(n) be the first derivative of -2/3*n**3 + 62 + 12*n**2 + 26*n. Factor w(x).
-2*(x - 13)*(x + 1)
Let c be ((-432)/(-288) - 0/(-1)) + 6/4. Let f(s) be the first derivative of 19 - 1/7*s**2 + 0*s - 2/21*s**c. Determine l so that f(l) = 0.
-1, 0
Let o(c) = 30*c**4 + 326*c**3 + 185*c**2 - 632*c + 79. Let y(q) = -11*q**2 - 1. Let i(n) = 2*o(n) - 2*y(n). Solve i(a) = 0.
-10, -2, 2/15, 1
Let u be (-33074)/29479*(-41 - 0). Factor 1/2*n**4 - 45*n**2 + 14*n**3 + u*n - 31/2.
(n - 1)**3*(n + 31)/2
Let l(y) = -y**2 - 3*y + 1. Let s be l(-2). Suppose -2*x = -6, 0 = -4*o - 0*x - s*x + 25. Factor -c**3 - 2*c**2 - c**5 + c**2 + 2*c**3 + 16*c**o - 15*c**4.
-c**2*(c - 1)**2*(c + 1)
Let d(n) be the second derivative of 3*n**5/140 - 13*n**4/28 + 6*n**3/7 - 8*n - 76. Factor d(x).
3*x*(x - 12)*(x - 1)/7
Let f be (-15)/10*8/(-6). Suppose f*t - 10 = -0*t - 2*k, 2*k + 5 = 3*t. Find h such that 24*h**2 + h**3 - 4*h**4 - 12*h**t + 16*h + 7*h**3 - 32 = 0.
-2, 1, 2
Let v = -972489 + 972492. Factor -8/9*b**2 + 2/9*b**4 - 4/9*b**v + 2/3 + 4/9*b.
2*(b - 3)*(b - 1)*(b + 1)**2/9
Let w = 1304691/124256 + -3/124256. Factor 27/2*u**2 + 3/2*u**4 + w*u + 3 + 15/2*u**3.
3*(u + 1)**3*(u + 2)/2
Let m(b) = -b**3 + 30*b**2 + 31*b + 4. Let a be m(31). Factor 3*u**a + 181*u - 7*u + 66*u - 576 + 36*u**2 - 27*u**3.
3*(u - 4)**3*(u + 3)
Let l be (-2)/(55/(-77) + 351/(-126)). Suppose -12/7*j**2 + 12/7*j - l + 4/7*j**3 = 0. Calculate j.
1
Let z = 380 + -376. Suppose 3*b + l + 24 = 20, z*l = -5*b - 16. Determine g, given that 2/11*g**2 + b - 4/11*g = 0.
0, 2
Let w(v) be the first derivative of 16*v - 7/10*v**4 + 23/5*v**3 - 59 + 1/25*v**5 - 68/5*v**2. Factor w(c).
(c - 5)*(c - 4)**2*(c - 1)/5
Let b(f) be the first derivative of -44 - 13*f**3 + 0*f + 9*f**2 + 15/4*f**4. Factor b(h).
3*h*(h - 2)*(5*h - 3)
Suppose 8*l + 17 = -23. Let i(h) = 3*h**2 - 8. Let k(a) = 4*a**2 + a - 9. Let m(g) = l*i(g) + 4*k(g). Factor m(d).
(d + 2)**2
Let v(s) be the first derivative of -7*s**3/3 + 15*s**2 + 72*s - 1137. Find y such that v(y) = 0.
-12/7, 6
Let x(j) = 9*j**4 - 25*j**3 - 109*j**2 - 167*j - 77. Let f(w) = 2*w**4 - w**3 - w - 1. Let d(q) = -5*f(q) + x(q). Determine y so that d(y) = 0.
-12, -6, -1
Suppose -5 = 5*c - 5*j, 3*c + 86*j = 82*j + 4. Let 0*h - 1/5*h**2 + c = 0. What is h?
0
Let i(v) = -2*v**4 + 36*v**3 + 40*v**2 - 42*v - 32. Let n(b) be the first derivative of -b**2/2 + b + 88. Let k(l) = i(l) - 6*n(l). What is o in k(o) = 0?
-1, 1, 19
Determine j, given that -76800/7 + 960/7*j - 3/7*j**2 = 0.
160
Let z be (2*(-2)/12)/((-11)/(-55)*-5). Find d such that d + 8/3*d**2 + 2*d**3 + 0 + 0*d**4 - z*d**5 = 0.
-1, 0, 3
Let q(v) be the first derivative of 3*v**5 + 47*v**4/4 + 12*v**3 + 2*v**2 + 2445. Find o, given that q(o) = 0.
-2, -1, -2/15, 0
Let m(p) = -p**3 + 28*p**2 - 23*p - 107. Let s be m(27). Let j be 56/(-56) - (s - 2). Factor j - 11/2*o**2 - 1/2*o**4 - 7/2*o**3 - 5/2*o.
-o*(o + 1)**2*(o + 5)/2
Let y = 707410 - 707407. Factor 10*i - 6*i**2 + 2/3*i**y + 50/3.
2*(i - 5)**2*(i + 1)/3
Factor -2*w**2 - 70880 + w**2 - 56699 - 68670 + 886*w.
-(w - 443)**2
Let q = 813225 - 813223. Solve -24/5*k - 2/5*k**q + 26/5 = 0.
-13, 1
Let k(v) = 67*v**2 + 2*v. Let d be k(-1). Let r = 68 - d. Suppose 8/9*j**2 - 8/9*j**r + 0 + 0*j + 2/9*j**4 = 0. What is j?
0, 2
Let a be -2 + 132/(-242)*(-13 + 2). Let f(h) be the third derivative of -1/150*h**6 - 1/25*h**5 - 1/15*h**a + 0 - 6*h**2 + 0*h + 0*h**3. Factor f(x).
-4*x*(x + 1)*(x + 2)/5
Let p(k) be the first derivative of k**4 + 300*k**3 + 25086*k**2 - 51076*k + 2283. Let p(m) = 0. What is m?
-113, 1
Let u(n) be the second derivative of n**4/48 + 557*n**3/12 - 1115*n**2/8 - 48*n + 20. Determine w, given that u(w) = 0.
-1115, 1
Let r(h) be the second derivative of -h**6/120 + 3*h**5/20 - 19*h**4/24 + h**3/2 + 63*h**2/8 + 2211*h. Factor r(a).
-(a - 7)*(a - 3)**2*(a + 1)/4
Let y(c) = 31*c**3 - 227*c**2 + 246*c + 50. Let g(a) = 5*a**3 - 38*a**2 + 41*a + 8. Let j(h) = -25*g(h) + 4*y(h). Find w, given that j(w) = 0.
0, 1, 41
Factor 0*b + 6480*b**3 + 0*b**2 + 180*b**4 + 0 + 5/4*b**5.
5*b**3*(b + 72)**2/4
Let f = 377905 + -377901. Determine y, given that -2/5*y**2 - f*y + 0