first derivative of l(k). Solve f(s) = 0 for s.
-1, 2
Let t = -2/106539 - 43503421/213078. Let q = -395/2 - t. Find d such that -q*d**3 - 4/3*d**2 + 0 + 8/3*d + 4/3*d**4 + 4*d**5 = 0.
-1, 0, 2/3, 1
Let r(n) be the third derivative of -n**7/420 - 131*n**6/240 - 987*n**5/20 - 8379*n**4/4 - 30870*n**3 - n**2 + 2*n - 3012. Factor r(g).
-(g + 5)*(g + 42)**3/2
Let c = -2 + 2. Suppose 0 = -63*j + 48*j + 30. Factor -4*q + 14*q**3 - 16*q**3 + c*q**2 - 6*q**j.
-2*q*(q + 1)*(q + 2)
Let d = 2/146251 + 2193757/585004. What is o in 0 - d*o + 3/4*o**2 = 0?
0, 5
Let z(p) = -p**3 + 9*p**2 + p. Let s be (6/5)/(4/(-60)). Let f(t) = t**2. Let i(a) = s*f(a) + 2*z(a). Factor i(j).
-2*j*(j - 1)*(j + 1)
Suppose 4*y = -3*g + 5*g + 634, 646 = 4*y + 2*g. Suppose -22*s - y = -30*s. Factor s + 4/5*w**2 - 8*w.
4*(w - 5)**2/5
Let h(d) = -18*d**3 + 68*d**2 - 64*d. Let s(m) = 43*m**3 - 136*m**2 + 128*m. Let o(u) = 5*h(u) + 2*s(u). Factor o(t).
-4*t*(t - 16)*(t - 1)
Let t(h) be the second derivative of -h**6/90 + 58*h**5/15 - 2281*h**4/6 + 13340*h**3/9 - 13225*h**2/6 + 319*h. Factor t(c).
-(c - 115)**2*(c - 1)**2/3
Let y(g) be the third derivative of -g**5/12 - 130*g**4/3 - 27040*g**3/3 + g**2 - 323. Determine n, given that y(n) = 0.
-104
Let l(f) be the first derivative of 169*f**4 - 168*f**4 + 4*f**3 + 15 + 4*f**2 + 40. Let l(a) = 0. Calculate a.
-2, -1, 0
Let k = -73 - -75. Let 5*v**4 + 0*v**2 - 12*v**3 + 5*v**2 + 3*v**4 - v**k = 0. Calculate v.
0, 1/2, 1
Let a(l) = -4*l**2 - 284*l + 9254. Let z(w) = 7*w**2 + 566*w - 18507. Let k(r) = -11*a(r) - 6*z(r). Factor k(b).
2*(b - 68)**2
Find c such that -886/3*c - 1/6*c**2 - 590 = 0.
-1770, -2
Let s(k) be the first derivative of 6561*k**3 + 243*k**2 + 3*k + 1679. Factor s(c).
3*(81*c + 1)**2
Let h be (-6517)/(-21812) - (-13)/((-3731)/14). Factor -3/4*r**3 - 1/4*r**2 + h*r**4 + 1/4*r**5 + 1/2*r + 0.
r*(r - 1)**2*(r + 1)*(r + 2)/4
Let x(w) be the second derivative of 0*w**2 + 0 - 261*w + 1/140*w**5 + 1/28*w**4 - 1/70*w**6 - 1/42*w**3. Suppose x(l) = 0. What is l?
-1, 0, 1/3, 1
Let m be (-270)/(-8) - ((-517)/(-44) - 11). Suppose 1222*j = 1233*j - m. Solve 2/17*p - 4/17 + 16/17*p**2 + 10/17*p**j = 0 for p.
-1, 2/5
Factor -705*w**3 - 174*w**2 + 353*w**3 + 349*w**3 - 1050 - 677*w - 544*w.
-3*(w + 1)*(w + 7)*(w + 50)
Factor 288/5*k + 2/5*k**2 - 58.
2*(k - 1)*(k + 145)/5
Factor 26*h**2 + 1/3*h**3 + 17248/3 + 672*h.
(h + 22)*(h + 28)**2/3
What is m in -2/9*m**4 - 18*m - 166/9*m**3 + 0 - 326/9*m**2 = 0?
-81, -1, 0
Let w(h) be the first derivative of 2058*h**6 - 51744*h**5/5 + 2107*h**4 + 4120*h**3/3 - 400*h**2 - 8485. Suppose w(q) = 0. What is q?
-2/7, 0, 5/21, 4
Determine v, given that 11*v**3 - 15*v**3 - v**4 - 64*v**3 - 302*v**2 + 13*v - v**4 - 361*v = 0.
-29, -3, -2, 0
Let o = 528 - 525. Factor -11*n**3 + 0*n**o - 12*n + 10*n**3 + 13*n**2.
-n*(n - 12)*(n - 1)
Let b(d) = 2*d**4 + 91*d**2 + 81*d - 51. Let r(h) = -h**4 + 3*h + 17. Let w(g) = -4*b(g) - 12*r(g). Factor w(n).
4*n*(n - 10)*(n + 1)*(n + 9)
Suppose 0 = 13*o - 16*o + 60. Suppose 0*w + 5*k = w - 20, -5*w + 5*k = -o. Suppose 3*v**2 + 9*v**4 + w*v**5 - 7*v**3 + 16*v**3 + 3*v**5 = 0. What is v?
-1, 0
Let n(q) be the third derivative of -1/112*q**8 + 1/105*q**7 + 1/120*q**6 + 149*q**2 + 0*q + 0*q**4 + 0*q**3 + 0 + 0*q**5. Solve n(s) = 0.
-1/3, 0, 1
Let w = -2/1753 + 1801/42072. Let g(p) be the third derivative of 0*p - 1/3*p**3 + 0 - w*p**5 + 1/6*p**4 + 1/240*p**6 - 14*p**2. Factor g(b).
(b - 2)**2*(b - 1)/2
What is u in 235/2*u**3 - 475/4 - 235/2*u + 120*u**2 - 5/4*u**4 = 0?
-1, 1, 95
Let t(q) = -q**3 + 12*q**2 + 14*q - 13. Let c be t(13). Suppose 5*a = -5*o + 25, c = -0*o - o - 2*a + 6. Factor -6 - 2 + 8 + o*f**2 - 4*f.
4*f*(f - 1)
Let i(o) be the first derivative of -143*o**2 + 70 - 1/2*o**4 + 46/3*o**3 + 242*o. Factor i(d).
-2*(d - 11)**2*(d - 1)
Let d(r) be the second derivative of -r**5/5 - 815*r**4/3 - 332926*r**3/3 - 331298*r**2 - 7*r. Factor d(w).
-4*(w + 1)*(w + 407)**2
Let s be (64/48)/((4/6)/1). Factor -6 + 2*h**2 + 1 - 6*h + 1 - 4*h**s.
-2*(h + 1)*(h + 2)
Let c be (-141)/18 - -8 - (-14)/4788*87. What is y in 36/19*y**3 + 82/19*y**2 - c + 16/19*y = 0?
-2, -1/2, 2/9
Let b(x) be the second derivative of x**5/10 - 99*x**4/2 + 296*x**3/3 + 163*x - 3. Factor b(p).
2*p*(p - 296)*(p - 1)
Suppose -12*l = 9104 - 9140. Solve -3/8*q**5 + 0*q + 0 - 1/4*q**2 - 9/8*q**l - 5/4*q**4 = 0 for q.
-2, -1, -1/3, 0
Let h(r) = -6*r**3 - 12*r**2 + 19*r + 58. Let y(v) = 6*v - 188. Let x be y(31). Let b(t) = 3*t**3 + 6*t**2 - 10*t - 28. Let c(n) = x*h(n) - 5*b(n). Factor c(d).
-3*(d - 2)*(d + 2)**2
Let j(h) be the second derivative of -h**6/450 - h**5/30 + h**4/5 - 113*h**3/6 - 137*h. Let l(v) be the second derivative of j(v). Factor l(d).
-4*(d - 1)*(d + 6)/5
Let k(n) = -21*n**2 - 6*n. Let i(d) = 42*d**2 + 12*d. Let h be (12/14)/(13/91). Suppose -h*m + 4 = -74. Let u(r) = m*k(r) + 6*i(r). Factor u(f).
-3*f*(7*f + 2)
Factor 0*v + 0 + 2/7*v**4 + 48*v**2 - 172/7*v**3.
2*v**2*(v - 84)*(v - 2)/7
Factor 104 - 6064*q + 12204*q - 4*q**2 - 6040*q.
-4*(q - 26)*(q + 1)
Suppose 0 + 264/13*j**4 + 768/13*j**3 + 96/13*j + 2*j**5 + 736/13*j**2 = 0. Calculate j.
-6, -2, -2/13, 0
Let t(o) be the first derivative of 0*o**2 + 8/27*o**4 + 0*o + 10/3*o**3 - 2/135*o**5 + 33 + 1/3240*o**6. Let n(v) be the third derivative of t(v). Factor n(p).
(p - 8)**2/9
Let b(c) be the third derivative of -75*c**8/4 - 3994*c**7/7 - 14414*c**6/15 + 80*c**5 + 752*c**4/3 - 96*c**3 - 2*c**2 + 8*c + 84. What is k in b(k) = 0?
-18, -1, -2/7, 2/15
Let b be 12/144 + (-321)/(-36). Let y = -3 + b. Find z, given that 6/7 + 18/7*z**4 + 48/7*z**2 - 3/7*z**5 - 27/7*z - y*z**3 = 0.
1, 2
Let k(a) be the second derivative of 0*a**3 + 0*a**4 - 2 + 1/3*a**6 - 1/4*a**5 + 0*a**2 + 9*a - 5/42*a**7. Factor k(z).
-5*z**3*(z - 1)**2
Let w be 49/(4459/26) + 64/168. Let 10/3 - 4*l + w*l**2 = 0. Calculate l.
1, 5
Solve 3*i**3 - 112*i - 8*i**3 - 272*i + 190*i**2 - 121*i - 20084 + 19384 = 0.
-1, 4, 35
Let c(y) = 4*y**3 - 24*y**2 - 536*y - 1802. Let m(i) = 9*i**3 - 47*i**2 - 1076*i - 3605. Let z(a) = 5*c(a) - 2*m(a). Determine w so that z(w) = 0.
-6, 25
Let h(m) be the third derivative of 2*m**7/1155 + 23*m**6/660 + 17*m**5/66 + 31*m**4/33 + 20*m**3/11 + 2*m**2 + 4*m - 10. What is u in h(u) = 0?
-6, -5/2, -2, -1
Let m(p) be the first derivative of 3*p**4/7 + 323*p**3/7 + 1653*p**2/14 - 474*p/7 - 2640. Find w such that m(w) = 0.
-79, -2, 1/4
Let w(x) = -x**3 - 7*x**2 - 6*x - 4. Let r be w(-6). Let h be 4*(95/20 + r). Suppose 2 - h*c + 2*c + 4*c**2 + 5*c + 2*c = 0. Calculate c.
-1, -1/2
Suppose -19*w + 16*w + 162 = 0. Let f = w - 30. Suppose 4*g**3 - f + 2*g**3 + 28 - 4*g**3 - 6*g = 0. What is g?
-2, 1
Let 495/4*c**2 + 3/2*c + 0 = 0. Calculate c.
-2/165, 0
Let -7 + o**5 - 38*o**4 - 36*o**4 + 14*o**2 + 17*o + 13 - 2*o**5 + 70*o**4 = 0. What is o?
-3, -1, 2
Factor -99*b - 2*b**2 + 39*b + 29530*b**3 - 29528*b**3.
2*b*(b - 6)*(b + 5)
Suppose -1/3*q**4 + 2*q + 0 + 7/6*q**3 - 1/6*q**5 + 10/3*q**2 = 0. Calculate q.
-2, -1, 0, 3
Let j(x) = 45*x + 84*x**2 + 61*x - 37*x + 15*x**3. Let p(y) = -3*y**3 - 17*y**2 - 14*y. Let h(k) = -5*j(k) - 24*p(k). Factor h(t).
-3*t*(t + 1)*(t + 3)
Let y(d) be the second derivative of -d**4/9 - 868*d**3/3 - 282534*d**2 - 659*d. Solve y(l) = 0 for l.
-651
Let d be 2/11 + 4/(-22). Suppose d + 12 = 4*f. Factor 3*k**3 - 5*k**5 - 91*k**4 - 18*k**f - 5*k**2 + 76*k**4.
-5*k**2*(k + 1)**3
Solve -331*u - u**2 - 68 + 68 - 213*u + 66*u = 0 for u.
-478, 0
What is q in -8 + 1/2*q**2 - 1/10*q**3 + 17/5*q = 0?
-5, 2, 8
Let z(i) be the second derivative of -i**4/4 + 813*i**3 - 4875*i**2/2 - 8455*i. Factor z(a).
-3*(a - 1625)*(a - 1)
Let l(j) be the first derivative of j**6/90 - j**5/36 - j**4/12 - j**2/2 + 54*j + 47. Let s(t) be the second derivative of l(t). Factor s(i).
i*(i - 2)*(4*i + 3)/3
Let u(w) be the second derivative of -1/3*w**4 + 0 + 17*w - 1/2*w**3 - 8*w**2 - 1/12*w**5. Let a(i) be the first derivative of u(i). Factor a(t).
-(t + 1)*(5*t + 3)
Let h(p) = p. Let m(d) = -d**3 + 8*d**2 - 20*d + 12. Let j = -56 + 58. Let u(r) = j*h(r) + 2*m(r). Determine c, given that u(c) = 0.
1, 3, 4
Let p(d) = -47*d**4 + 181*d**3 - 198*d**2 + 20*d - 12. Let a(o) = -23*o**4 + 91*o**3 - 99*o**2 + 5*o - 6. Let w(x) = -7*a(x) + 4*p(x). Factor w(t).
-3*(t - 1)**3*(9*