). Let x = u - 54. Solve 2290 - 2*c**3 - 2290 + 4*c**2 + x*c = 0 for c.
-1, 0, 3
Let z(o) be the second derivative of o**4/48 + 11*o**3/6 - 141*o**2/8 + 307*o. Factor z(t).
(t - 3)*(t + 47)/4
Let i = -316 + 319. Factor -128*c + 40*c**2 + 800 - 5*c**i - 333 - 339 + c**3.
-4*(c - 4)**2*(c - 2)
Let s(g) be the second derivative of 10*g**6/27 - 7*g**5/18 - 17*g**4/54 + 2*g**3/27 + 27*g + 12. Solve s(y) = 0.
-2/5, 0, 1/10, 1
Factor 3998/11*j**2 + 0 - 4002/11*j**3 + 4/11*j.
-2*j*(j - 1)*(2001*j + 2)/11
Determine y, given that 7/3*y**3 + 32/3*y + 0 - 20*y**2 = 0.
0, 4/7, 8
Let y = 971/1407 + -11/469. Let -y*z**2 + 8/3 + 0*z = 0. Calculate z.
-2, 2
Let c(j) be the third derivative of -1/72*j**6 + 9*j**2 + 109/36*j**5 + 0 - 15125/18*j**3 - 14575/72*j**4 + 17*j. Factor c(f).
-5*(f - 55)**2*(f + 1)/3
Let z be (-3225)/774*(-4)/10. Factor 4*h - 7/3*h**3 + 0 - z*h**2.
-h*(h - 1)*(7*h + 12)/3
Let j(i) = -4*i**4 - 114*i**3 - 365*i**2 - 119*i + 2352. Let v(a) = -2*a**4 - 54*a**3 - 183*a**2 - 59*a + 1176. Let z(y) = 6*j(y) - 14*v(y). Factor z(m).
4*(m - 2)*(m + 6)*(m + 7)**2
Suppose 2*x - 4 = p, 2 - 4 = -2*p - x. Suppose p = -5*w - 0*w + 15. Solve -8*r**3 + 20*r**3 - 11*r**w - 5*r**3 + r + 3*r**2 = 0 for r.
-1/4, 0, 1
Let z(t) be the second derivative of 17/12*t**4 + 3/20*t**5 - 5*t + 3*t**3 - 4*t**2 + 5. What is i in z(i) = 0?
-4, -2, 1/3
Let b(x) be the first derivative of 2*x**5/25 - 9*x**4/2 + 296*x**3/15 + 144*x**2 - 5248*x/5 - 5386. Let b(a) = 0. What is a?
-4, 4, 41
Suppose 8*m = 3*m - u + 167, -2*m + 2*u = -74. Let c be (m/14 - 1)/(8/56). Factor -10*v + 29*v - 4 - c*v - 3*v**2 - 2.
-3*(v - 2)*(v - 1)
Let k(p) = -9*p**2 - 149*p - 2075. Let u(v) = 8*v**2 + 156*v + 2076. Let b(y) = -4*k(y) - 5*u(y). Factor b(a).
-4*(a + 20)*(a + 26)
Suppose 18*w = 40 + 14. Suppose -t**4 + 4*t**4 - 36*t**2 - 3*t**5 - 299*t**3 + 323*t**w = 0. What is t?
-3, 0, 2
Let l(u) be the third derivative of -u**5/480 + 19*u**4/192 - 13*u**3/8 - 363*u**2 + 2*u. Factor l(o).
-(o - 13)*(o - 6)/8
Let h(c) = 8 + 109*c**2 - 20*c**3 - 5 + 8*c + 0*c**3 - 83*c**2 - 27*c + c**4. Let v(u) = 20*u**3 - 24*u**2 + 20*u - 4. Let k(l) = 4*h(l) + 3*v(l). Factor k(n).
4*n*(n - 2)**2*(n - 1)
Let q(x) be the first derivative of -3*x**5/35 + 15*x**4/28 + 31*x**3 + 399*x**2/2 - 2567. Factor q(f).
-3*f*(f - 19)*(f + 7)**2/7
Let h(v) be the third derivative of -v**6/180 - 19*v**5/90 - 5*v**4/2 - 8*v**3 + 553*v**2. Determine m so that h(m) = 0.
-12, -6, -1
Let w(j) be the first derivative of 4*j**3/3 + 3348*j**2 + 2802276*j + 2615. Solve w(h) = 0.
-837
Let d(p) be the third derivative of p**6/180 + p**5/15 + 13*p**3 + 2*p**2 + 21. Let z(u) be the first derivative of d(u). Let z(j) = 0. What is j?
-4, 0
Let t be ((-4)/14)/(6300/(-34300)). Factor -32/9 - 16/9*r - 2/9*r**3 + t*r**2.
-2*(r - 4)**2*(r + 1)/9
Let p(h) be the first derivative of -4*h**3/27 + 476*h**2/3 - 56644*h + 129. Suppose p(m) = 0. What is m?
357
Let u be -29 + 3796/650*5. Let u*p**2 + 8/5*p + 0 = 0. Calculate p.
-8, 0
Let j(h) be the third derivative of 0 + 0*h - 8*h**4 - 512*h**3 - 1/20*h**5 - 95*h**2. Factor j(g).
-3*(g + 32)**2
Let j(g) be the first derivative of g**4/2 + 3074*g**3/3 + 3071*g**2 + 3070*g + 13089. Solve j(o) = 0 for o.
-1535, -1
Let z(u) be the third derivative of -u**5/12 + 65*u**4/12 - 220*u**3/3 - 528*u**2. What is y in z(y) = 0?
4, 22
Let s be 24/72 + 22/6. Let k(d) be the third derivative of 1/3*d**s + 1/10*d**5 + 0*d - 10*d**2 + 1/3*d**3 + 0. Solve k(n) = 0.
-1, -1/3
Let z(q) be the second derivative of q**6/150 - q**5/50 - q**4/12 + q**3/5 - 78*q. Factor z(t).
t*(t - 3)*(t - 1)*(t + 2)/5
Let p(s) be the first derivative of s**7/84 - s**6/20 + 3*s**5/40 - s**4/24 + 2*s + 80. Let h(q) be the first derivative of p(q). Determine z so that h(z) = 0.
0, 1
Solve -238/3*y - 25/3*y**2 + 116 + 59/6*y**3 - 1/6*y**4 = 0 for y.
-3, 2, 58
Let n = 11239/2 + -5619. Let f(h) be the second derivative of n*h**3 + 3/5*h**2 + 1/5*h**4 + 3/100*h**5 - 7*h + 0. Factor f(r).
3*(r + 1)**2*(r + 2)/5
Let y = 29494/3 + -10190. Let p = y + 359. Suppose -8/3 - 2*q**2 - p*q**3 - 4*q = 0. What is q?
-2
Let o(u) be the second derivative of -u**6/30 - 461*u**5/10 - 211597*u**4/12 + 70994*u**3 - 106722*u**2 - 2*u - 111. Find a such that o(a) = 0.
-462, 1
Factor -92/5*f**2 + 0 - 4/5*f**3 - 48*f.
-4*f*(f + 3)*(f + 20)/5
Let m(g) be the first derivative of -4*g**3/3 + 2178*g**2 - 4352*g - 3887. Factor m(u).
-4*(u - 1088)*(u - 1)
Let m be (-15)/20*(0 + 4) + 6. Suppose -10*k = -3*z - 12*k, 0 = -3*z - 3*k - m. Suppose -2/17*x**z - 4/17*x + 0 = 0. Calculate x.
-2, 0
Let i(h) be the first derivative of -h**4/6 + 2*h**3/9 + 2*h**2 + 250. Determine w, given that i(w) = 0.
-2, 0, 3
Factor -2187*y**2 - 206*y**3 + 203*y**3 + 228816 - 43275537 - 531441*y.
-3*(y + 243)**3
Let y(j) = -j**3 + 7*j**2 + 8*j + 3. Let r be y(8). Let 117*o - 25*o - 31*o**r + 20 - 72*o**2 - 8*o**4 - 37*o**3 + 36 = 0. What is o?
-7, -2, -1/2, 1
Let -9/2*t**4 + 159/8*t**3 - 159/4*t**2 + 3/8*t**5 - 12 + 36*t = 0. What is t?
1, 2, 4
Let n(u) be the first derivative of -23*u - 14 + 0*u**2 + 1/3*u**4 + 2/3*u**3. Let i(y) be the first derivative of n(y). Suppose i(h) = 0. What is h?
-1, 0
Suppose -5 = -7*i + 72. Suppose -3*n - 4*j + 7 = i, 4*j = -n - 12. Determine m, given that -14/3*m**2 - 2 + 17/3*m + 4/3*m**n - 1/3*m**5 + 0*m**3 = 0.
-2, 1, 3
Let r(k) = -k**3 + 6*k**2 + 4*k + 24. Suppose 0 = -l + 7. Let f be r(l). What is g in -232*g - f*g**3 + 232*g + 3*g**2 = 0?
0, 1
Let n(p) be the first derivative of 1/24*p**3 + 5/8*p**2 + 48 + 9/8*p. Factor n(c).
(c + 1)*(c + 9)/8
Let k(v) be the first derivative of -v**5/390 - 2*v**4/39 + 3*v**3/13 + 14*v**2 + 48. Let y(u) be the second derivative of k(u). Factor y(d).
-2*(d - 1)*(d + 9)/13
Suppose -3*t = 3*z - 12, -3*z + 31 = t + 19. Factor -z*f**2 + 11*f + 5 - 25 + 3*f**2 - 2*f.
-(f - 5)*(f - 4)
Let x(g) be the second derivative of -g**4/32 - 253*g**3/16 + 144*g**2 - 901*g - 2. Factor x(c).
-3*(c - 3)*(c + 256)/8
Suppose 7*f = 12*f + 5*b, 15 = -5*b. Let j(t) = -t + 1. Let p(g) = -2*g**2 + 9*g - 13. Let h(s) = f*j(s) - p(s). Factor h(y).
2*(y - 4)*(y - 2)
Let c(i) = -2*i**2 + 21*i + 13. Let p be c(11). Let a = 7086 - 21257/3. What is s in 0*s + 1/4*s**p + 1/12*s**3 - a = 0?
-2, 1
Let z be (-17)/(-51)*-3 + 40/16. Factor -3/4*g**5 + 3/4*g + 0 + 3/2*g**2 + 0*g**3 - z*g**4.
-3*g*(g - 1)*(g + 1)**3/4
Let x = 2/1365773 + 4097315/2731546. Suppose -1/2*m**2 - x*m - 1 = 0. What is m?
-2, -1
Let s(i) be the third derivative of -i**8/84 - 2*i**7/5 + 49*i**6/30 + 23*i**5/5 + 388*i**2 - 2*i. Suppose s(x) = 0. Calculate x.
-23, -1, 0, 3
Let u be (28/(-5))/((-2)/15). Let j = 1028 + -1025. Find l such that -19*l**j + u*l**3 - 3*l**4 - 17*l**3 = 0.
0, 2
Let m(f) be the first derivative of 0*f + 153 - 5*f**5 - 5/2*f**4 + 0*f**2 + 0*f**3. Find q, given that m(q) = 0.
-2/5, 0
Let x(g) = 50*g**3 - 196*g**2 - 596*g - 398. Let c(l) = -8*l**3 + l**2 + 2*l + 1. Let f(v) = 12*c(v) + 2*x(v). Determine n so that f(n) = 0.
-2, -1, 98
Let g(l) be the second derivative of -l**5/12 + 445*l**4/12 - 880*l**3/3 + 2630*l**2/3 + 3*l - 497. Factor g(k).
-5*(k - 263)*(k - 2)**2/3
Let 908/7*j - 298/7*j**2 - 608/7 - 2/7*j**3 = 0. What is j?
-152, 1, 2
Factor -1/3*t**4 + 0 - 44/3*t**2 + 8*t**3 + 0*t.
-t**2*(t - 22)*(t - 2)/3
Let j(q) be the second derivative of q**4/54 + 2924*q**3/27 + 2137444*q**2/9 + 2*q - 2131. Determine l, given that j(l) = 0.
-1462
Factor 796/13*m - 2/13*m**2 - 794/13.
-2*(m - 397)*(m - 1)/13
Let x(g) be the second derivative of 1/21*g**4 + 0*g**2 - 2/21*g**3 + 9*g - 2 - 2/105*g**6 + 1/35*g**5. Factor x(z).
-4*z*(z - 1)**2*(z + 1)/7
Suppose -5062562/5 + 6364/5*x - 2/5*x**2 = 0. Calculate x.
1591
Let o(g) = 13*g**2 - 26808 + 26825 + 0*g - 3*g. Let v(f) = -3*f**2 + f - 4. Let d = 23 + -41. Let l(k) = d*v(k) - 4*o(k). Factor l(r).
2*(r - 2)*(r - 1)
Determine g, given that -38/3*g**4 + 0 + 0*g + 0*g**3 + 0*g**2 + 1/3*g**5 = 0.
0, 38
Let g = 5/5369 + 55219/5369. Suppose -3/7*i**2 - 432/7 + g*i = 0. Calculate i.
12
Suppose 10*q = -769 + 9479. Let a = 875 - q. Factor 2/11*g**3 + 0 + 0*g + 0*g**2 + 2/11*g**5 + 4/11*g**a.
2*g**3*(g + 1)**2/11
Let x = 1/3880 - -379/34920. Let m(u) be the third derivative of 0*u**4 + 0 + 0*u - 34*u**2 - x*u**6 - 3/4*u**3 + 1/1260*u**7 + 1/20*u**5. F