0*t**5 + 18*t. Factor v(x).
-(x + 1)**2*(2*x - 3)/2
Let f(b) be the first derivative of -b**5/210 - 5*b**4/63 - 4*b**3/21 - b**2 - 45*b - 78. Let c(d) be the second derivative of f(d). Find u such that c(u) = 0.
-6, -2/3
Suppose -3*x = -w + 33 - 1, 20*w + 5*x = x. Determine i so that 2/19*i + 0 - 6/19*i**w = 0.
0, 1/3
Let q be 5 - 3*(-6)/18. Let a be (-4)/q - 11/((-66)/16). Determine j so that 10*j**a - 11*j**2 - j + 2*j + 2 = 0.
-1, 2
Let l = 435 + -432. Let d be (-6 + 14)/(l + 0/2). Determine w so that d*w + 1/3*w**2 + 16/3 = 0.
-4
Factor -49*l**4 - 133 - 10570 + 60180*l + 1800*l**3 - 33709*l**2 + 394 - 18591 + 678*l**3.
-(l - 1)**2*(7*l - 170)**2
What is c in -24/17*c - 2/17*c**3 + 8/17*c**4 + 0 + 2/17*c**5 - 32/17*c**2 = 0?
-3, -2, -1, 0, 2
Let y(n) be the second derivative of -2*n**7/315 - 7*n**6/360 - n**5/90 + n**4/72 - 26*n**2 + n + 96. Let u(m) be the first derivative of y(m). Factor u(t).
-t*(t + 1)**2*(4*t - 1)/3
Suppose -54*x + 60*x = -6. Let z be 2 - (6/24)/x. Factor 0*n + 0 - 3/4*n**3 + z*n**2.
-3*n**2*(n - 3)/4
Let j = -1535 - -7676/5. Let a(b) be the second derivative of 0 + 8*b + 7/60*b**4 + 1/50*b**5 + 7/30*b**3 + j*b**2. Find z, given that a(z) = 0.
-2, -1, -1/2
Suppose -4*m + 136 = 4*t, 3*m = -0*m + 12. Suppose t = r + r. Suppose 13*g**4 + 52*g**3 + 6*g**2 + 2*g**2 - 6*g**4 - r*g**4 - 52*g**5 = 0. Calculate g.
-1, -2/13, 0, 1
Let l = 122/2409 + 14/73. Let g(j) be the first derivative of 3/11*j**4 - 8/55*j**5 + 1/11*j**2 - l*j**3 + 1/33*j**6 + 0*j + 30. Factor g(x).
2*x*(x - 1)**4/11
Let b(q) be the third derivative of q**6/600 + 13*q**5/300 + 47*q**4/120 + 7*q**3/6 - 711*q**2 + 2*q. Find g such that b(g) = 0.
-7, -5, -1
Let u = 3294 - 82348/25. Let s(a) be the first derivative of 0*a**2 - 10 - u*a**5 + 0*a + 1/30*a**6 + 0*a**3 - 3/20*a**4. Factor s(q).
q**3*(q - 3)*(q + 1)/5
Factor 6*p**3 - p**4 - 6*p**4 - 9*p**2 + 12 - 4*p + 6*p**4.
-(p - 3)*(p - 2)**2*(p + 1)
Let c = -83 - -92. Let w be 6/(-2)*(2 + (-57)/c). Factor 1 + 368*r**2 - 372*r**2 + 16*r - w.
-4*(r - 3)*(r - 1)
Let z be -21 + 35 + -23 + (-13)/(-1). Factor -20/3*a**3 + 361/6 + 1/6*a**z + 73*a**2 - 380/3*a.
(a - 19)**2*(a - 1)**2/6
Let p(c) be the first derivative of 70 - 2/3*c**3 - 31/3*c**2 - 20/3*c. Solve p(r) = 0.
-10, -1/3
Suppose -1761 = -1984*o + 2207. Let t be 1/2*(2 + -2). Solve 9/2*d**o - 21/4*d**4 + 57/4*d**3 + 0 + t*d = 0 for d.
-2/7, 0, 3
Let -2536/9*r - 2/9*r**3 + 640/9*r**2 + 2528/9 = 0. What is r?
2, 316
Let w(j) be the third derivative of j**10/6048 + 5*j**9/3024 + j**8/168 + j**7/126 + 8*j**4/3 + 22*j**2. Let z(k) be the second derivative of w(k). Factor z(s).
5*s**2*(s + 1)*(s + 2)**2
Suppose -4*p = -2*z, 0*p + 2*p + 6 = 4*z. Factor 2*o**4 + 539*o**3 + z + 2*o**2 - 6*o**2 - 539*o**3.
2*(o - 1)**2*(o + 1)**2
Let f(i) be the first derivative of 157 + 0*i + 21/2*i**4 + 0*i**2 + 0*i**3 - 3/5*i**5. Find q, given that f(q) = 0.
0, 14
Suppose 29*q - 421 = -2596. Let o = q + 527/7. Factor 0 + o*u**3 + 0*u**2 + 0*u + 2/7*u**4.
2*u**3*(u + 1)/7
Let c(d) be the first derivative of 2*d**5/45 + 404*d**4/9 + 16080*d**3 + 2138400*d**2 - 8748000*d + 2261. Determine o, given that c(o) = 0.
-270, 2
Suppose 9*b - 23*b - 13*b = -54. Let k(f) be the second derivative of 0 + 2/21*f**3 + 1/5*f**5 + 8*f + 11/42*f**4 + 0*f**b. Factor k(i).
2*i*(2*i + 1)*(7*i + 2)/7
Let u(p) be the first derivative of 0*p - 84*p**3 + 3969*p**2 + 144 + 1/2*p**4. Determine m so that u(m) = 0.
0, 63
Let p(l) = 52*l**2 + 3*l - 28*l**2 - 2 - 23*l**2. Let f be p(1). Let f*r**2 - 7 + 5 + 10 + 8*r = 0. Calculate r.
-2
Let s(z) be the first derivative of 0*z**2 + 2/21*z**3 + 0*z + 165 + 1/28*z**4. Determine h, given that s(h) = 0.
-2, 0
Let j be 0/20 + (-185)/40 + 5. Determine y, given that 3*y**2 - 27/4 + j*y**3 - 33/8*y = 0.
-9, -1, 2
Find d such that -2/3*d**4 + 0 + 80*d**2 - 544/3*d - 6*d**3 = 0.
-17, 0, 4
Let k(h) be the first derivative of h**6/9 - 12*h**5/5 + 10*h**4 + 400*h**3/9 + 801. Factor k(x).
2*x**2*(x - 10)**2*(x + 2)/3
Let p be (-120)/(-570)*(-760)/(-16) + -7. What is g in 45/2*g + 407/4*g**2 + 7/4 - 16*g**5 + 84*g**4 + 181*g**p = 0?
-1, -1/4, 7
Let v(t) be the third derivative of t**7/1155 - 61*t**6/165 + 218*t**5/5 + 15128*t**4/33 + 61504*t**3/33 + 1953*t**2. Let v(c) = 0. Calculate c.
-2, 124
Let a be (3/(-2))/((-585)/182 + 3). Suppose a = -4*k + 2*q - 3, k + 5*q = 25. Solve 4/5*v**2 + 0 + 2/5*v**3 + k*v - 2/5*v**4 = 0.
-1, 0, 2
Find q such that -47*q + 3*q - 4*q**3 + 3*q - 11*q + 56*q**2 = 0.
0, 1, 13
Let o(p) = -p**2 + 8*p - 6. Let d(n) = -13*n + 8*n**2 - 67*n + 47 + 15*n. Let i(j) = 6*d(j) + 51*o(j). Factor i(m).
-3*(m - 4)*(m - 2)
Let r(m) be the third derivative of -25/2*m**3 - 15/8*m**4 + 9/20*m**5 + 196*m**2 + 0 - 1/40*m**6 + 0*m. Suppose r(b) = 0. What is b?
-1, 5
Let k(g) be the first derivative of -20*g + 66 - g**5 + 5*g**3 - 5/2*g**4 + 10*g**2. Solve k(f) = 0 for f.
-2, 1
Let d = 45 + -36. Factor d + 16*u**2 - 2*u**4 - 21 - 15 - 5.
-2*(u - 2)**2*(u + 2)**2
Suppose 10*q - 3 = 7. Let z be 2 + 10 - -3*q. Factor -20*b**3 - 17*b**2 - 4*b**4 - 8*b**2 - z*b - 3*b**2 + 3*b.
-4*b*(b + 1)**2*(b + 3)
Suppose -8893 = 33*y - 181. Let t be (-1218)/y + 24/(-66). Factor 11/2*l**3 + 2*l**4 + t*l + 1/4*l**5 + 1 + 7*l**2.
(l + 1)**4*(l + 4)/4
Let t(p) be the third derivative of -p**6/1260 - 53*p**5/210 - 2809*p**4/84 + 49*p**3/2 + 182*p**2. Let a(h) be the first derivative of t(h). Factor a(l).
-2*(l + 53)**2/7
Let d be ((-147)/(-5) - 5) + (-4)/10. Suppose -3*h - 9 = -4*i, 5*h - 29 + d = 0. Suppose 5/3*z**2 + 0*z**i - 4/3 - 1/3*z**4 + 0*z = 0. Calculate z.
-2, -1, 1, 2
Factor 246*m + 278*m + 150 + 110 + m**2 + 207 + 56.
(m + 1)*(m + 523)
Let u = -286 - 108. Let v = u + 3548/9. Solve 4/3 + v*d**2 - 10/9*d = 0 for d.
2, 3
Let n(j) = -59*j + 18. Let m(b) = -b**2 - 61*b + 20. Let u(t) = 3*m(t) - 2*n(t). Let v be u(-22). Suppose 2/3*p**3 + 4/3 + 8/3*p**v + 10/3*p = 0. What is p?
-2, -1
Let d be ((-1)/45)/(-48*(-72)/(-51840)). Factor 1/3*k**2 - d + 7/3*k - 7/3*k**3.
-(k - 1)*(k + 1)*(7*k - 1)/3
Let i = -123/5 + 2593/105. Let q(a) be the second derivative of 2/5*a**6 - 2*a**2 - 2/3*a**4 + 2*a**3 - 2/5*a**5 - 32*a - i*a**7 + 0. Let q(f) = 0. Calculate f.
-1, 1
Let z be 3/420*155 - (-36)/(-42). Let t(m) be the first derivative of z*m - 3/8*m**2 - 1/3*m**3 - 51. Factor t(u).
-(u + 1)*(4*u - 1)/4
Let o(v) be the first derivative of 2/55*v**5 - 2/11*v**3 - 8/11*v - 1/11*v**4 + 8/11*v**2 + 186. Solve o(i) = 0 for i.
-2, 1, 2
Let c(b) be the second derivative of -47*b**4/9 + 184*b**3/9 + 8*b**2/3 + 444*b. Factor c(x).
-4*(x - 2)*(47*x + 2)/3
Let k(g) be the first derivative of -200 + 4/5*g**5 + 1/36*g**6 - 13/6*g**4 + 1/9*g**3 + 17/4*g**2 - 13/3*g. Determine u, given that k(u) = 0.
-26, -1, 1
Let k = 536750 + -536747. Suppose 2/3*g**k - 4*g**2 + 6*g - 8/3 = 0. What is g?
1, 4
Factor -256*l + 0*l**3 + 13034 + l**3 - 12650 + 24*l**2 + 3*l**3.
4*(l - 4)*(l - 2)*(l + 12)
Let i(m) be the first derivative of -m**6/720 - m**5/30 + 3*m**4/16 + m**3 - 3*m + 108. Let j(a) be the third derivative of i(a). Solve j(x) = 0.
-9, 1
Suppose 7*r = 5 + 72. Solve -8*x - 1 + 2*x**2 + 0 + r - 2 = 0.
2
Let y(c) be the first derivative of 4/5*c - 144 + 7/10*c**3 + 11/10*c**2 + 1/50*c**5 + 1/5*c**4. What is t in y(t) = 0?
-4, -2, -1
Let c(m) = -87*m**3 - 376*m**2 - 4360*m - 11395. Let z(d) = 488*d**3 + 2068*d**2 + 23980*d + 62672. Let q(a) = 28*c(a) + 5*z(a). Factor q(v).
4*(v - 57)*(v + 5)**2
Let u be -6 - -1 - (8 + -15). Let q(m) = m**4 + 8*m**3 + 9*m**2 - 8*m - 4. Let t(c) = -c**4 + c**2 - 2. Let i(n) = u*q(n) + 6*t(n). Factor i(g).
-4*(g - 5)*(g - 1)*(g + 1)**2
Let x be (-21)/21 - (-3)/1. Suppose -11*n**3 - 40*n**2 + 7*n**3 + 4*n**x = 0. What is n?
-9, 0
Find h, given that 54*h**2 + 190*h**4 - 182*h**4 - 124*h**2 - 4*h**5 - 10*h**2 + 28*h**3 + 48*h = 0.
-3, 0, 1, 2
Suppose 157/6*t**2 + 0 - 164/3*t**3 + 8/3*t**4 + 10*t = 0. Calculate t.
-1/4, 0, 3/4, 20
Let c(p) = -p**2 + p + 1. Let f(s) be the second derivative of 2*s**4 - 10*s**3 + 22*s**2 + 48*s. Let u(v) = 20*c(v) + f(v). Factor u(x).
4*(x - 8)*(x - 2)
Let m(h) be the third derivative of -2*h**2 - 1/15*h**4 - 1/5*h**3 - 102 - 1/150*h**5 + 0*h. Determine z, given that m(z) = 0.
-3, -1
Let c be (-92)/138 + (-2)/6 + -2. Let l be c - (16/6)/(75/(-90)). Suppose l*v**2 