t**2 - 327 + 49*t + 345 = 0.
-9, -1
Suppose -2/11*t**2 - 450/11 - 60/11*t = 0. What is t?
-15
Let t(n) be the third derivative of -n**8/672 + 13*n**7/840 - n**6/15 + 37*n**5/240 - 5*n**4/24 + n**3/6 + 3*n**2 - 2. Find u, given that t(u) = 0.
1/2, 1, 2
Factor 3/7*n**4 - 2/7*n**3 + 0*n + 0*n**2 - 1/7*n**5 + 0.
-n**3*(n - 2)*(n - 1)/7
Factor 968/7 + 2/7*p**2 + 88/7*p.
2*(p + 22)**2/7
Let y(a) be the second derivative of -a**4/18 - 2*a**3/9 + 25*a - 3. Find t such that y(t) = 0.
-2, 0
Let h(p) be the first derivative of -p**3 + 0*p + 1/5*p**5 + 0*p**2 - 1/2*p**4 + 37. Factor h(r).
r**2*(r - 3)*(r + 1)
Let y(z) be the third derivative of z**6/300 + 17*z**5/25 + 289*z**4/5 + 39304*z**3/15 - 292*z**2. Factor y(b).
2*(b + 34)**3/5
Factor -7*c**2 + 826 + 4*c**2 - 2*c**2 - 846 + 20*c.
-5*(c - 2)**2
Let 67*p**4 + 32 + 86*p - 182*p - 208*p + 520*p**2 - 7*p**4 - 308*p**3 = 0. What is p?
2/15, 1, 2
Suppose -3 = 3*u - 10*x + 5*x, 2*x + 10 = 4*u. Determine w so that 2/9*w**u + 2/3*w**2 - 2/9*w - 2/3*w**3 + 0 = 0.
0, 1
Let d(n) = n**3 + n**2 - n + 1. Suppose q + 4 = -2*o + 5, 0 = -3*o + 5*q + 21. Let v be d(o). Factor -8*a**4 + v*a**3 - 5*a**3 + 11*a**4 - 3 - 6*a.
3*(a - 1)*(a + 1)**3
Let d(a) be the second derivative of -a**6/60 - 3*a**5/20 - 5*a**4/24 - 160*a. Factor d(s).
-s**2*(s + 1)*(s + 5)/2
Let s(h) = h - 10. Let r be s(13). Let l(m) = 4*m - 4. Let u be l(r). Factor 10*o**3 - 8 + 4*o**3 + 2*o**3 + 16*o**4 + 0*o**5 + 4*o**5 - 20*o - u*o**2.
4*(o - 1)*(o + 1)**3*(o + 2)
Suppose u**5 + 10870*u + 46*u**2 + 20209*u - 206*u**2 - 112*u**3 - 7783*u - 172*u**3 + 100352 - 4*u**4 = 0. Calculate u.
-8, 14
Let c(d) be the first derivative of -d**5/20 + 7*d**4/8 - 6*d**3 + 28*d**2 + 9. Let y(j) be the second derivative of c(j). Factor y(h).
-3*(h - 4)*(h - 3)
Suppose 5/2 - 223/4*r**3 + 6*r**4 - 93/4*r + 133/2*r**2 + 4*r**5 = 0. Calculate r.
-5, 1/4, 1, 2
Let y(v) = -44*v**2 - 36*v - 18. Let f(n) = 44*n - 89*n - 5*n**2 + 41*n - 2. Suppose 5*b = -40 + 10. Let r(w) = b*y(w) + 52*f(w). Find a such that r(a) = 0.
-1
Suppose -3*h = -5*k - 630 + 191, -4*h + 4*k = -580. Let x = -143 + h. Suppose x + 2/9*g - 4/9*g**4 - 2/9*g**5 + 4/9*g**2 + 0*g**3 = 0. Calculate g.
-1, 0, 1
Suppose 0 = -7*w + 154 - 133. Factor 2/11*g**2 - 2/11*g**4 + 0*g**w + 0*g + 0.
-2*g**2*(g - 1)*(g + 1)/11
Let s be (-82)/(-45) + (-432)/270. Factor 0 + s*m + 2/9*m**2.
2*m*(m + 1)/9
Let m be -1*((-10)/(-3))/((-26)/39). Find u, given that 7*u**3 + 3*u**4 - 3*u**m + 10*u**3 - 11*u**3 = 0.
-1, 0, 2
Let t be (4/22 + (-768)/(-616))*(-231)/(-396). Suppose -t*z + 5/2*z**4 + 25/6*z**2 - 35/6*z**3 + 0 = 0. Calculate z.
0, 1/3, 1
Let r be -3 - (3 + -13 + 2). Suppose w - 2*w - 12 = -2*n, -r*w - 12 = 2*n. Solve f + 6*f + n*f**2 - 4*f - 7*f = 0.
0, 1
Suppose 6*v - 40 = -2*v. Suppose -219*w**4 - 447*w**3 + 359*w**2 + 243*w**v - 159*w**4 + 204*w - 5*w**2 - 11 + 35 = 0. What is w?
-1, -2/9, 1, 2
Let w(b) = -20*b**4 + 188*b**3 - 544*b**2 - 1168*b + 1536. Let i(v) = -13*v**4 + 125*v**3 - 363*v**2 - 778*v + 1024. Let x(a) = 8*i(a) - 5*w(a). Factor x(p).
-4*(p - 8)**2*(p - 1)*(p + 2)
Let r(d) be the second derivative of 5*d**4/12 + 20*d**3/3 - 45*d**2/2 - 159*d. Let r(w) = 0. What is w?
-9, 1
Let b(f) be the second derivative of 5/16*f**4 + 17/8*f**3 + 9/4*f**2 - 10*f + 0. Factor b(u).
3*(u + 3)*(5*u + 2)/4
Let f = 72 - 69. Factor -3/4*x**2 - 9/4 - f*x.
-3*(x + 1)*(x + 3)/4
Let z(k) = 3*k**4 + 69*k**3 - 126*k**2 + 63*k. Let b(l) = 7*l**4 + 208*l**3 - 381*l**2 + 190*l. Let s(t) = 3*b(t) - 8*z(t). Factor s(p).
-3*p*(p - 22)*(p - 1)**2
Let g(c) be the second derivative of -c**6/40 - c**5/80 + 7*c**4/16 + 25*c**3/24 + 3*c**2/4 + 26*c + 4. Find o such that g(o) = 0.
-2, -1, -1/3, 3
Suppose -6*p = -7*p - 2, 3*k = 2*p + 463. Let y = k - 129. Factor 3/2*z**2 + y + 12*z.
3*(z + 4)**2/2
Let x(q) = 27*q - 51. Let t(p) = -p**2 - 28*p + 52. Let v = 3 - -1. Let r(u) = v*x(u) + 3*t(u). Factor r(n).
-3*(n - 4)**2
Let p be -15*(-9 + 879/99). Suppose 0*n + p*n**3 + 0 - 6/11*n**2 - 2*n**4 + 8/11*n**5 = 0. What is n?
0, 3/4, 1
Suppose -2*h = -3*g - 1, 5*g - 14 = 3*g + 5*h. Let w be g - (-1)/(2/300). Factor -156*v + 85*v**2 - 28 - 295*v**2 + w*v**3 + 3 + 1.
3*(v - 2)*(7*v + 2)**2
Let x(s) be the third derivative of s**5/6 - 17*s**4/36 + 2*s**3/9 + 396*s**2. Factor x(f).
2*(f - 1)*(15*f - 2)/3
Let n(o) be the third derivative of o**7/70 - o**5/20 - 27*o**2 - 3*o. Factor n(u).
3*u**2*(u - 1)*(u + 1)
Let a(v) be the first derivative of -12*v**3 - 580*v**2 - 256*v - 654. Solve a(s) = 0 for s.
-32, -2/9
Let n be (-52)/12 - -5*1. Let z(b) be the first derivative of -13/3*b**2 + 8/3*b + n*b**3 + 3. Factor z(j).
2*(j - 4)*(3*j - 1)/3
Let c be (-2)/3*(65 + -66). Let z be -50 + 52 - (-2)/(-12)*10. Factor c*b + 1/3 + z*b**2.
(b + 1)**2/3
Let l(z) = 5*z**3 + 3*z**2 + 10*z + 2. Let h(o) = -3*o**3 - o**2 + o - 1. Let b(a) = -2*h(a) - l(a). Factor b(t).
t*(t - 4)*(t + 3)
Let v(j) be the third derivative of 0 + 0*j - 1/16*j**4 + 1/18*j**3 + 7/360*j**5 - 2*j**2. Factor v(z).
(z - 1)*(7*z - 2)/6
What is g in g**2 + 10*g**2 + 42*g - 13*g**2 - 56 - 20*g + 36*g = 0?
1, 28
Determine m so that 98/5*m**5 - 112*m**4 + 294/5*m + 1048/5*m**3 - 36/5 - 844/5*m**2 = 0.
2/7, 3/7, 1, 3
Let c(x) be the second derivative of x**8/6720 - x**7/560 + x**6/288 + x**3/6 - 28*x. Let z(j) be the second derivative of c(j). Suppose z(h) = 0. What is h?
0, 1, 5
Let v(y) = y**2 + 2. Suppose 3 = -7*u + 10. Let a be v(u). Let 0*j + 2/7*j**4 + 0 + 4/7*j**a + 2/7*j**2 = 0. Calculate j.
-1, 0
Factor 1/4*i**5 + 0*i + 0 + 5/4*i**2 + 7/4*i**4 + 11/4*i**3.
i**2*(i + 1)**2*(i + 5)/4
Let o(f) be the second derivative of 3*f**5/100 + 39*f**4/4 + 2535*f**3/2 + 164775*f**2/2 - 122*f. Find a, given that o(a) = 0.
-65
Let a(p) = p**3 + 1. Let o(w) = w**3 - 4*w**2 + 5. Let b(g) = -g**2 - 1. Let u(q) = -2*b(q) - o(q). Let i(d) = 3*a(d) + u(d). Determine n so that i(n) = 0.
-3, 0
Let r(o) be the first derivative of -9*o**6/2 + 108*o**5/5 - 9*o**4 - 118*o**3/3 - 49*o**2/2 - 6*o + 23. Determine q so that r(q) = 0.
-1/3, 2, 3
Let v be (-569)/(-3) + 2/6. Determine u, given that 187*u - v*u - 2 + u**2 + 2 = 0.
0, 3
Let c = 1/5477 - -224547/54770. Let f = -4 + c. Factor -f*l**2 + 1/10*l + 1/5.
-(l - 2)*(l + 1)/10
Suppose 46/3*o**2 - 2/3*o**3 + 200 - 320/3*o = 0. Calculate o.
3, 10
Let m = 36351/3020 - 241/20. Let w = m - -161/755. Find z, given that -w - 1/5*z**4 + 4/5*z - 6/5*z**2 + 4/5*z**3 = 0.
1
Let q(f) be the first derivative of f**4 - 116*f**3 + 5046*f**2 - 97556*f - 213. Find p, given that q(p) = 0.
29
Let h(n) = n + 2. Let j be h(1). Suppose -j*g - 2*g = -10. Factor g*l**2 - 15*l + 17*l - 3*l**2 - 1.
-(l - 1)**2
Let f(k) = -150*k**2 - 2*k + 152*k**2 + 3 + 3*k. Let t be f(0). Let t*s - 3/4*s**2 - 9/4 = 0. Calculate s.
1, 3
Let a = 115 + -111. Let v(t) be the third derivative of -1/48*t**a + 0*t + 1/240*t**6 + 9*t**2 + 0*t**5 + 1/840*t**7 + 0 - 1/24*t**3. Factor v(c).
(c - 1)*(c + 1)**3/4
Suppose -74*f**2 + 9*f - 10 - 2 + 77*f**2 = 0. What is f?
-4, 1
Let x(r) be the third derivative of 1/36*r**4 + 2/3*r**3 - 17*r**2 + 0*r + 0 - 1/90*r**5. Factor x(i).
-2*(i - 3)*(i + 2)/3
Let j(a) be the second derivative of -a**7/840 + a**6/240 - a**4/48 + a**3/24 + 4*a**2 + 2*a. Let r(m) be the first derivative of j(m). Factor r(o).
-(o - 1)**3*(o + 1)/4
Let k be (3672/85)/((-1)/(-5)). Let t = 216 - k. Factor 3/2*x**3 + t + 3*x**2 + 3/2*x.
3*x*(x + 1)**2/2
Solve -2/11*p**4 + 0 - 14*p**2 + 32/11*p**3 + 196/11*p = 0 for p.
0, 2, 7
Let h(d) be the first derivative of 8*d**3/3 + 2*d**2 - 150. Solve h(i) = 0 for i.
-1/2, 0
Let m(z) be the first derivative of -z**5/5 - 3*z**4 + 5*z**3 + 13*z**2 - 166. Solve m(g) = 0 for g.
-13, -1, 0, 2
Let a(f) = f**3 - 9*f**2 - 24*f + 24. Let h be a(11). Solve -4*r**h - 5*r**2 - 36*r + 6*r**2 = 0.
-12, 0
Suppose 78 = -7*m - 41. Let d(v) = -14*v + 23*v**2 - 2*v + 4*v + 23. Let i(t) = -8*t**2 + 4*t - 8. Let w(n) = m*i(n) - 6*d(n). Solve w(p) = 0 for p.
1
Let u(v) = 5*v**2 - 2*v + 35. Let y(t) = -4*t**2 + t - 34. Let r(i) = 3*u(i) + 4*y(i). Let n(c) = 5. Let w(z) = 30*n(z) + 5*r(z). Factor w(k).
-5*(k + 1)**2
Factor 1/2*j**4 + 5/2*j**3 + 2*j**2 + 0*j + 0.
j**2*(j + 1)*(j + 4)/2
Let p(g) be the second derivative of -12*g - 3*g**2 + 1/30*g**5 + 0 + 0*g**3 + 0*g**4 - 1/60*g**6. Let n(i) be the