t t(a) = 180*a**3 + 60730*a**2 + 5170375*a + 10100215. Let q(k) = -4*t(k) + 35*y(k). Factor q(r).
-5*(r + 2)*(2*r + 335)**2
Let d(g) = -g**2 + 32*g - 109. Let f be d(28). Solve -2*l**3 - 2*l**4 + 2*l**3 - 2*l**2 + 5*l**3 + 2*l**3 - 3*l**f = 0.
0, 1
Let m(o) = o**3 - 12*o**2 - 86*o - 3. Suppose 4*a - 5*i = 0, -2*a = i + 149 - 135. Let h be m(a). Factor 2*x - 1/2*x**2 - h.
-(x - 2)**2/2
Let p be (10 - 1)*(-350)/(-225). Find c, given that 3*c**3 - 2*c**3 + 65 + 32*c + 63 - p*c**2 = 0.
-2, 8
Let p(x) be the second derivative of -3*x**7/14 - 71*x**6/10 + 657*x**5/10 - 369*x**4/2 + 461*x**3/2 - 261*x**2/2 - 3*x + 2422. What is v in p(v) = 0?
-29, 1/3, 1, 3
Let l(m) be the third derivative of 0*m**4 + 0 + 0*m - 35*m**2 - 1/6*m**5 + 1/24*m**6 + 0*m**3 + 1/42*m**7. What is f in l(f) = 0?
-2, 0, 1
Factor -400 + 562*z - 5*z**4 + 73*z**2 + 62*z**2 - 319*z**2 + 1458*z + 100*z**2 - 79*z**3.
-(z - 4)*(z + 10)**2*(5*z - 1)
What is o in 0 - 1/4*o**2 + 1/2*o = 0?
0, 2
Let v = -357437 + 357437. Factor -16/9 + 4*l**2 + v*l.
4*(3*l - 2)*(3*l + 2)/9
Let p = 1/15393 + 18917995/30786. Let s = p + -614. Factor -1/2 - 1/2*g**4 - g**3 + 1/2*g + g**2 + s*g**5.
(g - 1)**3*(g + 1)**2/2
Let v be (-54)/8*56/(-21). Let p(g) = -g**3 + 17*g**2 + 19*g - 12. Let a be p(v). Factor 51*x**2 + 0 - a*x**2 - 20*x**3 + 4 - 30*x + 1.
-5*(x - 1)**2*(4*x - 1)
Suppose 20*w - 48*w + 56*w = -5*g - 70, -42 = 3*g. Solve 2*m**2 + w - 16/7*m + 2/7*m**3 = 0.
-8, 0, 1
Let x(j) be the first derivative of j**8/168 - j**7/42 + j**6/40 + j**5/60 - j**4/24 - j**2 - 9*j - 77. Let q(s) be the second derivative of x(s). Factor q(l).
l*(l - 1)**3*(2*l + 1)
Suppose -2*g = 2*d + 4, -3*d + 3*g + 9 = -5*d. Suppose 0*u + 10 = 5*u. Determine z, given that z**2 + 61*z**3 + 0*z**4 - 2*z**5 + u*z - 67*z**d - 7*z**4 = 0.
-2, -1, 0, 1/2
Let t(o) = -9*o**3 - 46*o**2 - 61*o - 24. Let y(n) be the second derivative of 0 + 0*n**2 + 1/12*n**4 + 1/6*n**3 + 18*n. Let w(p) = -t(p) + 5*y(p). Factor w(b).
3*(b + 1)*(b + 4)*(3*b + 2)
Let r(i) be the third derivative of -i**6/180 - 3*i**5/20 + 11*i**4/6 - 3*i**3/2 + i**2 + 27. Let s(m) be the first derivative of r(m). Factor s(u).
-2*(u - 2)*(u + 11)
Let p = 414 + -412. Solve -40*n**2 + 70*n**p + 3*n**4 - 12*n + 3*n**3 - 42*n**2 = 0 for n.
-2, -1, 0, 2
Let y(u) be the first derivative of 69 + 1/9*u**6 + 0*u + u**4 + 1/3*u**2 - 8/15*u**5 - 8/9*u**3. Determine g, given that y(g) = 0.
0, 1
Let m(f) be the third derivative of -f**6/80 - 177*f**5/20 - 705*f**4/16 - 88*f**3 + 344*f**2 + 2*f. Solve m(t) = 0.
-352, -1
What is a in 40/17 + 2/17*a**2 + 24/17*a = 0?
-10, -2
Suppose 29*h - 47 + 482 = 0. Let n be (h/(-4))/(55/22). Determine o, given that -o + 1/4*o**4 - o**3 + n*o**2 + 1/4 = 0.
1
Let s(a) = -a**3 + 91*a**2 + 1339*a + 6098. Let m(r) = -4*r**3 + 272*r**2 + 4016*r + 18310. Let f(c) = 6*m(c) - 20*s(c). Find j such that f(j) = 0.
-25, -11
Let f(a) be the third derivative of -1/6*a**3 + 0 - 3/320*a**6 + 2*a**2 + 7/32*a**4 - 5/96*a**5 + 0*a. Determine j, given that f(j) = 0.
-4, 2/9, 1
Let p(t) be the first derivative of t**3/3 + 3*t**2 + 5*t + 1. Let g be p(-7). Factor -l**3 - g*l + l**4 + l**5 - 5*l + 17*l - l**2.
l**2*(l - 1)*(l + 1)**2
Let y(q) be the third derivative of q**6/360 + 73*q**5/180 - 19*q**4/18 - 74*q**3/9 - 1527*q**2 + 1. Solve y(k) = 0 for k.
-74, -1, 2
Let t(c) be the second derivative of c**5/70 - 145*c**4/42 + 41*c**3/3 - 143*c**2/7 + 615*c. Factor t(m).
2*(m - 143)*(m - 1)**2/7
Let k(r) be the second derivative of -1/75*r**6 - 1/15*r**4 - 1/10*r**5 + 0*r**2 - 1 + 8/15*r**3 - 7*r. Factor k(g).
-2*g*(g - 1)*(g + 2)*(g + 4)/5
Let l(b) be the second derivative of b**9/756 + b**8/60 - 47*b**7/630 + 7*b**6/90 + 85*b**4/12 - 3*b + 3. Let v(z) be the third derivative of l(z). Factor v(y).
4*y*(y - 1)*(y + 7)*(5*y - 2)
Suppose 2*o + 189 = 4*k + 15, 5*o - 195 = -4*k. Suppose -k = -4*c + 87. Factor 16*a**4 - 7*a**4 + 8*a**2 + 4*a**2 + c*a**3 - 57*a**3.
3*a**2*(a - 2)*(3*a - 2)
Let x be 16/9 - ((-4)/18)/1. Suppose -d + 8 = -5*u, x*u + 3 + 2 = d. Solve -13*i**3 - 11*i**d + 19*i**3 - 5*i**2 + 5*i + 5 = 0.
-1, 1
Let w(u) = u**4 + 259*u**3 - 997*u**2 + 989*u. Let c(p) = 2*p**4 + 260*p**3 - 996*p**2 + 988*p. Let f(k) = -3*c(k) + 4*w(k). Solve f(x) = 0 for x.
0, 2, 124
Determine o, given that -25*o + 91*o + 9*o**2 + 42 + 63 = 0.
-5, -7/3
Let j(d) = -2*d**2 - 210*d - 2390. Let b be j(-92). Factor 0 - 3/4*i**3 - 3*i**b + 3*i + 3/4*i**4.
3*i*(i - 2)*(i - 1)*(i + 2)/4
Suppose 35 = 18*v - 19. Find m, given that 34*m**2 - 24*m + 7*m**5 - 153*m**4 + 8 + 38*m**3 - 24*m + 111*m**4 + v*m**5 = 0.
-1, 1/5, 1, 2
Suppose -9*q + 8 = -5*q. Let u be (-8)/(44/33 + -4). Find d such that 0*d + 0 - 5/3*d**4 + 2/3*d**q - d**u = 0.
-1, 0, 2/5
Let z = -278635 + 3622257/13. Determine f so that 8/13 + 8/13*f - 2/13*f**3 - z*f**2 = 0.
-2, -1, 2
Suppose -4*w = 0, 2*o + 36 = 6*o + w. Let h(k) = 31*k**2 + 33*k + 23. Let m(b) = -14*b**2 - 16*b - 12. Let g(a) = o*m(a) + 4*h(a). Factor g(n).
-2*(n + 2)*(n + 4)
Let t(p) = p**3 + 8*p**2 - 7*p + 27. Let d be t(-10). Let j = 107 + d. Factor 15*n + 12*n + 2*n**2 + 0*n**5 - 28*n + n**5 - 2*n**j.
n*(n - 1)**3*(n + 1)
Let p be ((-40)/(-45) - 4/6)*519/346. Factor 2/3*h + 0 - 2/3*h**3 + p*h**2 - 1/3*h**4.
-h*(h - 1)*(h + 1)*(h + 2)/3
Factor -542/5*r**2 + 822*r - 90 + 18/5*r**3.
2*(r - 15)**2*(9*r - 1)/5
Let z(p) be the first derivative of 4*p**3/3 - 1026*p**2 + 4088*p - 5750. Solve z(a) = 0.
2, 511
Let h be (-11 - -16) + (-53)/2. Let t = h - -29. Factor -45/4*j - t*j**2 + 0 - 5/4*j**3.
-5*j*(j + 3)**2/4
Let v(w) = -63*w**2 + 2478*w + 169. Let l(s) = 29*s**2 - 1239*s - 78. Let u(r) = -13*l(r) - 6*v(r). Suppose u(z) = 0. What is z?
-1239, 0
Suppose 46*u - 1540 = -9*u. Let l be (-7)/u*4/(-3). Factor -1/9*y**2 + 2/9*y + l.
-(y - 3)*(y + 1)/9
Let s(u) = -162*u**5 - 716*u**4 - 134*u**3 + 694*u**2 + 298*u + 36. Let l(p) = -2*p**4 - 3*p**2 - p - 2. Let a(h) = 2*l(h) + s(h). Find k, given that a(k) = 0.
-4, -1, -2/9, 1
Factor 4*q**2 + 45 + 414 + 165053*q + 6*q**2 + 2*q**2 - 164432*q.
3*(q + 51)*(4*q + 3)
Let m(g) be the second derivative of -5/51*g**4 + 3/170*g**5 + 90*g - 4/17*g**2 + 0 + 11/51*g**3. Suppose m(p) = 0. What is p?
1, 4/3
Let v(r) be the first derivative of r**4/5 + 1096*r**3/15 + 546*r**2/5 + 6994. Factor v(p).
4*p*(p + 1)*(p + 273)/5
Let i(m) be the third derivative of -2/9*m**5 + 0*m**3 - 4*m + 11/105*m**7 - 1/5*m**6 + 14*m**2 + 0 - 5/504*m**8 + 0*m**4. Determine k, given that i(k) = 0.
-2/5, 0, 2, 5
Let m(t) be the second derivative of 0*t**3 - 17/3*t**5 + 52/9*t**6 - 5/42*t**7 + 0*t**2 - 14*t - 2 + 0*t**4. Determine z, given that m(z) = 0.
0, 2/3, 34
Suppose 2*m = 15 + 1. Let z(d) = 7*d - 36. Let t be z(m). Solve t*l**2 - 256*l + 0*l**4 + 248*l - 4*l**4 + 4*l**5 - 12*l**3 = 0.
-2, 0, 1
Let m(b) be the first derivative of -b**3/3 + 20*b**2 + 1131. Factor m(f).
-f*(f - 40)
Let t be (-4)/(-2)*(-5)/2. Let k be 11/1 + ((-15)/t - 6). Let -4*s**2 + 10*s**5 - 2*s**5 + k*s**3 + 25*s**4 - s**5 - 6*s**4 = 0. What is s?
-2, -1, 0, 2/7
Suppose f - x - 4 = 0, 5*f + 8*x = 7*x + 14. Factor 9*h**2 - 3*h**f - 172*h + 1014 - 179*h - 73*h**2 - 8*h**2.
-3*(h - 2)*(h + 13)**2
Factor 1/5*d**3 - 9/5*d - d**2 + 9.
(d - 5)*(d - 3)*(d + 3)/5
Suppose -45/2 + 3/4*s**2 + 87/4*s = 0. Calculate s.
-30, 1
Let u(f) be the first derivative of -81/8*f**4 + 0*f - 1/4*f**2 - 3*f**3 + 11. Solve u(r) = 0.
-1/9, 0
Let u(g) be the first derivative of -16/5*g + 83 - 2/5*g**3 + 14/5*g**2. Determine t so that u(t) = 0.
2/3, 4
Factor 2/25*n**2 - 408/25*n + 808/25.
2*(n - 202)*(n - 2)/25
Let y(z) be the second derivative of -z**6/150 + z**5/100 + z**4/60 - z**3/30 - 723*z. Factor y(k).
-k*(k - 1)**2*(k + 1)/5
Suppose 5*k = 3*k - 2. Let y be 20/(-15)*3*(k - 4). Find j such that y*j**2 + 16 - 48*j + 34*j**3 + 28*j**3 - 36*j**4 - 14*j**3 = 0.
-1, 2/3, 1
Suppose 5*c - 43 = -j, 3*j + c - 88 = 41. Suppose 23*f = -j*f. Determine l so that 8/9*l**5 + f + 4/9*l - 32/9*l**4 + 14/3*l**3 - 22/9*l**2 = 0.
0, 1/2, 1, 2
Suppose -4*d = -16*d - 9*d + 84. Let i(c) be the first derivative of -15/2*c**2 - d*c**3 - 3/4*c**4 - 6*c + 23. Factor i(h).
-3*(h + 1)**2*(h + 2)
Suppose -124*v - 1895*v**2 + 2159*v**2 + 768 - 367*v - 27*v**3 - 325*v = 0. Calculate v.
16/9, 4
Let u(v) be the first derivative of 61 + 16/3*v - 5/3*v**2 