. Let x be 16/q*65 - -3. Determine y so that -5/9*y**2 + 4/9*y + 2/9*y**3 - x = 0.
1/2, 1
Let s(w) be the first derivative of 3*w**5/5 - 27*w**4/10 + 12*w**3/5 + 12*w**2/5 + 3854. Factor s(k).
3*k*(k - 2)**2*(5*k + 2)/5
Let s = -7425 + 7430. Let n(j) be the first derivative of 1/6*j**6 + 0*j**s + 1/2*j**2 + 0*j + 4 - 1/2*j**4 + 0*j**3. Factor n(c).
c*(c - 1)**2*(c + 1)**2
Let v(k) be the second derivative of 2*k**6/15 + 4*k**5/5 - 17*k**4 - 620*k**3/3 - 800*k**2 - 2*k + 9. Factor v(z).
4*(z - 8)*(z + 2)*(z + 5)**2
Let r be (-233 + 68)*4/(-5). Suppose r*p = 121*p. Factor -4/5*j**3 + 0 + p*j + 4*j**2.
-4*j**2*(j - 5)/5
Let q(s) be the first derivative of 17*s**3/27 - 7*s**2/6 - 10*s - 468. Determine w, given that q(w) = 0.
-30/17, 3
Let f(d) = -3*d**2 - 11*d - 1. Let s be ((-4)/2 + 2)/(-1). Suppose s = -6*l + 21 + 15. Let q(j) = j**2 + 5*j. Let c(i) = l*f(i) + 15*q(i). Factor c(z).
-3*(z - 2)*(z - 1)
Suppose -1983 + 5*z**2 + 455*z + 536 + 426 + 561 = 0. What is z?
-92, 1
Let t(l) = -3*l**2 - 10*l + 6. Let o(f) = f**2 + f - 1. Let z(p) = -6*o(p) - t(p). Let u(b) = 9*b**2 - 11*b + 64 - 64. Let w(i) = -2*u(i) - 7*z(i). Factor w(g).
3*g*(g - 2)
Suppose 3*v**3 - 31*v**2 + 5*v**3 - 4*v**3 - 32 - 74*v - 3 - 4 = 0. What is v?
-1, 39/4
Factor 1200 - 25/2*z**3 - 229/2*z**2 + 1/2*z**4 + 85/2*z.
(z - 32)*(z - 3)*(z + 5)**2/2
Suppose 5*b = 5*y - 20, -3*y - 5*b = -3*b + 8. Suppose y = 3*v + 8*v - 33. What is r in -1/2*r**v + 1/2*r + 1 - r**2 = 0?
-2, -1, 1
Let q = 12361/3116 + -547/164. Solve q*b + 2/19*b**4 + 0 - 4/19*b**3 - 10/19*b**2 = 0.
-2, 0, 1, 3
Let q(w) be the first derivative of 2*w**3/21 + 7730*w**2/7 + 29876450*w/7 - 8991. Factor q(k).
2*(k + 3865)**2/7
Let y(z) be the first derivative of 5*z**4/4 - 5*z**3 - 45*z**2 + 200*z - 3643. Determine t so that y(t) = 0.
-4, 2, 5
Let n(t) be the first derivative of -t**4/26 - 350*t**3/39 - 7743*t**2/13 - 15138*t/13 - 1763. Suppose n(k) = 0. Calculate k.
-87, -1
Suppose 1 = 5*z - 149. Let a = z + -28. Factor 3*x**2 + x**a - 24 + 0*x - 4*x.
4*(x - 3)*(x + 2)
Let j(d) be the second derivative of -d**5/100 + 13*d**4/60 - 13*d**3/15 - 56*d**2/5 - 269*d + 8. Factor j(b).
-(b - 8)*(b - 7)*(b + 2)/5
Solve -420*l + 823*l**3 + 87*l**2 - 406*l**3 - 415*l**3 - 41*l**2 = 0.
-30, 0, 7
Let o(q) = q**3 - 70*q**2 - 21*q - 18. Let g(x) = 4*x**2 + x + 1. Let s(b) = -90*g(b) - 5*o(b). Let s(y) = 0. What is y?
-3, 0, 1
Let x be 1809/16884 + 415/308. Factor -2/11*m**5 + 0*m - x*m**3 + 0 - 10/11*m**4 - 8/11*m**2.
-2*m**2*(m + 1)*(m + 2)**2/11
Let d(s) = 7. Let h(r) = 44*r**2 - 740*r - 178. Let v(x) = -6*d(x) - h(x). Determine q, given that v(q) = 0.
-2/11, 17
Let s(n) be the third derivative of 71*n**2 + 0 - 10/3*n**5 + 0*n + 7/2*n**4 + 4/3*n**3. Factor s(d).
-4*(2*d - 1)*(25*d + 2)
Solve -654*d**4 - 12*d**5 + 3*d**5 - 1217*d - 6*d**5 + 654*d**2 - 1308*d + 279*d**3 + 2261*d = 0.
-44, -1, 0, 2/5, 1
Solve -72/5*s + 39/5*s**3 + 6*s**2 + 3/5*s**4 + 0 = 0 for s.
-12, -2, 0, 1
Let p(g) = 3*g**2 + 28*g - 17. Let r be 1/(4 + 164/(-40)). Let o be p(r). Factor 3 - 9/4*t**2 - 3/4*t**o + 0*t.
-3*(t - 1)*(t + 2)**2/4
Let c = 10495/24 - 3493/8. What is r in 2*r + 4/3 - c*r**3 + 0*r**2 = 0?
-1, 2
Let -1034*g - 296*g + 63*g**2 - 136*g**2 + 68*g**2 - 88445 = 0. What is g?
-133
Let h = 43504 - 217364/5. Let t be (-2)/(-6) + 13172/30. Suppose -8/5 - t*d**3 - h*d - 1014/5*d**2 = 0. Calculate d.
-2/13
Suppose 4440/7*s + 2/7*s**2 + 2464200/7 = 0. What is s?
-1110
Let h = 82643 + -82641. Factor -2/13*j**h - 6/13 - 8/13*j.
-2*(j + 1)*(j + 3)/13
Let x(d) be the second derivative of -1/6*d**4 + 0*d**2 + 0*d**3 + 1/10*d**5 + 0 - 77*d. Determine o so that x(o) = 0.
0, 1
Let r(y) = y**3 - 2*y**2 - 13*y - 2. Let v be r(6). Suppose -v = -7*p + 34. Find l, given that 16*l**2 + p*l + 3*l + 2*l**3 - 3*l = 0.
-7, -1, 0
Let k(s) be the first derivative of 0*s**2 + 1/80*s**5 - 18*s + 1/6*s**4 + 0*s**3 - 21. Let g(r) be the first derivative of k(r). What is c in g(c) = 0?
-8, 0
Let a(v) = v**3 - 5*v**2 + 7*v - 4. Let s be a(4). Suppose h = 10 - s. Factor -196*j**3 + 3*j**2 + 191*j**3 - 4*j + 9*j**h.
-j*(j - 2)*(5*j - 2)
Suppose -3*w - a + 13 + 0 = 0, w + 4*a - 19 = 0. Let -467 + 467 + 0*m**3 - 6*m**4 + 9*m**5 + 0*m**3 - w*m**3 = 0. What is m?
-1/3, 0, 1
Let l(g) = -37*g**2 - g - 2. Let f(n) = 75*n**2 - 57*n - 386. Let j(w) = f(w) + 2*l(w). Let j(b) = 0. What is b?
-6, 65
Let o(r) = 6*r**3 + 7*r**2 - 14*r + 1. Let u(p) = -31*p**3 - 35*p**2 + 70*p - 4. Suppose -49*v - 198 = -43*v. Let m(h) = v*o(h) - 6*u(h). Factor m(j).
-3*(j - 1)*(j + 3)*(4*j - 1)
Let d = -948125 - -6636877/7. Factor d*b**2 - 46/7 + 44/7*b.
2*(b - 1)*(b + 23)/7
Let y(c) be the third derivative of c**6/24 + 5*c**5/4 + 55*c**4/24 - 325*c**3/2 - 7985*c**2. Suppose y(m) = 0. Calculate m.
-13, -5, 3
Let c(t) be the second derivative of -t**6/40 - 57*t**5/80 + 67*t**4/16 + 19*t**3/8 - 99*t**2/4 + 16*t - 3. Let c(r) = 0. What is r?
-22, -1, 1, 3
Factor 128*n**2 - 87*n**2 - 160098 - 29998 - 45*n**2 - 1744*n.
-4*(n + 218)**2
Let d = 28/1003 + 11896/5015. Factor -16/5 - 32/5*q - 4/5*q**2 + d*q**3.
4*(q - 2)*(q + 1)*(3*q + 2)/5
Let f(o) = 3*o + 38. Suppose 4*a + 24 = -20. Let g be f(a). Solve 12*p**3 - 32*p + 49 - p**2 + g*p**2 - 33 = 0.
-2, 2/3, 1
Suppose -1611 = 238*g - 1611. Factor g + 75/2*l - 5/2*l**2.
-5*l*(l - 15)/2
Let v = 25680 - 25677. Let r(j) be the second derivative of -j - 1/9*j**4 - 20/9*j**v - 6*j**2 + 0. Let r(i) = 0. Calculate i.
-9, -1
Factor 0 + 113/5*r**2 - r**3 + 117/5*r - 1/5*r**4.
-r*(r - 9)*(r + 1)*(r + 13)/5
Let a(f) = 6*f**3 + 3*f**2 - 6. Let m be ((-28)/(-10))/((-2)/(-20)). Let b(s) = 9*s + 5*s**3 - m*s + 18*s + 3*s**2 - 5. Let o(t) = 2*a(t) - 3*b(t). Factor o(h).
-3*(h - 1)*(h + 1)**2
Let m(s) be the first derivative of 4*s - 2/3*s**3 - 56 - s**2. Find h, given that m(h) = 0.
-2, 1
Let r(p) be the first derivative of p**6/120 - p**5/12 - p**4/24 + 5*p**3/6 + 3*p**2/2 - 31. Let u(z) be the second derivative of r(z). Factor u(l).
(l - 5)*(l - 1)*(l + 1)
Let u = 48754/2367 + 778/263. Solve -2/9 - 5618/9*j**2 - u*j = 0 for j.
-1/53
Let y(x) = 12*x**4 + 65*x**3 - 167*x**2 + 97*x + 53. Let a(c) = 12*c**4 + 66*c**3 - 168*c**2 + 97*c + 63. Let w(h) = 6*a(h) - 7*y(h). Factor w(q).
-(q - 1)**2*(q + 7)*(12*q - 1)
Let d(k) = k**2 - 6*k + 2. Let b be d(6). Suppose b*s + 1 = -2*j + 11, s = j - 1. Let -z**3 - 56*z**2 + 2*z**4 + 58*z**s + 5*z**3 = 0. What is z?
-1, 0
Let l(m) be the first derivative of m**5/4 + 725*m**4/16 + 2220*m**3 + 3240*m**2 + 720. Solve l(k) = 0.
-72, -1, 0
Let q be (-1 + 0)*2*-2. Suppose -4*a + 4 = 4*u, q*u - 3 = u + 4*a. Find w, given that -w**2 + 9 + 13*w**2 + 1 - u - 39*w = 0.
1/4, 3
Let j be (2 + 5 - 988/65) + 22 + -13. Factor -2/15*m**3 + 0 + j*m**2 - 2/3*m.
-2*m*(m - 5)*(m - 1)/15
Factor 18*z + 12*z**2 - 14/3*z**4 - 2/3*z**5 - 18 - 20/3*z**3.
-2*(z - 1)**2*(z + 3)**3/3
Let d(l) be the second derivative of -3*l**5/100 - 7*l**4/20 + l**3/10 + 21*l**2/10 - 1119*l. Factor d(b).
-3*(b - 1)*(b + 1)*(b + 7)/5
Factor 14/5*x**2 + 0 + 2/5*x**3 - 36/5*x.
2*x*(x - 2)*(x + 9)/5
Let o = -15/698 - -1531/6282. Let z(q) be the first derivative of -2/27*q**3 - 1/9*q**2 + 1/18*q**4 + 14 + o*q. Suppose z(b) = 0. What is b?
-1, 1
Let p(u) be the first derivative of -u**5/5 + 41*u**4/4 - 221*u**3/3 + 391*u**2/2 - 210*u - 9610. Solve p(b) = 0 for b.
1, 2, 3, 35
Let r(h) = -25*h**3 - 135*h**2 - 10*h + 170. Let w(i) = -i**3 - 2*i**2 - 7*i + 1. Let s(g) = -r(g) + 10*w(g). Factor s(j).
5*(j + 1)*(j + 8)*(3*j - 4)
Let k(q) = -5*q**3 + 31*q**2 - 8*q + 3. Let p be k(6). Let y be 1/p + (55/33)/5. Factor 10/9*i + 8/9 + y*i**2.
2*(i + 1)*(i + 4)/9
Let a(h) be the first derivative of -2*h**5/45 - 5*h**4/18 - 8*h**3/27 - 2917. Factor a(n).
-2*n**2*(n + 1)*(n + 4)/9
Factor 0*l + 48*l**2 + 0 - 76/3*l**3 + 2/3*l**4.
2*l**2*(l - 36)*(l - 2)/3
Let w(i) = 2*i - 18. Let c be w(11). Suppose -j = -3*r - 3, -4*j - c*r - 5 + 1 = 0. Factor -2/13*y**2 + 0 - 2/13*y**4 + j*y + 4/13*y**3.
-2*y**2*(y - 1)**2/13
Suppose -178*m + 1141 = 785. Let 8/3*t**5 + 0 + 4/9*t + 58/9*t**4 + 8/9*t**3 - 22/9*t**m = 0. What is t?
-2, -1, 0, 1/4, 1/3
Let v = -601 - -975. Find r such that 36*r + v*r**3 - 129*r**3 - 90*r**2 + 36*r**2 - 133*r**2 + 3*r**2 - 25*r**4 = 0.
0, 2/5, 9
Suppose -34 = -2*h - 2*i - 32, -5*i + 1 = 3*h. Suppose h