t p(z) be the first derivative of -1/4*z**4 - 225 - 56/5*z - 59/5*z**2 + 53/15*z**3. Factor p(f).
-(f - 7)*(f - 4)*(5*f + 2)/5
Suppose 178*r + 138 - 850 = 0. Let w(t) be the third derivative of -1/4*t**5 + 0*t + 44*t**2 + 0*t**3 + 0 + 5/48*t**6 + 3/16*t**r. Factor w(c).
c*(5*c - 3)**2/2
Suppose -z - 6 = c - 0, 5*z = 2*c + 5. Let u(n) = 3*n**4 + 2*n**3 + 10*n**2 + 4*n - 5*n + 7*n. Let y(d) = -d**4. Let i(k) = z*u(k) - 5*y(k). Factor i(r).
2*r*(r - 3)*(r + 1)**2
Let p be (-36)/90*(114 + 1). Let y = p + 49. Factor 9*v**2 + 12*v + 7*v**3 - y*v**4 + 12*v**2 - v**3.
-3*v*(v - 4)*(v + 1)**2
Suppose 4*d = 7*d, -5*s = d - 15. Solve 169*j**3 - 347*j**s + 179*j**3 - 7*j + 6*j**2 = 0 for j.
-7, 0, 1
Let o(b) be the second derivative of 0*b**3 + b + 125 - 5/12*b**4 + 0*b**2. Suppose o(i) = 0. What is i?
0
Let i(d) = -3*d**4 + 18*d**3 + 12*d**2. Let u(p) = 6*p**4 - 29*p**3 - 26*p**2. Let w(v) = -5*i(v) - 3*u(v). Factor w(z).
-3*z**2*(z - 2)*(z + 3)
Suppose 0 = -2*c + 5*q + 16, -3*c + 4*q = -c - 14. Determine z, given that -4*z - 20*z**4 + 4*z**4 - 88*z**5 + 84*z**5 - 16 + 8*z**c + 32*z**2 = 0.
-4, -1, 1
Factor 2/5*x**2 + 294/5 + 104/5*x.
2*(x + 3)*(x + 49)/5
Factor -154/17 - 2/17*b**3 - 118/17*b + 2*b**2.
-2*(b - 11)*(b - 7)*(b + 1)/17
Let h = -7858/77 - -23651/231. Solve 86/3*y + h*y**2 + 1849/3 = 0 for y.
-43
Suppose 20 = -m + 24. Let y(b) = 6*b**2 + 3*b. Let q be y(m). Solve -43*w + 20 + 15*w - 55*w**2 + q*w - 45*w**3 = 0 for w.
-2, -2/9, 1
Let m = 2911837/8778 + -7/1254. Let c = m + -330. Suppose c*i**3 + 8/7 - 8/7*i - 22/7*i**2 + 18/7*i**4 = 0. What is i?
-1, 2/3
Determine z, given that -3582*z + 765*z**2 - 1538*z**2 + 770*z**2 - 1359531 + 290304 = 0.
-597
Let q(m) be the second derivative of 2*m**6/105 - 11*m**5/35 + 11*m**4/7 - 10*m**3/21 - 100*m**2/7 + 3114*m. Factor q(k).
4*(k - 5)**2*(k - 2)*(k + 1)/7
Let 317988/5*r**3 - 127896/5*r**2 + 0*r + 4374/5*r**4 + 3*r**5 + 0 = 0. Calculate r.
-146, 0, 2/5
Suppose 3*w - 51 = -m - 2*m, 56 = 3*w + 2*m. Let h be 4/(-22) + 48/w. Factor 0*r**3 + 5 - h - 3*r**2 + r**3 + 1.
(r - 2)**2*(r + 1)
Let v(d) = 10*d**3 + 2*d**2 - 2. Let i be v(3). Let l = i + -282. Factor -22/3*c - l*c**3 + 2/3*c**5 - 2/3*c**4 + 28/3*c**2 + 2.
2*(c - 1)**4*(c + 3)/3
Let b = -524 - -526. Factor 46*x**2 - 20*x + 16*x**5 + 10*x**b - 48*x**3 + 8*x**4 - 12*x**5.
4*x*(x - 1)**3*(x + 5)
Let f(n) be the first derivative of -16 + 0*n**2 - 3/20*n**5 + 0*n**3 + 1/4*n**4 - 18*n. Let w(j) be the first derivative of f(j). Solve w(g) = 0.
0, 1
Let n(i) be the second derivative of i**4/36 + 37*i**3/6 + 109*i**2/3 + 647*i. Factor n(x).
(x + 2)*(x + 109)/3
Factor -205/3*n + 430/3 - 5/3*n**2.
-5*(n - 2)*(n + 43)/3
Let d(u) be the first derivative of 0*u + 5*u**2 + 1/63*u**3 - 1/126*u**4 + 1/630*u**5 - 28. Let p(b) be the second derivative of d(b). Factor p(m).
2*(m - 1)**2/21
Find k such that 2022111/5*k + 3/5*k**3 + 4932/5*k**2 - 4063974/5 = 0.
-823, 2
Let k(v) be the third derivative of 7*v**5/90 - 19*v**4/18 + 31*v**3/9 + 771*v**2. Let k(c) = 0. What is c?
1, 31/7
Let p = 1132 - 1130. Suppose -p*o - 10 + 22 = 2*l, -3*l = -12. Determine s so that -10/3*s**3 + 0*s + 2/3*s**4 + 8/3*s**o + 0 = 0.
0, 1, 4
Let r(w) be the second derivative of 17*w - 1/60*w**4 + 0 + 3/10*w**3 - 9/5*w**2. Factor r(g).
-(g - 6)*(g - 3)/5
Let b be (1/(-28) - (-7)/(-28)) + (-2146)/(-1827). Let 4/9*f**3 + 0 + b*f**4 - 4/9*f**5 + 0*f - 8/9*f**2 = 0. Calculate f.
-1, 0, 1, 2
Let c(n) be the second derivative of 3*n**5/70 - n**4/42 - 16*n**3/7 + 16*n**2/7 + 1251*n. Factor c(o).
2*(o - 4)*(o + 4)*(3*o - 1)/7
Let i(z) = -11*z + 316. Let t(o) = 53*o - 1574. Let x(s) = -11*i(s) - 2*t(s). Let q be x(22). Factor 5/3*f - 4/3*f**4 + 2/3 - 4/3*f**3 + 2/3*f**q - 1/3*f**5.
-(f - 1)*(f + 1)**3*(f + 2)/3
Let a(d) be the first derivative of -3/10*d**4 + 4/25*d**5 + 0*d + 0*d**2 - 127 - 2/3*d**3. Determine s, given that a(s) = 0.
-1, 0, 5/2
Let a(c) be the first derivative of -13/3*c**3 - 1/4*c**4 + 53 + 0*c**2 + 0*c. Solve a(v) = 0.
-13, 0
Let r = -135 - -192. Solve -35*w - 49*w**2 + 5*w**4 + r*w**2 - 45*w**3 + 67*w**2 = 0.
0, 1, 7
Let x = 81/10 - 15/2. Let o = 541405 - 541403. Determine q so that -1/5*q**3 - 1/5*q + 3/5*q**4 - x*q**o + 2/5*q**5 + 0 = 0.
-1, -1/2, 0, 1
Let z(p) be the first derivative of p**6/48 + p**5/8 - 3*p**4/32 - 29*p**3/24 + p**2/8 + 3*p - 1729. Find n, given that z(n) = 0.
-4, -3, -1, 1, 2
Find s such that -144/13*s**2 + 2/13*s**3 + 2112/13 + 760/13*s = 0.
-2, 8, 66
Let d(y) = -11175*y + 17 + 11141*y + 24*y**2 + 3. Let u(z) = z**2 + z + 2. Let i(o) = d(o) - 6*u(o). Let i(h) = 0. Calculate h.
2/9, 2
Let j = 16 - -343. What is y in -448*y + 2*y**4 + 666*y**2 - 367*y**2 - j*y**2 + 490 + 16*y**3 = 0?
-7, 1, 5
Let j(u) = -u**3 + 1. Let o(n) = 3*n**3 - 9*n**2 - 27*n - 31. Let p be 8/10 - 230/(-25). Suppose 28 = 3*d - p*d. Let b(g) = d*j(g) - o(g). Factor b(y).
(y + 3)**3
Let g = -139314 - -139316. Find h such that -7*h - 4 - 1/2*h**3 - 7/2*h**g = 0.
-4, -2, -1
Let l(s) be the third derivative of s**5/90 + 343*s**4/36 - 346*s**3/3 - 39*s**2 + 3. Factor l(g).
2*(g - 3)*(g + 346)/3
Suppose -3*n - 39 + 45 = 0. Find r such that -20*r - 164*r - 4*r**n + 32 + 48*r**2 = 0.
2/11, 4
Find q, given that 411/5*q**4 - 6/5*q**5 - 42*q + 642/5*q**2 + 1056/5*q**3 - 213/5 = 0.
-1, 1/2, 71
Let l(t) be the second derivative of 47*t**4/30 + 3*t**3 - 2*t**2/5 - 401*t. Find u, given that l(u) = 0.
-1, 2/47
Let k(n) = -3*n**4 - 138*n**3 - 357*n**2 + 480*n. Let v(s) = 9*s**4 + 415*s**3 + 1071*s**2 - 1438*s. Let l(y) = -19*k(y) - 6*v(y). Determine g so that l(g) = 0.
-41, -4, 0, 1
Let s(q) be the first derivative of 1/3*q**6 - 8/3*q**3 - 3*q**4 - 125 + 13*q**2 - 12*q + 4/5*q**5. Factor s(p).
2*(p - 1)**3*(p + 2)*(p + 3)
Factor -1640*b - 336*b**3 - 27*b**4 + 2*b**4 + 20*b**4 + b**4 + 2488*b**2 + 3276 - 3784*b.
-4*(b - 3)**2*(b - 1)*(b + 91)
Suppose -28*x + 18 = -19*x. Let -5*s**4 + 57*s**3 + s**4 + 6859*s - 1083*s**2 + 4*s**4 + x*s**4 - 3*s**4 = 0. What is s?
0, 19
Solve 886/3*y**2 - 122*y**3 + 237*y - 25/3*y**5 - 297 - 105*y**4 = 0 for y.
-11, -9/5, 1
Let u(x) = -12*x**3 - 571*x**2 - 8443*x - 38918. Let d(l) = -8*l**3 - 381*l**2 - 5629*l - 25942. Let h(c) = 7*d(c) - 5*u(c). Suppose h(g) = 0. What is g?
-19, -9
Let u(y) be the first derivative of y**3/15 + 411*y**2/5 - 823*y/5 - 1991. Factor u(x).
(x - 1)*(x + 823)/5
Let f = 2204770/9 + -244822. Factor -196/3*r - 4/9*r**3 - f - 28/3*r**2.
-4*(r + 7)**3/9
Let z = -8/35703 - -2927734/392733. Find v such that -882/11 + z*v**2 - 2/11*v**3 - 798/11*v = 0.
-1, 21
Suppose -4*t + 2*r = 15 + 17, 3*t - 3*r + 21 = 0. Let q be (30/50)/(t/(-40)). Factor -q*s - 2/9*s**2 - 8.
-2*(s + 6)**2/9
Let c(r) be the third derivative of -r**5/150 - 83*r**4/10 - 20667*r**3/5 + 12*r**2 + 52*r. Factor c(f).
-2*(f + 249)**2/5
Suppose 2*q + 2*q - 17 = -3*l, -3*l + 9 = 0. Factor 4*f**5 - 50*f**3 + 12*f**4 - 6 + 22 - 6*f**5 + 76*f**q + 4*f**4 - 56*f.
-2*(f - 2)**3*(f - 1)**2
Let v(w) be the second derivative of w**5/150 + 23*w**4/45 - 196*w**3/45 + 40*w**2/3 - 2820*w. Factor v(x).
2*(x - 2)**2*(x + 50)/15
Let d(b) be the third derivative of b**8/84 + 22*b**7/175 - 82*b**6/75 + 16*b**5/15 + 32*b**4/5 - 32*b**3/3 + 119*b**2 + 4*b - 1. Find o such that d(o) = 0.
-10, -1, 2/5, 2
Let y(p) be the third derivative of -p**7/1470 - p**6/840 + p**5/70 + p**4/42 - 4*p**3/21 - 1228*p**2 + 2. Suppose y(j) = 0. Calculate j.
-2, 1, 2
Let m(h) be the first derivative of h**7/7140 - 7*h**6/3060 + 4*h**5/255 - h**4/17 + h**3 - 19*h + 75. Let w(c) be the third derivative of m(c). Factor w(y).
2*(y - 3)*(y - 2)**2/17
Suppose -o - 9*i + 7*i - 6 = 0, -5*o + i + 14 = 0. Solve -4 - 491*w**o - 107*w**2 + 69*w**2 - 92*w = 0 for w.
-2/23
Let i = 253645 - 1775502/7. Factor i*u + 1/7*u**2 + 0.
u*(u + 13)/7
Let w(n) be the first derivative of -1/8*n**4 - 1/30*n**5 + 0*n**2 + 0*n + 109 + 5/9*n**3. Determine h, given that w(h) = 0.
-5, 0, 2
Let v(l) = -3*l**4 - l**3 + 3*l**2 + l. Suppose z + 7*z - 32 = 0. Let i(h) = -h**z + 41*h**3 + h**2 - 41*h**3. Let w(t) = -6*i(t) + 3*v(t). Factor w(f).
-3*f*(f - 1)*(f + 1)**2
Let w(x) be the third derivative of x**10/75600 + 19*x**5/60 + 56*x**2. Let q(g) be the third derivative of w(g). Let q(y) = 0. Calculate y.
0
Let d(l) be the third derivative of 3*l**7/560 + l**6/24 + l*