such that -37*x**3 + 9*x**3 + 4*x**4 - 20*x + 58*x**2 - 4*x**2 - q*x**2 = 0.
0, 1, 5
Let h(s) be the first derivative of s**3/9 + 3395*s**2/3 + 11526025*s/3 - 11308. Determine q so that h(q) = 0.
-3395
Let z(c) be the first derivative of -9*c**2/2 + 5*c + 16. Let r be z(0). Let k - r*k + k**2 - 3*k + 5*k = 0. What is k?
0, 2
Let -3/2*a**3 + 3043/2*a**2 + 0 + 1015*a = 0. Calculate a.
-2/3, 0, 1015
Let q(p) be the second derivative of 1/135*p**6 - 21*p - 5/27*p**3 + 1/18*p**4 + 0 - 4/9*p**2 + 1/18*p**5. Factor q(t).
2*(t - 1)*(t + 1)**2*(t + 4)/9
Let f(z) = -101*z**3 + 0*z - 6*z + 8 + 92*z**3 - 7*z**2. Let n(h) = -h**3 - h + 2. Let x(v) = f(v) - 4*n(v). Find b, given that x(b) = 0.
-1, -2/5, 0
Let f be 10/4 - (-75)/30. Let y(t) = 11*t**3 + 18*t**2 + 7*t - 5. Let x(i) = 6*i**3 + 9*i**2 + 3*i - 3. Let l(z) = f*x(z) - 3*y(z). Let l(v) = 0. What is v?
-2, -1, 0
Suppose 112 = 4*s + 5*h, 4*s + 2 = 2*h + 114. Let k(r) be the second derivative of -5/12*r**4 - s*r + 10*r**2 + 0*r**3 + 0. Factor k(f).
-5*(f - 2)*(f + 2)
Find n, given that 1128*n + 1500*n + 4*n**2 + 5624 - 171*n + 363*n = 0.
-703, -2
Let w be 6/(-180)*-6*10. Solve 36*f**3 + 315*f**w - 1 + 16 - 130*f - 224*f**3 + 68*f**3 - 80*f**4 = 0 for f.
-3, 1/4, 1
Factor 2/5*f**3 + 6174/5 + 1862/5*f + 154/5*f**2.
2*(f + 7)**2*(f + 63)/5
Factor 0*t**2 + 0 - 1/8*t**5 - 1/8*t + 0*t**4 + 1/4*t**3.
-t*(t - 1)**2*(t + 1)**2/8
Let t(i) = 3*i**2 - 5*i - 1. Let g(d) = 44*d**2 - 650*d - 14. Let v(y) = 2*g(y) - 28*t(y). Solve v(q) = 0 for q.
0, 290
Let f(h) be the first derivative of -h**6/15 - 4*h**5/25 + h**4/2 + 4*h**3/3 - 4*h**2/5 - 16*h/5 - 1220. Solve f(t) = 0.
-2, -1, 1, 2
Let k(j) be the second derivative of -j**5/4 - 565*j**4/12 - 5095*j**3/6 + 5665*j**2/2 - 5*j + 187. Let k(w) = 0. Calculate w.
-103, -11, 1
Let q(h) be the first derivative of -5/2*h**2 + 1/2*h**5 - 9/4*h**4 - 11/2*h**3 + 0*h + 13. Factor q(j).
j*(j - 5)*(j + 1)*(5*j + 2)/2
Let w be (-241)/(-13)*(81 + -26). Let i = -1019 + w. Factor 6/13*f - 2/13 + 0*f**2 - i*f**3.
-2*(f + 1)*(2*f - 1)**2/13
Suppose 3*b = -3*g + 66, -4*g - 10 = -9*g. Factor -3*d**4 - 3*d**5 + b*d**3 - 9*d**2 - 6*d**3 + d**3.
-3*d**2*(d - 1)**2*(d + 3)
Suppose 43/4*o + 1/4*o**2 - 255 = 0. Calculate o.
-60, 17
Let s = -50 + 42. Let y be (296/40 + s)*-2. Factor -21/5*c**2 - y*c + 0.
-3*c*(7*c + 2)/5
Let v(t) be the third derivative of -71*t**2 + 0*t - 1/30*t**5 + 0 + 0*t**3 + 1/12*t**4. Find n, given that v(n) = 0.
0, 1
Let g = -315 - -309. Let u be 4/g*6*4/(-3). Factor -32/3 - 2/3*v**2 + u*v.
-2*(v - 4)**2/3
Find d such that 37/6*d**2 + 4/3 - 99/2*d = 0.
1/37, 8
Let k(i) be the first derivative of 0*i - 45 - 2/3*i**6 + 8*i**2 - 3*i**4 + 20/3*i**3 - 4*i**5. What is z in k(z) = 0?
-4, -1, 0, 1
Let v(s) = 7*s + 168. Let r be v(-8). Determine n, given that 101*n**2 - 6 + 17*n**2 - r*n - 182*n**2 + 2 - 236*n**2 = 0.
-1/3, -1/25
Suppose 34*g + 10566 = 80810. Let o = 8269/4 - g. Factor -5/4*c**5 + 5/4 - 5/4*c + o*c**4 - 5/2*c**2 + 5/2*c**3.
-5*(c - 1)**3*(c + 1)**2/4
Let v(x) be the first derivative of 69*x**3 - 42*x**2 - 70*x**3 - 27 - 81*x - 25. Factor v(l).
-3*(l + 1)*(l + 27)
Let b(t) = 10*t**4 + 72*t**3 - 72*t**2 - 317*t - 28. Let s(r) = -3*r**4 - 23*r**3 + 24*r**2 + 106*r + 8. Let q(k) = 2*b(k) + 7*s(k). Factor q(g).
-g*(g - 3)*(g + 2)*(g + 18)
Let s(m) be the third derivative of m**5/210 - 37*m**4/7 + 6157*m**2. Factor s(c).
2*c*(c - 444)/7
Let i = -17291 - -17293. Factor -16/7*o**4 + 20/7*o**3 + 4/7*o**5 + 0 + 0*o - 8/7*o**i.
4*o**2*(o - 2)*(o - 1)**2/7
Let m(v) = -v**2. Let x(g) = -9*g**2 + 18*g - 4. Let h = -27 + 22. Let c(b) = h*m(b) - x(b). Find q such that c(q) = 0.
2/7, 1
Let j be -31 - -54 - 14 - (9 + 0). Find m such that j*m**3 + 22/9*m**2 + 16/9 + 4*m - 2/9*m**4 = 0.
-2, -1, 4
Let t(o) be the third derivative of 0*o - 1/210*o**7 + 1/1680*o**8 - 64*o**2 + 0*o**3 + 1/75*o**5 - 1/15*o**4 - 2 + 1/100*o**6. Factor t(q).
q*(q - 2)**3*(q + 1)/5
Suppose 0 = -13*n + 22*n - 45. Find j such that 64*j**4 + 61*j**3 + 55*j**3 + 65*j**2 - 23*j**n + 27*j**5 - 9*j**2 = 0.
-14, -1, 0
Let k(x) be the second derivative of -11*x**4/15 + 512*x**3/15 - 138*x**2/5 - 120*x + 6. Suppose k(j) = 0. What is j?
3/11, 23
Let n(k) be the first derivative of 11*k**4/26 + 152*k**3/39 - 96*k**2/13 - 4471. Factor n(m).
2*m*(m + 8)*(11*m - 12)/13
Let r(n) be the second derivative of -1/16*n**4 + 3/40*n**6 + 0*n**3 - 5 + 0*n**2 - 1/8*n**5 + 6*n + 1/42*n**7. Solve r(x) = 0 for x.
-3, -1/4, 0, 1
Let w(x) be the first derivative of 4*x**5/35 + x**4/2 - 190*x**3/7 + 936*x**2/7 + 1080*x/7 + 4664. Suppose w(z) = 0. Calculate z.
-15, -1/2, 6
Let k(n) be the first derivative of -5*n**6/6 + 21*n**5 + 225*n**4/4 + 115*n**3/3 + 39. Suppose k(p) = 0. What is p?
-1, 0, 23
Let z(q) be the second derivative of q**6/45 + q**5/90 - q**4/2 - q**3/3 + 19*q - 58. What is p in z(p) = 0?
-3, -1/3, 0, 3
Let u(x) be the second derivative of -3*x**5/20 - 6*x**4 - 101*x**3/2 - 171*x**2 - 104*x - 5. Determine c so that u(c) = 0.
-19, -3, -2
Let f = 1396372/7 + -200156. Let n = f - -676. Factor -16/7*a**2 + 0*a**4 + 0 + n*a**3 + 6/7*a - 2/7*a**5.
-2*a*(a - 1)**3*(a + 3)/7
Let c(b) be the third derivative of 5/56*b**4 + 0 + 0*b**3 + 0*b + 1/140*b**5 - 46*b**2. Let c(x) = 0. Calculate x.
-5, 0
Find d such that -35 - 133*d**3 + 16*d**4 + 28*d + 6*d**4 - 13 + 79204*d**2 - 79028*d**2 = 0.
-1/2, 6/11, 2, 4
Let z(k) be the first derivative of -12*k**3 - 52 + 0*k + 54*k**2 - 177/4*k**4 + 25/2*k**6 + 6*k**5. Suppose z(o) = 0. What is o?
-6/5, 0, 1
Factor 208/3*n**3 - 1399489/3 - 4394*n**2 + 246064/3*n - 1/3*n**4.
-(n - 91)**2*(n - 13)**2/3
Determine z so that -6*z**2 - 1/4*z**3 + 44 - 9*z = 0.
-22, -4, 2
Let n(x) = -x**3 - x**2 - 3*x - 4. Let a(s) = -9*s**3 + 117*s**2 + 240*s - 24. Let t(p) = a(p) - 6*n(p). Solve t(l) = 0 for l.
-2, 0, 43
Let r(g) = -8*g**4 + 338*g**3 - 2111*g**2 + 1800*g + 19. Let t(z) = -z**4 + 56*z**3 - 352*z**2 + 300*z + 3. Let j(k) = -3*r(k) + 19*t(k). Factor j(p).
5*p*(p - 4)*(p - 1)*(p + 15)
Let w be 4 + (-744)/(819/(-154) + 6). Let g = -1087 - w. Determine h so that g*h**2 + 1/5*h - 2/5 = 0.
-2, 1
What is h in 152/3 + 74/3*h - 1/3*h**2 = 0?
-2, 76
Suppose 3*u + 1 + 11 = 0, -4*u - 46 = -d. Suppose 12*f + 3 - 1233*f**3 - 45*f**4 - d*f**2 + 542*f**3 + 607*f**3 = 0. What is f?
-1, -1/5, 1/3
Suppose 0 = 2*a + 2*q + 8 - 6, -5*q - 20 = 0. Let t(u) be the first derivative of -1/6*u**a + 1/24*u**4 - 2 + 1/6*u**2 + 0*u. Factor t(d).
d*(d - 2)*(d - 1)/6
Let g(t) be the third derivative of 7*t**2 + 12 + 11/3*t**3 + 0*t + 1/6*t**4 + 1/330*t**5. Factor g(w).
2*(w + 11)**2/11
Let d(v) be the third derivative of v**5/180 + 29*v**4/18 - 13*v**3/2 - 17*v**2. Factor d(b).
(b - 1)*(b + 117)/3
Let w(q) be the third derivative of 0*q**7 + 0*q**4 - 1/220*q**6 + 1/165*q**5 + 79*q**2 + 1/1848*q**8 + 0*q + 0 + 0*q**3. Factor w(i).
2*i**2*(i - 1)**2*(i + 2)/11
Let y(l) be the third derivative of 3/4*l**4 + 7/10*l**5 + 1/672*l**8 + 0*l**3 + 0*l + 1/30*l**7 + 61/240*l**6 + 0 - 38*l**2. Factor y(f).
f*(f + 1)**2*(f + 6)**2/2
Let p(v) be the first derivative of v**5/60 + 13*v**4/24 - 113*v**2/2 - 60. Let q(g) be the second derivative of p(g). Let q(j) = 0. Calculate j.
-13, 0
Let b be (-1)/(((-115)/20)/23). Suppose -2*y + y = 2*l - 2, -5*y - 4*l = -28. Suppose -y*q**2 - 2*q**4 + 1 + 3 + 6*q**b = 0. What is q?
-1, 1
Let l(t) be the second derivative of 2*t**6/15 - 612*t**5/5 + 93022*t**4/3 + 125256*t**3 + 188498*t**2 + 3*t - 256. Factor l(m).
4*(m - 307)**2*(m + 1)**2
Let x(h) = -268*h - 20100. Let g be x(-75). Suppose -2/7*p**4 - 10/7*p**3 + g*p + 2/7*p**5 - 6/7*p**2 + 0 = 0. What is p?
-1, 0, 3
Let d(m) be the third derivative of m**8/1008 - 31*m**7/630 + 17*m**6/24 - 5*m**5/4 + 11*m**2 - 7*m. Factor d(f).
f**2*(f - 15)**2*(f - 1)/3
Let n(r) be the second derivative of r**6/840 + 13*r**5/280 + 16*r**3/3 - r**2 + 9*r - 3. Let y(l) be the second derivative of n(l). Find v such that y(v) = 0.
-13, 0
Factor 0*v + 0 + 2/23*v**3 + 0*v**2 + 2/23*v**4.
2*v**3*(v + 1)/23
Let o(n) = -29*n**3 - 61*n**2 + 622*n + 682. Let a(p) = -9*p**3 - 21*p**2 + 207*p + 227. Let f(t) = -7*a(t) + 2*o(t). Factor f(d).
5*(d - 5)*(d + 1)*(d + 9)
Let g be (10/(-3) - -4)/((-825)/(-45) - 5). Let o(a) be the second derivative of -g*a**5 - 1/8*a**2 - 1/120*a**6 + 35*a - 