1
Find t, given that 122/5*t**3 - 776/5*t - 128/5 - 1168/5*t**2 + 18/5*t**5 + 60*t**4 = 0.
-16, -2, -1/3, 2
Let w(d) = d**2 + 4*d - 1. Let m(a) = -a**3 + 101*a**2 - 365*a + 349. Let f(i) = -2*m(i) + 42*w(i). Factor f(c).
2*(c - 74)*(c - 5)*(c - 1)
Let j(m) be the second derivative of -m**6/6 - 5*m**5/4 + 265*m**4/6 - 700*m**3/3 + 671*m. Determine a, given that j(a) = 0.
-14, 0, 4, 5
Suppose -116/3 + 1/3*x**2 - 56/3*x = 0. What is x?
-2, 58
Let j be (-994)/(-84) - (-1)/6. Factor 54*v**2 + j*v**4 - 30*v**2 + 65*v**3 - 9*v + 9*v**4 - 9*v**4 - 20*v**3.
3*v*(v + 1)*(v + 3)*(4*v - 1)
Let m(h) = -h**2 - 2*h. Suppose -o - 21 = -4*o. Let n(a) = -3308 + 2*a**2 + 4*a + 1658 + 1650. Let x(s) = o*m(s) + 3*n(s). Solve x(t) = 0 for t.
-2, 0
Let z be (1*8/(-12))/(-15*(-6)/360*-2). Let 0 + 16/3*s + 32/3*s**2 + 20/3*s**3 + z*s**4 = 0. What is s?
-2, -1, 0
Let m be 6/(-16) + 570/(-16). Let g be 32/6 - (-120)/m. Factor -4116/5*n - 84/5*n**3 + 3/5*n**4 + 7203/5 + 882/5*n**g.
3*(n - 7)**4/5
Let z(w) be the second derivative of -2*w**7/21 - 58*w**6/15 - 106*w**5/5 - 154*w**4/3 - 202*w**3/3 - 50*w**2 + 7*w - 29. Suppose z(f) = 0. Calculate f.
-25, -1
Let f = -444/743 - -47697/1486. Determine i so that 3*i - 69/2*i**3 + 0 + f*i**2 = 0.
-2/23, 0, 1
Find q, given that 27/2*q**3 - 3/8*q**4 + 108 - 861/8*q**2 - 27/2*q = 0.
-1, 1, 12, 24
Suppose 0 = -5*k + 2*r + 14, -79*r + 8 = k - 82*r. Factor 6*z**k + 3/5*z**3 + 72/5 + 84/5*z.
3*(z + 2)**2*(z + 6)/5
Let v(h) = -316*h**2 + 1598*h + 8314. Let f(s) = -19*s**2 + 94*s + 489. Let u(n) = -100*f(n) + 6*v(n). Solve u(b) = 0 for b.
-41, -6
Let x be (-724)/(-1664) + ((-1035)/(-117) - 9). Let f(h) be the first derivative of -3/40*h**5 + 0*h**3 + 0*h**2 + 17 + 0*h + x*h**4. Factor f(d).
-3*d**3*(d - 3)/8
Let 234*z**2 + 25*z**3 + 52*z**3 + 2*z**4 - 126*z**3 + 420*z - 8*z**3 - 600 + z**4 = 0. Calculate z.
-2, 1, 10
Let v(g) = -2*g**3 + 26*g**2 - 18*g - 15. Let d be v(12). Let l = 57 - d. Factor 2/13*i**4 + l + 0*i**3 - 2/13*i**2 + 0*i.
2*i**2*(i - 1)*(i + 1)/13
Let j = -133 + 136. Suppose z**4 + 6*z - 5*z**2 - 4*z**j - 3*z**2 - 2*z**5 + 4*z**4 + 3*z**4 = 0. Calculate z.
-1, 0, 1, 3
Factor -26615902527*s**3 - 35154620377*s**3 - 2067889142931*s**4 - 8266757018185*s**4 - 243 - 33872175596*s**3 - 310752450*s**2 - 448740*s - 704115290759*s**4.
-3*(1385*s + 3)**4
Let k = -28477/693 + 371/9. Let c = 3/11 - k. Solve c*o**2 + 0*o - 1/7 = 0.
-1, 1
Let j(s) be the second derivative of s**5/40 - 11*s**4/24 - 7*s**3/6 + 6*s**2 + 2*s - 119. Factor j(d).
(d - 12)*(d - 1)*(d + 2)/2
Let x(y) be the first derivative of -y**4/12 - y**3 - 10*y**2/3 - 4*y - 3128. Factor x(k).
-(k + 1)*(k + 2)*(k + 6)/3
Let g(n) be the third derivative of 3 - 2*n**3 - 1/6*n**4 + 0*n + 1/30*n**6 + 1/5*n**5 - 13*n**2. Factor g(s).
4*(s - 1)*(s + 1)*(s + 3)
Let z = 187669/3 - 62556. Factor 1/6*g**4 + z*g**3 + 0*g + 0 - 1/2*g**2.
g**2*(g - 1)*(g + 3)/6
Let m(l) be the first derivative of 3*l**4/28 + 422*l**3/7 - 177. Find a, given that m(a) = 0.
-422, 0
Let u(n) be the third derivative of 0*n**4 + 0*n + 15*n**2 + 2*n**3 + 1/240*n**6 + 1/80*n**5 + 0. Let p(q) be the first derivative of u(q). Factor p(l).
3*l*(l + 1)/2
What is n in 148840 + 2/5*n**2 - 488*n = 0?
610
Let d be 634/7056 - (-379)/(-18571). Let r(u) be the second derivative of 605/12*u**2 + d*u**4 - 55/18*u**3 + 0 + 32*u. Factor r(w).
5*(w - 11)**2/6
Let d be 12 - (4920/400 + 15/(-10) + 1). Factor 0 + d*z - 1/5*z**3 + 1/5*z**2 - 1/5*z**4.
-z*(z - 1)*(z + 1)**2/5
Let l(s) = 19*s + 53 + 46*s + 17*s**2 - 4*s**2 - 37*s**3 - 45*s**3 + 77*s**3. Let q(m) = 5*m**3 - 12*m**2 - 65*m - 52. Let n(j) = -2*l(j) - 3*q(j). Factor n(o).
-5*(o - 5)*(o + 1)*(o + 2)
Let x = 14439808/11 - 1312664. Find v such that -354/11*v**2 + 6/11*v**5 - 150/11*v**4 + 522/11*v**3 + x - 48*v = 0.
-1, 1, 2, 21
Let n(p) be the third derivative of -p**8/252 - 76*p**7/315 + 19*p**6/18 + 188*p**5/15 - 80*p**4 + 262*p**2 + 2*p. Find c, given that n(c) = 0.
-40, -4, 0, 3
Find o such that 312/11*o**2 - 158/11*o**4 + 0*o + 152/11*o**3 + 2/11*o**5 + 0 = 0.
-1, 0, 2, 78
Let z be -4*66/2145*-10. Determine l so that -162/13*l**3 - 152/13*l - z - 396/13*l**2 = 0.
-2, -2/9
Let p(r) = -r**5 - r**4 - r**2. Let j(q) = -10*q**5 - 20*q**4 - 5*q**2. Let l(f) = j(f) - 5*p(f). Factor l(v).
-5*v**4*(v + 3)
Suppose 52*z - 60*z - 3984 = 0. Let s = z - -4490/9. Factor -2/9*p**3 - 10/9*p - s*p**2 - 4/9.
-2*(p + 1)**2*(p + 2)/9
Let p = -80 - -641/8. Suppose -6*o + 30 = -5*f, -18*f = -16*f + 3*o - 15. Factor 0 + 1/8*y + f*y**2 - p*y**3.
-y*(y - 1)*(y + 1)/8
What is z in 8767*z**3 - 247*z**2 + 7679*z**3 - 218*z**2 + 21 + 55848*z**4 - 2704*z**5 - 22*z + 3233*z**3 - 357*z = 0?
-1/4, 1/13, 21
Suppose m + 2*k - 1 - 4 = 0, 3 = 2*m - 3*k. Factor 31 + 13 + 112*v**2 + 36*v**2 - 180*v - 5*v**3 - 7*v**m.
-4*(v - 11)*(v - 1)*(3*v - 1)
Let u(i) be the third derivative of 0*i + 1/72*i**4 + 1/120*i**6 + 4*i**2 - 1 + 1/60*i**5 + 1/630*i**7 + 0*i**3. Find w, given that u(w) = 0.
-1, 0
Let v(c) = 4*c**3 - 213*c**2 + 30*c + 1219. Let i be v(53). Let 1/2*m**5 - m**2 + 0 + i*m**3 + m**4 - 1/2*m = 0. Calculate m.
-1, 0, 1
Let d(n) be the third derivative of -n**7/1470 - 11*n**6/105 - 29*n**5/140 - 5*n**2 - 87. Suppose d(i) = 0. What is i?
-87, -1, 0
Let c(h) be the first derivative of 0*h - 34 + 2/5*h**2 + 2/15*h**3. Let c(b) = 0. Calculate b.
-2, 0
What is p in 0*p - 64*p**3 + 22*p**2 - 89/2*p**4 - 7/2*p**5 + 0 = 0?
-11, -2, 0, 2/7
Let p be ((-2)/8*-6 - (-235)/15510) + 2/3. Solve -2/11*i**3 + 16/11*i - p + 2/11*i**2 = 0.
-3, 2
Suppose -h - 23 + 2 = -5*j, 2*j + 2*h = 18. Suppose j*f = 113 - 113. Suppose 1/3*m**2 + 1/3*m**3 + f - 1/3*m**4 + 0*m - 1/3*m**5 = 0. What is m?
-1, 0, 1
Let h(x) = -2*x**3 - 2*x + 1. Let b(v) = -4*v**4 + 96*v**3 - 100*v**2 - 8*v + 4. Let a(g) = b(g) - 4*h(g). Factor a(d).
-4*d**2*(d - 25)*(d - 1)
Let u(c) be the third derivative of c**5/160 - 73*c**4/16 - 447*c**3/4 + 4867*c**2. Suppose u(l) = 0. What is l?
-6, 298
Let x(l) be the first derivative of l**7/189 - l**6/9 - l**5/90 + 5*l**4/18 + 40*l + 135. Let m(d) be the first derivative of x(d). What is s in m(s) = 0?
-1, 0, 1, 15
Determine h, given that 120/7*h + 3/7*h**2 - 123/7 = 0.
-41, 1
Let m(u) be the first derivative of -2*u**3/33 - 454*u**2/11 - 103058*u/11 + 1954. Solve m(t) = 0.
-227
Let j be (44/(-14) - -4)/(16/21). Let o(p) be the first derivative of -3/4*p**2 - j*p + 1/8*p**4 - 1/40*p**5 - 20 + 1/12*p**3. Find n such that o(n) = 0.
-1, 3
Let m be -5 - -1*(-7)/((-28)/36). Suppose f - 24 = -m*x - 5, 7 = x + f. Let 0 + 2/7*d**x + 0*d + 0*d**2 + 4/7*d**3 = 0. Calculate d.
-2, 0
Let k(x) = -x**3 + 2*x**2 + 2*x. Let p(c) = 3*c**3 - 5*c**2 - 5*c. Suppose -9*l - 6 = -11*l. Let j be 16/3 + (-1)/l. Let z(h) = j*k(h) + 2*p(h). Factor z(t).
t**3
Solve 110*a**2 + 2*a**4 + 74*a**3 - 35*a**2 - 15*a**4 + 136*a + 23*a**4 + 32 + 93*a**2 = 0 for a.
-4, -2, -1, -2/5
Let u(c) be the first derivative of c**4/2 + 106*c**3/3 + 150*c**2 - 8287. Suppose u(m) = 0. What is m?
-50, -3, 0
Let k(q) = -q**2 + 9*q - 14. Let h be k(5). Let h - 8*d + 238*d**2 - 119*d**2 - 117*d**2 = 0. Calculate d.
1, 3
Factor -151/2*p + 14*p**2 - 90 - 1/2*p**3.
-(p - 20)*(p - 9)*(p + 1)/2
Let l(x) = -6*x - 286. Let u(t) = -t**2 - 49*t - 438. Let r be u(-10). Let b be l(r). Find k, given that -1/3*k**b - 3 + 10/3*k = 0.
1, 9
Let j = 41609/8 - 5201. Suppose -9/8*a**4 + 0 - 7/8*a**2 - j*a**5 + 0*a - 15/8*a**3 = 0. Calculate a.
-7, -1, 0
Let s(r) be the first derivative of 1/7*r**4 - 1556068/7*r + 31974/7*r**2 - 297 - 292/7*r**3. Factor s(n).
4*(n - 73)**3/7
Let a(s) be the first derivative of 5*s**3/3 - 65*s**2 + 600*s - 121. Determine k so that a(k) = 0.
6, 20
Factor 2/3*x**2 - 8000/3*x + 8000000/3.
2*(x - 2000)**2/3
Let a(g) be the first derivative of -2*g**3/33 + g**2 + 52*g/11 - 103. Factor a(k).
-2*(k - 13)*(k + 2)/11
Let p = -1130218/7 + 161460. Factor 0*m - 2/7 + p*m**2.
2*(m - 1)*(m + 1)/7
Let p(o) be the second derivative of 4*o**2 - 1/6*o**4 + o**3 + 0 + 131*o. Find d, given that p(d) = 0.
-1, 4
Let x(n) be the second derivative of n**4/6 - 4462*n**3/3 + 4977361*n**2 + 1164*n - 4. What is r in x(r) = 0?
2231
Suppose -5*l + 21 = 3*j, 0 = -4*l + 5*j - j + 4. Let t be (-21)/(-221) - l/(-51). Find i, given that -2/13*i**3 - 4/13*i**2 + 0 - t*i = 0.
-1, 0
Let 