2*f + 3*p = 500, 0 = 2*f + 5*p - 4*p - 492. Let n = f - 730/3. Determine k so that 0 + n*k**3 - 8/3*k**4 - 2/3*k + 8/3*k**2 = 0.
-1, 0, 1/4, 1
Let q be -1 - 2 - (3 + (-8)/1). Let o(t) = -t**3 + 4*t. Let b be o(q). Factor 14*u**3 + b*u**4 + 35*u**2 - 49*u**2 - 36 - u**4 + 84*u - 47*u**2.
-(u - 6)**2*(u - 1)**2
Let j = -5963 - -5966. Let o(v) be the second derivative of 1/18*v**4 + 0*v**j + 1/45*v**6 + 19*v + 0 + 0*v**2 + 1/15*v**5. Factor o(k).
2*k**2*(k + 1)**2/3
Let o(c) be the first derivative of 34/9*c**2 + 264 + 8*c + 14/27*c**3 - 1/36*c**4. What is r in o(r) = 0?
-2, 18
Let k(t) be the third derivative of 21/4*t**4 + 0 - 31*t - 2*t**2 + 1/20*t**5 - 43/2*t**3. Factor k(c).
3*(c - 1)*(c + 43)
Factor 0 - 136/5*r**2 + 2/5*r**3 + 2312/5*r.
2*r*(r - 34)**2/5
Let l(w) = -w**3 + 3*w**2 + 2. Let n be l(3). Suppose 2*y - n*b - 3*b = -15, 15 = 5*b. Find x such that -2 + x**2 + x**3 + y*x - x + 0 + 1 = 0.
-1, 1
Let g(a) be the third derivative of -a**5/300 + 149*a**4/60 - 2397*a**2. Determine y so that g(y) = 0.
0, 298
Let g be -2*(21/4)/(-3). Let q = 5335/2202 + 85/1101. Suppose 9*x**2 - g*x**3 - q*x**4 + 4 + 14*x = 0. Calculate x.
-2, -1, -2/5, 2
Let v be -21*((-325)/175)/13 - -141. Solve -v - 1/4*j**2 + 12*j = 0.
24
Let z(k) be the first derivative of -k**4/20 - k**3 - 27*k**2/10 - 13*k/5 - 556. Factor z(m).
-(m + 1)**2*(m + 13)/5
Let r be -5*(0 + -1) - ((-3724)/(-630) + (-1296)/720). Factor 10/9 - 2/9*f**2 + r*f.
-2*(f - 5)*(f + 1)/9
Let n(c) be the first derivative of -c**5/12 + 15*c**3/2 - c**2/2 - 108*c + 110. Let k(g) be the second derivative of n(g). Let k(o) = 0. Calculate o.
-3, 3
Suppose 0*d + 168 = -4*d. Let q = 65 + d. Solve -q*p**2 - 6*p - 9 - 20*p**2 + 46*p**2 = 0.
-1, 3
Factor 2716 + 4*h**2 - 67*h - 262*h - 87*h.
4*(h - 97)*(h - 7)
Let u(p) = -6*p**3 - 38*p**2 + 2. Let z(t) be the first derivative of 7*t**4/4 + 37*t**3/3 - 3*t + 14. Let v(c) = 3*u(c) + 2*z(c). Factor v(g).
-4*g**2*(g + 10)
Suppose -8 = 13*h - 372. Suppose h*m = 38*m - 680. Determine k so that 0*k + m*k**2 + 196/3*k**3 + 16*k**4 - 16/3 = 0.
-2, -1/3, 1/4
Factor -1259 - 8406*j - 733 - 496552*j**2 + 2428*j + 496546*j**2.
-2*(j + 996)*(3*j + 1)
Let u(n) be the second derivative of n**6/240 - n**5/12 + 3*n**4/16 - 113*n**2/2 + 50*n. Let h(k) be the first derivative of u(k). What is m in h(m) = 0?
0, 1, 9
Let o(r) = -44*r + 266. Let f be o(6). Let v = 2470 - 2470. Factor -6/7*j**4 - 6/7*j**f - 15/7*j**3 + v + 0*j.
-3*j**2*(j + 2)*(2*j + 1)/7
Let v be (-136)/51*(-9)/8. Determine p so that 1/5*p**5 + 0 + 7/5*p**v - 6/5*p**2 - 8/5*p + 6/5*p**4 = 0.
-4, -2, -1, 0, 1
Let f = 710 + -706. Find k, given that 907*k**4 + 30*k**3 + 32*k - 903*k**4 - 6*k**5 + f*k**5 + 0*k**5 - 64*k**2 = 0.
-4, 0, 1, 4
Let h = -4 + -8. Let b = h + 15. Solve 19*f**b + f**4 + 16*f - 5*f**4 - 4 - 3*f**4 + f**5 - 25*f**2 = 0 for f.
1, 2
Let u(i) = 10*i**2 - 166*i - 579. Let k(m) = 3*m**2 + m - 21. Let q(a) = 6*k(a) - 2*u(a). Find c such that q(c) = 0.
-3, 172
Let l(y) be the second derivative of 0 + 2/11*y**3 - 7*y + 3/11*y**2 + 1/22*y**4. Find z, given that l(z) = 0.
-1
Let b(x) = -11*x**3 + 13 + 12 + 37*x + 15*x**3 - 20 + 21*x**3 - 46*x**2. Let t(o) = 26*o**3 - 44*o**2 + 38*o + 6. Let u(p) = 6*b(p) - 5*t(p). Factor u(q).
4*q*(q - 2)*(5*q - 4)
Find i such that -60*i + 21*i**2 - 22*i - 18 + 31*i - 6*i = 0.
-2/7, 3
Let 2*y**3 - 1/4*y**4 + y**2 - 8*y + 0 = 0. Calculate y.
-2, 0, 2, 8
Let i(u) be the first derivative of 99 + 32*u**2 + 3072*u + 1/9*u**3. Determine s so that i(s) = 0.
-96
Let y(v) = -v**3 + 18*v**2 - 3*v - 30. Let d(c) be the first derivative of -c**4/2 + c**3/3 - c**2/2 - 69. Let s(r) = -2*d(r) - y(r). Factor s(t).
5*(t - 3)*(t - 2)*(t + 1)
Let j(v) be the first derivative of -v**5/35 + 3*v**4/14 + 3*v**3/7 - v**2 + 1096. Factor j(d).
-d*(d - 7)*(d - 1)*(d + 2)/7
Let z(c) = c**4 + 334*c**3 - 2096*c**2 + 4282*c - 2878. Let a(j) = 3*j**4 + 1672*j**3 - 10478*j**2 + 21411*j - 14389. Let s(r) = -2*a(r) + 11*z(r). Factor s(k).
5*(k - 2)**3*(k + 72)
Let x(y) be the second derivative of y**7/21 + 5*y**6/3 + 39*y**5/5 - 27*y**4 - 261*y**3 - 567*y**2 - y + 4848. Determine t, given that x(t) = 0.
-21, -3, -1, 3
Let r(j) be the first derivative of 5*j**6/6 - 31*j**5 - 85*j**4/2 + 320*j**3/3 - 1229. Determine t so that r(t) = 0.
-2, 0, 1, 32
Let j = -233184 + 233186. Factor 31/3 - 10*p - 1/3*p**j.
-(p - 1)*(p + 31)/3
Let t(p) be the third derivative of 163*p**6/600 - 487*p**5/300 + 8*p**4/3 + 2*p**3/15 - 2414*p**2. Factor t(v).
(v - 2)*(v - 1)*(163*v + 2)/5
Let t = -2/1342073 - -5368310/12078657. Suppose -1/9*w**5 + 0*w**2 + t*w**4 + 5/9*w**3 + 0*w + 0 = 0. What is w?
-1, 0, 5
Let r = 2042/15 - 34684/255. What is p in 6*p**2 + 0*p + r*p**3 + 0 = 0?
-51, 0
Let x(j) be the third derivative of -2 + 0*j + 5/8*j**4 - 1/8*j**6 - 5/3*j**3 + 36*j**2 + 1/42*j**7 + 1/12*j**5. Determine z, given that x(z) = 0.
-1, 1, 2
Let f(y) = -y**3 - 11*y**2 - 10*y + 4. Let v(l) = -l**3 - 21*l**2 - 20*l + 9. Let z = 83 - 74. Let c(x) = z*f(x) - 4*v(x). Find o, given that c(o) = 0.
-2, -1, 0
Let x(b) be the first derivative of -5*b**3/3 - 15*b**2/2 + 140*b + 351. Solve x(d) = 0 for d.
-7, 4
Let h(q) be the first derivative of 3*q**4/16 - 7*q**3/12 - 9*q**2/4 - 2*q + 111. Factor h(b).
(b - 4)*(b + 1)*(3*b + 2)/4
Let q(g) be the first derivative of -g**4/16 + 1301*g**3/6 - 1692601*g**2/8 - 5798. Find h, given that q(h) = 0.
0, 1301
Let d be (-2)/12 - 15/((-1350)/465). Let g be (d - (-6 - (-154)/12)) + 2. Solve -f**2 - 2/3*f - 1/6 - g*f**4 - 2/3*f**3 = 0 for f.
-1
Suppose -5*s - a - 385 = -384, s + 5 = -5*a. Factor 4/3*k - 58/9*k**2 + s + 2*k**3.
2*k*(k - 3)*(9*k - 2)/9
Let a(t) be the first derivative of -2*t**5/65 + 75*t**4/13 + 608*t**3/39 + 2149. Find r, given that a(r) = 0.
-2, 0, 152
Let n be (7 + 0)*(-40 - -36). Let z be 5 + n/(-12) + 35/(-5). Factor -z*l - 1/6*l**2 + 1/2.
-(l - 1)*(l + 3)/6
Suppose -2*x + 2*m = -16 + 6, -5*x - 4*m = -16. Let p be 0 - (-2 + -5 + 4). Determine i, given that p*i**x - 24*i**3 + 651 - 651 = 0.
0, 8
Let f(j) be the third derivative of -j**8/336 + j**7/70 + j**6/30 - j**5/5 + 1625*j**2. Factor f(a).
-a**2*(a - 3)*(a - 2)*(a + 2)
Let l(r) = -112 - 92*r - 104 - 146 - 187. Let p be l(-6). Factor -2/5*j**p + 0*j + 0*j**2 - 8/5*j**4 + 0.
-2*j**3*(4*j + 1)/5
Let h(x) be the second derivative of 3*x**5/160 + 3*x**4/2 + 47*x**3/16 - 3380*x. Factor h(j).
3*j*(j + 1)*(j + 47)/8
Let -31/2*w**4 + 0*w - 17/2*w**3 + 8*w**2 + w**5 + 0 = 0. Calculate w.
-1, 0, 1/2, 16
Suppose -3*t - 86 = -4*o, 5*t - 38 = -2*o + 18. Suppose -o - 140*b + 196*b**2 + 18*b**3 - 6*b**3 - 5 - 40 = 0. Calculate b.
-17, -1/3, 1
Let f(t) = 1075*t**3 + 450*t**2 - 45*t. Let s(a) = -2*a**3 + 2*a**2 - a. Suppose -2*d + 4*z = 22, -3*z - 44 = -59. Let n(j) = d*f(j) + 25*s(j). Factor n(w).
-5*w*(5*w + 2)*(45*w - 2)
Determine w, given that 23/3*w**4 - 2/3*w + 92/3 - 1/6*w**5 - 115/3*w**2 + 5/6*w**3 = 0.
-2, -1, 1, 2, 46
Let l(n) = -n**4 - n**3 - n**2 + n + 2. Let k(x) = -x**5 + 5*x**3 + 6*x**2 - 6*x - 4. Let p(b) = -2*k(b) - 4*l(b). Suppose p(v) = 0. Calculate v.
-2, 0, 1
Let v(z) = 12*z**3 + 61*z**2 + 77*z + 7. Let g(k) = 159*k + 5*k**3 - 83*k + 63*k**2 + 6*k**3 - 1 + 7. Let j(o) = -7*g(o) + 6*v(o). Factor j(p).
-5*p*(p + 1)*(p + 14)
Suppose 3*z - 5*j + 31 = 0, -10 = 5*z + j - 5. Let w be -21 - -14 - (z - 5). Factor w + 5/2*q**2 + 0*q.
5*q**2/2
Suppose -75 - 230 - 325 = -159*u - 156*u. Factor 4/5*o**3 - 16/5*o**u - 36/5*o + 2/5*o**4 - 18/5.
2*(o - 3)*(o + 1)**2*(o + 3)/5
Let n = 2214/5 - 4427/10. Let h(o) be the second derivative of -3*o + 0 + 2*o**3 + n*o**6 + 3/4*o**5 + 0*o**2 + 2*o**4. What is k in h(k) = 0?
-2, -1, 0
Let u(d) be the first derivative of d**3/9 + 109*d**2 - 655*d/3 - 3982. Solve u(g) = 0.
-655, 1
Let i(t) be the second derivative of t**5/10 - 955*t**4/6 - 9710*t. Find w, given that i(w) = 0.
0, 955
Let h be (2 - (8 - (7 - 2))) + -22. Let r(n) = 9*n + 210. Let u be r(h). Factor 0*b**4 + 2/3*b**2 + b - 4/3*b**u + 1/3*b**5 - 2/3.
(b - 1)**3*(b + 1)*(b + 2)/3
Factor -16/3 - 2*d**2 - 2/9*d**3 - 52/9*d.
-2*(d + 2)*(d + 3)*(d + 4)/9
Let a = -110852 + 110856. Solve 48/7*v**2 - 47/7*v**3 - 1/7*v**a + 0 + 0*v = 0.
-48, 0, 1
Let l(z) = 8*z - 1. Let k(w) = -3*w**2 + 191*w + 977. Let a(n) = k(n) + 5*l(n). What is i in a(i) = 0?
-4, 81
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