0. Calculate k.
8
Let b(t) = 2*t**3 - 14*t**2 - 15*t - 5. Let g be b(8). Solve -10*u**2 - 34*u**2 + 3*u**4 + 11*u**2 - 6*u**g + 8*u + 28*u = 0.
-3, 0, 1, 4
Find w, given that 6158*w**2 - 9710*w**2 - 63301*w + 4*w**3 + 851845*w = 0.
0, 444
Factor 1222 + 65*x - 617 - 65*x**3 - 5*x**4 + 5*x**2 - 605.
-5*x*(x - 1)*(x + 1)*(x + 13)
Let j(s) be the second derivative of 166*s - 69/20*s**5 + 15/2*s**4 + 2/5*s**6 - 7/2*s**3 + 0 - 6*s**2. What is p in j(p) = 0?
-1/4, 1, 4
Let c(s) be the third derivative of s**5/48 - 5*s**4/32 - 35*s**3/6 + 3512*s**2. Factor c(t).
5*(t - 7)*(t + 4)/4
Suppose 9*f - 2*r = 5*f - 26, -2*f + 4*r - 52 = 0. What is b in 3*b**4 + f + 21/2*b**3 + 3*b + 21/2*b**2 = 0?
-2, -1, -1/2, 0
Let h(b) = -b**4 - b**3 - 2*b. Let v(i) = -9*i**4 - 18*i**3 + 36*i**2 + 180*i + 192. Let x(c) = -6*h(c) + v(c). Find j, given that x(j) = 0.
-4, -2, 4
Suppose 150 - 10*i**4 + 70*i**2 - 8*i**5 - 545*i + 383*i**3 + 23*i**5 - 653*i**3 + 590*i**2 = 0. Calculate i.
-5, 2/3, 1, 3
Suppose 0 = 5*z + 2*y - 18, 2*z = -2*z + 2*y. Suppose 5*c = 25, 5*c = -3*b - 9 + 40. Factor z*t - 7*t - t**b + t.
-t*(t + 4)
Factor -168*c**2 + 2/3*c**3 - 62500/3 + 10750*c.
2*(c - 125)**2*(c - 2)/3
Let h(i) be the first derivative of -2*i**5/45 - 2*i**4/3 + 10*i**3/9 + 26*i**2/9 + 1437. Let h(o) = 0. What is o?
-13, -1, 0, 2
Solve 343 - 695 + 1014*u**2 - 667*u**3 - 2*u**4 - 508*u + 352 + 163*u**3 = 0.
-254, 0, 1
Let k be ((-2)/10)/((-2)/170). Find t such that -k*t**3 + 130 - 8*t**3 - 310*t**2 + 132*t + 73*t = 0.
-13, -2/5, 1
Let f(u) = u**3 - 17*u**2 - 3. Let y(m) = -131*m**3 - 368*m**2 + 535*m - 17. Let o(x) = f(x) + y(x). Find p such that o(p) = 0.
-4, 1/26, 1
Let c(m) be the first derivative of -m**4 + 0*m**2 + 1/20*m**5 + 101 + 16/3*m**3 + 0*m. Suppose c(b) = 0. Calculate b.
0, 8
Let g(i) = -i + 60. Suppose 5*x + 5*z = -85, 2*z + 13 = x + 39. Let s be g(x). Factor -s*a + a**2 - a**2 + 5*a**2 + 254 + 66.
5*(a - 8)**2
Let a(g) be the second derivative of g**5/5 + 4*g**4/3 - 1990*g. Factor a(o).
4*o**2*(o + 4)
Let d(z) = 53*z - 313. Suppose 7*k + 36 = 13*k. Let s be d(k). Factor 0 + 0*c**3 + 3/2*c**s + 3*c**4 - 3*c**2 - 3/2*c.
3*c*(c - 1)*(c + 1)**3/2
Let p = -1/226113 + 226115/452226. Factor 0*s + p*s**4 - 3/2*s**2 - s**3 + 0.
s**2*(s - 3)*(s + 1)/2
Let m(y) be the second derivative of 36*y**2 + 0 + 0*y**3 + 53*y - 1/6*y**4. Factor m(s).
-2*(s - 6)*(s + 6)
Let f be 4 + (7 - 5) + -6. Let m(q) be the second derivative of -1/90*q**5 + 11*q + f*q**3 + 0*q**4 + 0*q**2 + 0. Solve m(k) = 0.
0
Let n(r) be the second derivative of r**7/42 + 49*r**6/15 + 1977*r**5/20 - 5194*r**4/3 + 22472*r**3/3 + 5*r + 9. Factor n(h).
h*(h - 4)**2*(h + 53)**2
Let t = 34470 + -68937/2. Factor -t - 1/2*k**2 + 5/2*k - 1/2*k**3.
-(k - 1)**2*(k + 3)/2
Let n(r) be the third derivative of -53*r**6/510 - 263*r**5/510 - 101*r**4/204 + 2*r**3/51 + 2*r**2 + 55*r. Suppose n(a) = 0. Calculate a.
-2, -1/2, 1/53
Let d = -162 - -43. Let j = 43 - d. Determine x, given that -j*x + 8 + 30*x - 142*x**2 - 1331*x**3 + 868*x**2 = 0.
2/11
Let m(p) be the first derivative of -2/27*p**3 - 4/3*p**2 + 26/9*p - 41. Factor m(o).
-2*(o - 1)*(o + 13)/9
Let g(o) = -480*o**2 + 9404*o - 45367. Let w(f) = -478*f**2 + 9420*f - 45366. Let p(a) = 3*g(a) - 2*w(a). Determine i so that p(i) = 0.
213/22
Let g(r) be the third derivative of r**6/3600 + 11*r**5/600 - 23*r**4/240 + 17*r**3 - 187*r**2. Let f(a) be the first derivative of g(a). Factor f(b).
(b - 1)*(b + 23)/10
Determine p so that 2/13*p**3 + 192/13 - 8/13*p - 48/13*p**2 = 0.
-2, 2, 24
Let v(d) be the second derivative of -d**6/10 - 69*d**5/20 - 15*d**4 - 251*d. Determine q, given that v(q) = 0.
-20, -3, 0
Let s(w) be the second derivative of 6*w**6/5 - 494*w**5/35 + 253*w**4/7 - 776*w**3/21 + 120*w**2/7 - 5*w - 66. Find p such that s(p) = 0.
2/7, 5/9, 1, 6
Let o(q) = -q**2 - 18*q - 30. Let c be o(-16). Suppose -k + 32 = 5*l, -2*l - 42 = -c*k - l. Factor -8*z**2 + k*z**3 - 30*z**3 + 53*z**2 - 27*z**3 - 10*z.
-5*z*(z - 1)*(7*z - 2)
Let g(f) be the first derivative of f**5/10 - f**4/21 - f**3/3 + 2*f**2/7 + 97*f + 78. Let t(b) be the first derivative of g(b). Find o, given that t(o) = 0.
-1, 2/7, 1
Suppose -18*v + 40 = -32. Find h such that 13*h**4 + 9*h**v + 15*h**3 + 3*h**4 + 13*h**4 - 48*h**4 - 5*h**5 = 0.
-3, 0, 1
Suppose 0 = -4*w + 43 + 173. Factor w*i - 12*i**4 + 0*i**5 - 3*i**5 + 48*i**2 - 21*i + 15*i.
-3*i*(i - 2)*(i + 2)**3
Let l be 41 + -1213 - (0 - -8). Let x = 15352/13 + l. Determine c so that 34/13*c - x - 10/13*c**2 = 0.
2/5, 3
Let g(a) = 9*a**2 + 144*a + 76. Let q(t) = 37*t**2 + 576*t + 302. Let l(o) = 18*g(o) - 4*q(o). Factor l(f).
2*(f + 20)*(7*f + 4)
Let s(p) = -2*p - 27. Let o be s(-14). Let b(d) = d**2 + 4*d - 3. Let w be b(o). Solve 6*h**w + 11 - 39 + 35*h + 16*h - 13*h = 0.
-7, 2/3
Let u = 7/30 + -1/90. Let d = u + 41/18. Determine q, given that d*q**2 + 15/4*q**3 + 0*q**4 + 0*q - 5/4*q**5 + 0 = 0.
-1, 0, 2
Factor 2/7*k**3 + 124/7*k**2 + 236/7 + 358/7*k.
2*(k + 1)*(k + 2)*(k + 59)/7
Let u(g) be the second derivative of 0 + 100*g + 1/114*g**4 + 12/19*g**2 + 7/57*g**3. Factor u(x).
2*(x + 3)*(x + 4)/19
Suppose -54*l = -56*l - 2410. Let y = l - -1209. Factor 0*g**2 + 0*g - 18*g**y + 0 - 6*g**3 - 27/2*g**5.
-3*g**3*(3*g + 2)**2/2
Solve 1/9*t**4 - 2/3*t**2 - 1/3*t**3 + 8/9*t + 0 = 0.
-2, 0, 1, 4
Let u(q) be the third derivative of -q**6/40 - 3*q**5/2 - 27*q**4/8 + 29*q**3 + 35*q**2 - 29*q - 2. Factor u(i).
-3*(i - 1)*(i + 2)*(i + 29)
Let m be (0/(-3) + -57)*1. Let q = m + 60. Let 438*s**q + 3*s**2 - 433*s**3 + 2*s**2 = 0. What is s?
-1, 0
Let c(a) = -15987*a**2 - 456*a + 3. Let o(r) = 3*r - 1. Suppose -15 = -w + 4*d, 24 = w - 2*d + 17. Let q(n) = w*c(n) - 6*o(n). Determine t, given that q(t) = 0.
-1/73
Let g(t) = -t**2 - 13*t - 24. Let m be g(-8). Let x = m - 14. Factor -54*p**x + 0*p + 30*p**2 + 4*p + 30*p**2 + 2*p**3.
2*p*(p + 1)*(p + 2)
Let z(s) be the first derivative of 16 - 13/4*s**4 + 0*s**2 - 2/3*s**3 - 21/5*s**5 + 0*s. Let z(f) = 0. Calculate f.
-1/3, -2/7, 0
Let q(x) be the first derivative of -5*x**3/3 - 1425*x**2/2 - 2830*x - 3223. Factor q(n).
-5*(n + 2)*(n + 283)
Let k(n) be the third derivative of -49/15*n**4 + 0*n - 14/75*n**5 + 1/840*n**8 + 13/20*n**6 + 0 + 0*n**3 + 4/75*n**7 - 47*n**2. Solve k(m) = 0.
-14, -1, 0, 1
Let h = -1804 + 1816. Suppose h*z = -9*z + 8*z. Factor n**2 + 2/3*n + z + 1/3*n**3.
n*(n + 1)*(n + 2)/3
Determine w so that -990*w**2 - 46/5*w**4 - 827/5*w**3 + 216/5 - 9828/5*w = 0.
-6, 1/46
Let m(b) be the first derivative of 2/15*b**3 + 1/10*b**2 - 13 - 2/5*b - 1/20*b**4. Factor m(y).
-(y - 2)*(y - 1)*(y + 1)/5
Let y = -360/11 - -1102/33. Suppose 3*m = 2*m + 4*m. Suppose m*l + 2/3 - y*l**2 = 0. Calculate l.
-1, 1
Let r(x) = 155*x**3 + 3735*x**2 + 13450*x + 3155. Let d(v) = 26*v**3 + 623*v**2 + 2242*v + 526. Let m(l) = 35*d(l) - 6*r(l). Suppose m(k) = 0. What is k?
-26, -4, -1/4
Let u(d) be the second derivative of -d**5/130 - 3*d**4/13 + 85*d**3/13 + 4624*d**2/13 - 2*d - 473. Factor u(i).
-2*(i - 16)*(i + 17)**2/13
Let y(d) = 30*d**2 - 30*d - 24. Let z be y(5). Let w = 579 - z. Determine g so that 1/4*g**w + 3/2 - 7/4*g + 0*g**2 = 0.
-3, 1, 2
Let t(f) be the first derivative of -23*f**3/8 - 33*f**2/4 + 3*f/2 - 555. Factor t(d).
-3*(d + 2)*(23*d - 2)/8
Let g(x) = x**3 + 9*x**2 + 7*x + 15. Let i be g(-8). Suppose -4*c + i = -n - 0*n, 8 = 4*c + 4*n. What is v in -5*v - 1 - c*v**2 + 3 + 28 + 0*v = 0?
-3, 2
Suppose -24 = -7*x + 4. Solve -39*a**5 + 128*a**x + 172*a**4 - 240*a + 960*a**2 - 192 - 435*a**3 - 405*a**3 = 0.
-4/13, 2
Let b(i) = 13*i**3 - 6*i**2 - 495*i + 500. Let n(d) = -d**3. Let r(j) = -b(j) - 12*n(j). Factor r(v).
-(v - 25)*(v - 1)*(v + 20)
Suppose 3*s = 9, 8*b + 4*s = 4*b - 1988. Let d = 8504/17 + b. What is x in -d*x + 0 + 10/17*x**2 - 8/17*x**3 + 2/17*x**4 = 0?
0, 1, 2
Factor 0 + 2/13*c**2 + 2868/13*c.
2*c*(c + 1434)/13
Let s(y) be the third derivative of -y**6/420 + 1793*y**5/35 - 3214849*y**4/7 + 46113794056*y**3/21 - 5*y**2 + 227. Factor s(g).
-2*(g - 3586)**3/7
Suppose 1378*u - 5997 = -621*u. Find q such that 7115526/7 + 6/7*q**4 + 39204/7*q**2 - 792/7*q**u - 862488/7*q = 0.
33
Let y(h) = 3*h**3 - 13*h**2 + 11*h + 41. Let a(m) = 4*m**3 - 19*m**2 + 16*m + 61. Let z = -25 - -55. Let o = -37 + z. Let w(j) = o*y(j) + 5*a(j)