v) be the second derivative of -v**8/5040 + 13*v**7/1260 - 169*v**6/1080 + 21*v**3/2 - v - 85. Let n(r) be the second derivative of l(r). Solve n(t) = 0.
0, 13
Let d = 21865/15554 + -54/1111. Let h(p) be the first derivative of -12/7*p + d*p**2 - 4 - 4/21*p**3. Factor h(n).
-(n - 4)*(4*n - 3)/7
Suppose 5*l - 140 = -110. Let -6*p**3 + 45 - 112 + 43 + 27*p**2 - 3*p**4 + l*p = 0. Calculate p.
-4, -1, 1, 2
Let c(a) be the second derivative of -33*a**5/10 - 65*a**4/3 + 8*a**3/3 + 4*a - 59. Factor c(s).
-2*s*(s + 4)*(33*s - 2)
Find h, given that 2*h + 16095*h**3 - 3*h**2 - 4*h - 16133*h**3 + 4*h**2 - 41*h**2 = 0.
-1, -1/19, 0
Let k(s) be the third derivative of s**5/12 + 575*s**4/24 + 565*s**3/3 - 670*s**2. Factor k(h).
5*(h + 2)*(h + 113)
Suppose 8*a + 456 = 128. Let v = 45 + a. Factor 0 + 0 + 12*h**3 - 10*h**3 + v*h**2 - 6*h.
2*h*(h - 1)*(h + 3)
Let 27*m + 483*m**2 - 2184*m**3 - 41*m + 2175*m**3 - 300*m - 4*m = 0. What is m?
0, 2/3, 53
Let o(s) be the second derivative of 5*s**4/48 - 5*s**3 + 315*s**2/8 - 37*s - 3. Factor o(q).
5*(q - 21)*(q - 3)/4
Let w(g) be the first derivative of -147 + 0*g + 37/2*g**2 - 1/3*g**3. Determine z, given that w(z) = 0.
0, 37
Suppose -r + 4*c = 52, 4*c + 60 - 8 = -r. Let z = 55 + r. Factor -2*v**z - 5*v**3 - 25 + 5 - v**3 + 56*v - 28*v**2.
-4*(v - 1)*(v + 5)*(2*v - 1)
Let b(i) = -440*i**3 + 2058*i**2 - 1118*i + 158. Let m(f) = -4*f**3 + f**2 + 3*f + 1. Let z(o) = -b(o) - 2*m(o). Solve z(s) = 0 for s.
2/7, 5/16, 4
Let w(z) = z - 1. Let x(c) = c - 15. Let u be x(18). Let l be w(u). Factor -54*f - 6*f**l - 243 - 8*f**2 + 11*f**2.
-3*(f + 9)**2
Let j = 137785 - 137783. Suppose 2/9*b**j + 8/9*b + 0 = 0. Calculate b.
-4, 0
Suppose 2*r + 30 = 17*r. Let q = 760 - 2278/3. Suppose -q - n**r - 5/3*n = 0. Calculate n.
-1, -2/3
Let m be ((-36)/(-19) - 2) + 44545/7847 - 1. Factor -m + 62/7*y - 2/7*y**3 - 4*y**2.
-2*(y - 1)**2*(y + 16)/7
Suppose -3*n - m = -6*n + 77, 3*m = -3*n + 69. Determine f so that 52*f**4 + 672*f + 664*f**2 - 2*f**4 + 106*f**3 - 386*f**3 + 144 - n*f**4 = 0.
-2/5, 6
Let s(a) = a**2 + 120*a + 269. Let n(z) = -26*z - 1. Let o(f) = 6*n(f) - s(f). Find w, given that o(w) = 0.
-275, -1
Let l = 23463/2774 + 58/1387. Let 17/2*k**2 + 0 + 0*k**3 - 2*k + 2*k**5 - l*k**4 = 0. Calculate k.
-1, 0, 1/4, 1, 4
Factor -20*y**2 + 35*y**2 - 25*y + 5*y**3 + 24*y**2 + 41*y**2 - 210 + 150*y.
5*(y - 1)*(y + 3)*(y + 14)
Let u(g) be the second derivative of -g**5/10 - 6*g**4 - 11*g**3 + 70*g**2 - 38*g + 8. Factor u(c).
-2*(c - 1)*(c + 2)*(c + 35)
What is u in 761 + 6336*u**3 - 77*u**4 - 2500*u - 7198*u**3 - 2865*u**2 - 1261 = 0?
-5, -10/11, -2/7
Let l(v) = -14*v + 96 - 11*v**2 - 37*v + 24*v**2. Let r(m) = -20*m**2 + 76*m - 144. Let x(c) = 8*l(c) + 5*r(c). Solve x(d) = 0.
3, 4
Suppose -40*h + 40 = -20*h. Factor 3*u**3 - 70*u - 3*u**2 + u**2 - u**h + 16*u - 6*u**2.
3*u*(u - 6)*(u + 3)
Let d(v) be the third derivative of v**8/1344 - 13*v**7/420 + 107*v**6/240 - 9*v**5/5 - 405*v**4/32 + 243*v**3/4 - v**2 + 112*v - 5. Factor d(k).
(k - 9)**3*(k - 1)*(k + 2)/4
Let t(q) be the second derivative of -23*q**4/102 + 9*q**3/17 + 50*q**2/17 - 1682*q. Determine u so that t(u) = 0.
-1, 50/23
Let b(z) be the second derivative of 108/35*z**5 - 8/7*z**3 + 0*z**2 + 27/14*z**7 + 4/7*z**4 + z - 162/35*z**6 - 16. Determine f so that b(f) = 0.
-2/7, 0, 2/3
Suppose -79888*a**2 + 159779*a**2 - 79888*a**2 + 393*a - 396 = 0. Calculate a.
-132, 1
Let n(q) = q**2 - 2*q + 2. Let g(w) = 4*w**2 - 4*w + 5. Suppose v - 7 = -2*m, -2*v + 5 = -23*m + 18*m. Let a(h) = v*n(h) - g(h). Solve a(b) = 0 for b.
1, 5
Let u(c) = 5*c - 100. Let v be u(16). Let a(i) = -6*i - 118. Let w be a(v). Factor 0 + n**w - 1/2*n**3 - 1/2*n.
-n*(n - 1)**2/2
Solve -345/7 - 342/7*k + 3/7*k**2 = 0 for k.
-1, 115
Suppose 0*m - 4*m**2 - 1/4*m**5 - 9/2*m**4 + 0 - 33/4*m**3 = 0. Calculate m.
-16, -1, 0
Suppose -6 = -10*w + 7*w. Let h = 55563 + -444483/8. Factor -27/8*n + 3/4 + h*n**w.
3*(n - 1)*(7*n - 2)/8
Let r(a) = -8*a**3 + 360*a**2 - 2781*a + 5531. Let c(b) = -10*b**3 + 360*b**2 - 2780*b + 5540. Let h(l) = 3*c(l) - 4*r(l). Factor h(p).
2*(p - 172)*(p - 4)**2
Let b be ((-5288)/14)/(-17 + 10818/630). Let s = -2202 - b. Factor 34/15*i - 16/15 - s*i**2 + 2/15*i**3.
2*(i - 8)*(i - 1)**2/15
Let k(d) = 8*d + 235. Let w be k(-29). Solve -52*z**4 - 4 + 1883*z**w - 1 - 1887*z**3 + 20*z**5 + 68*z**2 - 16*z - 11 = 0 for z.
-1, -2/5, 1, 2
Let k = 9661 + -9659. Factor -1 + 1/3*q + q**k - 1/3*q**3.
-(q - 3)*(q - 1)*(q + 1)/3
Let s(u) be the second derivative of 3*u**5/20 + 7*u**4/2 + 13*u**3/2 - 1226*u. Factor s(q).
3*q*(q + 1)*(q + 13)
Let c(j) = 208*j**2 - 283*j - 56. Let r(m) = 631*m**2 - 852*m - 168. Let y(g) = 10*c(g) - 3*r(g). Factor y(q).
(11*q + 2)*(17*q - 28)
Let x(p) = 10*p**2 - 434*p + 480. Let y(f) = -2*f**2 + 86*f - 96. Let k(g) = 6*x(g) + 28*y(g). Let k(b) = 0. Calculate b.
1, 48
Let t(l) = l. Let z be (-6)/2*(3 + -4). Let h(b) = b + 19*b**3 + b**2 - 12*b**z - 8*b**3. Let c(j) = h(j) - t(j). Solve c(q) = 0 for q.
0, 1
Let s = 151 - -182. Let k = s + -331. Let 18/5*j**k + 42/5*j**3 + 9/5*j**5 - 3/5 + 33/5*j**4 - 3/5*j = 0. Calculate j.
-1, 1/3
Let n be (-3)/12 - (231/(-12) + 4). Suppose p + 29*l - 28*l = 6, 0 = -5*l + n. Solve 2/3*k**4 + 0*k - 8/3*k**p + 8/3*k**2 + 0 = 0 for k.
0, 2
Let r = -270 - -279. What is y in -10*y**2 + y**4 + 8*y - r*y - 3*y**3 + 13*y**2 = 0?
0, 1
Solve 0*h + 100/3*h**2 - 48 + 4/3*h**4 + 40/3*h**3 = 0 for h.
-6, -3, -2, 1
Let l(t) be the second derivative of -t**7/42 - 31*t**6/30 + 3*t**5/20 + 95*t**4/12 + 31*t**3/3 - 379*t. Suppose l(r) = 0. Calculate r.
-31, -1, 0, 2
Let t be (2 + (-26)/8 - (-26)/8) + (-3320)/(-996). Factor 4/3*w**2 + 0 + t*w - 2/3*w**3.
-2*w*(w - 4)*(w + 2)/3
Let c(b) be the second derivative of -b**5/10 + 115*b**4 - 39904*b**3 + 236672*b**2 + 11*b - 46. Factor c(k).
-2*(k - 344)**2*(k - 2)
Let q be -1*(7 - 2) + (-1382)/(-77). Let j = 144/11 - q. Suppose 5/7*t**4 + 0 + 4/7*t**5 + 0*t**2 + 0*t + j*t**3 = 0. Calculate t.
-1, -1/4, 0
Let b(s) be the second derivative of -3*s**5/80 - 3*s**4/2 - 101*s**3/8 - 171*s**2/4 - 16*s + 1. Factor b(a).
-3*(a + 2)*(a + 3)*(a + 19)/4
Let i(m) be the third derivative of -1/30*m**5 + 6*m**2 - 6 + 0*m + 0*m**4 + 0*m**3 - 17/120*m**6. Let i(h) = 0. What is h?
-2/17, 0
What is v in -5625 - 7825/4*v**2 - 275/4*v**3 + 49/4*v**4 - 1/4*v**5 - 7500*v = 0?
-5, -1, 30
Let x = -150251 - -450755/3. Factor -p + 0 + x*p**3 + 23/6*p**2.
p*(p + 6)*(4*p - 1)/6
Let v(h) be the second derivative of -h**4/8 - 801*h**3/2 + 4809*h**2/4 + 8210*h. Determine x, given that v(x) = 0.
-1603, 1
Suppose -400/11 - 92/11*z + 2/11*z**2 = 0. Calculate z.
-4, 50
Let v(q) = 88*q + 5. Let t be v(1). Suppose -t - 27 = -5*m. Factor 32 + 2*n**2 - 3*n**2 - n**2 - 104 - m*n.
-2*(n + 6)**2
Factor 4/9*m**4 + 148/9*m**3 + 400*m + 0 + 448/3*m**2.
4*m*(m + 6)**2*(m + 25)/9
Let a(f) = -6*f + 6. Let r be a(-2). Factor -11*j + 3*j**3 - 10*j - 18*j**2 + 30*j - 12*j + r.
3*(j - 6)*(j - 1)*(j + 1)
Let k(b) be the second derivative of -2*b + 0*b**2 - 3 + 2*b**4 + 1/15*b**5 + 0*b**3. Factor k(h).
4*h**2*(h + 18)/3
Let u(j) be the third derivative of 9*j**2 + 0*j**3 + 0*j - 1/6*j**4 + 0 - 1/15*j**6 - 1/6*j**5 - 1/105*j**7. Find q, given that u(q) = 0.
-2, -1, 0
Suppose -1463 = -q - 6*q. Find w such that 548*w - 11*w**2 - 255*w + 47*w**2 - q*w - 4*w**3 + 44 = 0.
-1, 11
Let f(p) = 6*p + 36. Let r be f(-5). Suppose 5*z = 3*h + 13, -4*h + r*z = 2*z + 4. Factor -9*i**3 + 4*i**3 + i**h + 5*i**3 + i**5.
i**4*(i + 1)
Suppose 2383140 = -51*q + 2383242. Let 0*d + 6 - 9/2*d**q - 3/2*d**3 = 0. What is d?
-2, 1
Solve -94/5*a**2 + 94/5 - 1/5*a + 1/5*a**3 = 0.
-1, 1, 94
Solve 44581*i + 38363*i - 210*i**4 - 4752*i**3 - 521055*i**2 - 3*i**5 + 489951*i**2 = 0 for i.
-24, 0, 2
Suppose 20 = -4*g, -5*v + v + 5*g = -57. Suppose 0 = 3*a - v*a. Factor 8*x**3 + 12*x**2 - 105 + 2*x**4 + 8*x + a*x + 107.
2*(x + 1)**4
Let y(t) be the first derivative of t**3/6 - 31*t**2/4 + 54*t - 5552. Suppose y(l) = 0. Calculate l.
4, 27
Let s(i) = -i**3 - 6*i**2 + 17*i + 11. Let c be s(-8). Let j = 31 - 29. Factor -7*q + 3*q - j*q**4 + 9*q**3 - 5*q**c + 2*q**2.
-2*q*(q - 2)*(q - 1)*(q + 1)
Let u(k) be the third derivative of -k**2 + 0 + 1/120*k**5 + 0*k + 1/12*k**3 + 5/96*k**4. Find w such that u(w) = 0.
-2, -1/2