52 - 766. Suppose -794*p + w*p + 24 = 0. Factor 0*a + 1/4*a**p - 1/4*a**4 + 0 + 0*a**2.
-a**3*(a - 1)/4
Factor -428*x**3 + 2204*x**2 + 110*x**4 - 520*x**3 - 275*x + 485 - 710*x - 1009*x + 145 - 2*x**5.
-2*(x - 45)*(x - 7)*(x - 1)**3
Let r(d) be the first derivative of -39 - 1/33*d**3 + 3/22*d**2 + 28/11*d. Let r(q) = 0. What is q?
-4, 7
Suppose 818 = -4*g + 1538. Let h(q) be the first derivative of -30*q**2 - 5 - 5/3*q**3 - g*q. Factor h(b).
-5*(b + 6)**2
Let a(n) be the first derivative of -3/4*n**4 + 240*n + 54 + 13*n**3 - 84*n**2. What is v in a(v) = 0?
4, 5
Let i be (-24)/(-132) - (-420)/(-11). Let x = i - -41. Factor 7*a - 3*a**2 + 7*a + x - 14*a.
-3*(a - 1)*(a + 1)
Suppose 0 = 56*z - 91 - 133. Let z*s**2 + 5*s**4 - s**4 - 8 + 639*s**3 - 651*s**3 + 12*s = 0. What is s?
-1, 1, 2
Let 731*w - 576 - 49323*w**2 + 139*w - 288*w**3 + 3*w**4 + 49314*w**2 = 0. What is w?
-2, 1, 96
Suppose 2*l - 11 - 9 = -4*o, 2*o - 16 = -4*l. Factor 13*n + 10 - 3 + n + 6 - n**2 + 2*n**l.
(n + 1)*(n + 13)
Let f = 1857 - 1854. Let -6/5*b + 8/5*b**f + 0*b**4 - 2/5*b**5 + 4/5 - 4/5*b**2 = 0. Calculate b.
-2, -1, 1
Let r(m) be the first derivative of -2*m**3/7 - 87*m**2/14 - 150*m/7 + 401. Factor r(t).
-3*(t + 2)*(2*t + 25)/7
Let h(o) be the second derivative of o**5/190 - 1291*o**4/114 + 21896*o**3/3 + 21964*o**2 - 303*o. Factor h(g).
2*(g - 646)**2*(g + 1)/19
Suppose -3*i + 3*b - 1 = -13, -2*i = 4*b - 2. Let w be 3/1 - 0 - (-52)/(-52). Factor 0*k**3 + 1 - w*k**3 + k**i - 3*k + 3*k**2.
-(k - 1)**3
Suppose -8 = -9*i + 10. Let x be 30/(-12)*(-6)/5. Determine u, given that -7*u + i*u + x*u - u**2 + 2 + 3*u = 0.
-1, 2
Let c be 0/2*((400/6)/20)/10. Let -1/3*r**5 + 0 + c*r - 1/3*r**2 - r**3 - r**4 = 0. Calculate r.
-1, 0
Let g(h) be the second derivative of h**6/150 + 3*h**5/10 - 17*h**4/5 + 212*h**3/15 - 144*h**2/5 - 27*h + 35. Factor g(r).
(r - 2)**3*(r + 36)/5
Let w(h) be the first derivative of -h**4/10 - 14*h**3/3 - 183*h**2/5 - 522*h/5 - 1342. Factor w(x).
-2*(x + 3)**2*(x + 29)/5
Factor 0 + 2/3*u**2 + 3920/3*u.
2*u*(u + 1960)/3
Let p(x) = -9*x - 4. Let r be p(-1). Suppose -5*h - r = -4*m, 5*m + 3 = -h - 2*h. Solve 2*a**2 + m*a**2 - 7*a**2 = 0.
0
Suppose k - 14 = -5*m + 14, 2*k = 2*m + 32. Let s(x) = 2*x**2 + 1. Let z(i) = -19*i**2 - 29*i - 9. Let u(h) = k*s(h) + 2*z(h). Factor u(w).
-2*w*(w + 29)
Factor -2066/9*f + 0 - 2/9*f**2.
-2*f*(f + 1033)/9
Find k such that 2 - 20*k**2 + 95*k + 9*k**2 - 2 + 16*k**2 = 0.
-19, 0
Solve 32*h**4 + 3376*h**3 + 2*h**5 + 17466*h**2 + 13448*h + 814*h**3 + 142*h**4 = 0 for h.
-41, -4, -1, 0
Let x(l) be the first derivative of -9/2*l**4 - 192 + 108*l**2 + 0*l**3 + 0*l + 2/5*l**5. Determine r so that x(r) = 0.
-3, 0, 6
Let u be (504/1155)/((-25)/(-375)). Find b, given that 648/11 - u*b + 2/11*b**2 = 0.
18
Let k be 193414/519519 + 8/(-42). Factor 0 + 6/11*h - 8/11*h**2 + k*h**3.
2*h*(h - 3)*(h - 1)/11
Let z(r) be the second derivative of 3*r**5/40 - 5*r**4/2 + 17*r**3 - 48*r**2 - 1480*r. Let z(k) = 0. What is k?
2, 16
Suppose -526*b + 680*b - 462 = 0. Factor -5/3*n**2 - 2/3*n**b - 4/3*n - 1/3.
-(n + 1)**2*(2*n + 1)/3
Let t(b) be the second derivative of -b**7/63 - 11*b**6/15 - 33*b**5/5 - 214*b**4/9 - 104*b**3/3 + 43*b + 50. Determine d, given that t(d) = 0.
-26, -3, -2, 0
Let g(f) be the second derivative of -f**5/330 + 5*f**4/132 - 4*f**3/33 - 81*f**2/2 - 83*f. Let r(l) be the first derivative of g(l). Factor r(a).
-2*(a - 4)*(a - 1)/11
Let j(u) be the second derivative of -u**7/168 - 5*u**6/24 + 21*u**5/20 - u**4/12 - 14*u**3/3 - 3411*u. Let j(k) = 0. Calculate k.
-28, -1, 0, 2
Let i be -2*(0 - -4 - (-2109)/12). Let v = i + 379. Factor 243/2*x**3 - v*x + 3 - 405/2*x**4 + 27/2*x**2.
-3*(3*x - 1)**3*(5*x + 2)/2
Suppose -6*t - 11 = -149. Factor 2*u**2 - 9 + 4*u - 20*u + t + 18.
2*(u - 4)**2
Let q(x) = -3*x - 8. Let u be q(-5). Suppose p = u - 5. Let 16*b**p - 10*b**2 - 6*b**2 - b**3 + b = 0. What is b?
-1, 0, 1
Let k = 10 + -5. Suppose -9 = 4*l - 4*t - 1, -3*l - t + 10 = 0. Find j, given that -4*j + 4*j + k*j + l - 6 - j**2 = 0.
1, 4
Let c(p) be the third derivative of 3/5*p**3 + 0 - 1/2100*p**7 + 21/80*p**4 - 120*p**2 - 11/1200*p**6 + 17/600*p**5 + 0*p. Determine q, given that c(q) = 0.
-12, -1, 3
Factor 4/5*t**2 + 484/5*t - 488/5.
4*(t - 1)*(t + 122)/5
Let b(c) be the first derivative of -15*c**6/2 + 21*c**5 - 25*c**4/2 - 10*c**3 + 15*c**2/2 + 5*c - 1874. Factor b(x).
-5*(x - 1)**3*(3*x + 1)**2
Factor 18*u**3 - 114*u**4 - 77*u**3 - 18816 + 118*u**4 + 4232*u**2 - 9343*u - 185*u**3 - 4993*u.
4*(u - 28)**2*(u - 6)*(u + 1)
Suppose 1 - 124 = -3*s - 3*y, s - 25 = -5*y. Let h(b) be the first derivative of -s*b + 15*b**2 - 5/3*b**3 + 13. Factor h(j).
-5*(j - 3)**2
Suppose 9*t - 16 = 20. Factor c**5 - 62*c**3 + 32*c - 5*c**5 + 13*c**t + 7*c**4 + 38*c**3 - 16*c**2.
-4*c*(c - 2)**3*(c + 1)
Suppose -96 = -11*c + 14*c. Let z = c - -34. Let i(n) = 3*n**2 + 3*n - 2. Let w(t) = -4*t**2 - 4*t + 2. Let a(x) = z*w(x) + 3*i(x). Factor a(m).
(m - 1)*(m + 2)
Let q(f) = 3*f**2 - 6*f - 2. Let i be q(3). Let r be (i + (-162)/24)*0. Determine h, given that 0*h - 8/9*h**2 + 4/9*h**3 + r = 0.
0, 2
Let b(l) = -86*l - 28. Let i be b(-1). Suppose 8*j**3 + i + 4*j**5 - 58 + 12*j**4 + 0*j**3 = 0. What is j?
-2, -1, 0
Let u = -36 - -40. Suppose -28 = -8*b + u*b. Factor f + 7*f - 2*f**3 - b*f**3 + 5*f**3 + 4*f**2.
-4*f*(f - 2)*(f + 1)
Let r(f) be the first derivative of 1/4*f**4 + 1/2*f**5 - 5/6*f**3 + 0*f - 9 - 1/2*f**2. Solve r(k) = 0.
-1, -2/5, 0, 1
Let k(o) be the first derivative of 10 + 1/3*o**3 + 0*o**2 - 1/48*o**4 + 1/120*o**5 - 1/720*o**6 + 0*o. Let n(r) be the third derivative of k(r). Factor n(f).
-(f - 1)**2/2
Suppose -3*v - 4*a + 11 = 0, -2*v + 55*a + 11 = 54*a. Factor -16*r**2 - 32*r + 2*r**4 + 0 + 6*r**3 - 1/2*r**v.
-r*(r - 4)**2*(r + 2)**2/2
Let w(x) = -9*x**5 + 93*x**4 - 237*x**3 + 247*x**2 - 109*x + 13. Let i(s) = -s**4 + s**3 - s**2 + 2*s + 1. Let b(v) = -2*i(v) - 2*w(v). Factor b(d).
2*(d - 7)*(d - 1)**3*(9*d - 2)
Let t(p) = 2*p**2. Let u(d) = 11*d**2 + 5*d. Let c(f) = 11*f**2 + 6*f + 1. Let v(s) = 5*c(s) - 6*u(s). Let l(h) = 3*t(h) + v(h). Solve l(a) = 0.
-1, 1
Suppose -2*x + r = 0, -19 = 3*r - 13. Let t be (-1 - x)/(154/(-22)). Determine d so that t + 0*d**2 + 2/11*d - 2/11*d**3 = 0.
-1, 0, 1
Solve -142/9*l**3 - 37/9 - 11/3*l**4 - 49/3*l - 218/9*l**2 + 1/9*l**5 = 0.
-1, 37
Let 525/2*r - 144 - 277/4*r**2 - 3/4*r**3 = 0. Calculate r.
-96, 2/3, 3
Find x, given that -100/3*x + 4/3*x**2 + 200 = 0.
10, 15
Let l(g) be the third derivative of -g**7/525 + g**6/25 + 59*g**5/75 + 23*g**4/5 + 57*g**3/5 - 11*g**2 - 48*g. Find v, given that l(v) = 0.
-3, -1, 19
Let l be ((-18)/28*-3)/((-17655)/330 - -54). Suppose 6/7*c**2 + 0*c + 0 + 12/7*c**5 + 36/7*c**4 + l*c**3 = 0. What is c?
-2, -1/2, 0
Let b(i) = 4*i**3 - 22*i**2 - 12*i. Let x(p) = 11*p**2 - 11*p - 30*p**2 + 0*p - 2*p**3 + 7*p**3. Let k(g) = -5*b(g) + 6*x(g). Factor k(v).
2*v*(v - 1)*(5*v + 3)
Factor -2316*l**3 + 3184*l**2 + 1142*l**3 + 912*l + 1146*l**3.
-4*l*(l - 114)*(7*l + 2)
Factor -3/5*o**2 - 636/5 - 171/5*o.
-3*(o + 4)*(o + 53)/5
Factor 1766/3*x + 2/3*x**2 + 0.
2*x*(x + 883)/3
Determine x, given that 475*x**2 - 1001*x**2 + 70*x + 240 + 531*x**2 = 0.
-8, -6
Suppose 2028*j = 1355*j + 1346. Factor -1/4*v**3 - 3/4*v**j - 1/2*v + 0.
-v*(v + 1)*(v + 2)/4
Suppose 2*r - 5*g = 4*r - 11, -12 = 4*g. Let i = 15 - r. Determine m, given that 7*m**2 + m**2 + 6*m + 2*m**i - 5*m**3 - 11*m = 0.
0, 1
Let t(z) be the first derivative of z**4/26 - 172*z**3/39 - 356*z**2/13 - 720*z/13 - 3341. Factor t(i).
2*(i - 90)*(i + 2)**2/13
Let y be ((-12)/(-14))/((-2*2)/(-2324)). Factor 492*z**3 - y*z**3 + 5*z**2 - z**2.
-2*z**2*(3*z - 2)
Factor 122/9*z**2 + 2/9*z**3 - 2048/3 + 1664/9*z.
2*(z - 3)*(z + 32)**2/9
Find i such that 3870*i**2 + 148*i**4 - 1340*i + 5319*i + 1080 + 47*i**4 + 4*i**5 - 199*i + 6*i**5 + 1355*i**3 = 0.
-6, -1, -1/2
Let t be 2 - (-3)/((-9)/15). Let n(d) = d**3 - d**2 + 1. Let y(f) = -f**3 + f**2 - 2*f - 1. Let w(a) = t*n(a) - y(a). Factor w(z).
-2*(z - 1)**2*(z + 1)
Let z(x) be the second derivative of x**7/189 + 86*x**6/135 + 2929*x**5/90 + 24670*x**4/27 + 410800*x**3/27 + 1352000*x**2/9 - 186*x + 5. What is h in z(h) = 0?
-20, -13
Let p(m) be the third derivative of m**7/168 - 2*m**6/9 - m**5/24 + 10*m**4