r**4 - 29108*r**3 - 133114*r**3 - 15648*r**3 - 1056 - 8834*r = 0.
-44, -2/11
Let l(v) = -9*v**2 - 23*v - 18. Let c(w) be the second derivative of w**4/6 + w**3/6 + 133*w. Let k(z) = 4*c(z) + l(z). Factor k(m).
-(m + 1)*(m + 18)
Let n be (-13)/(5 + -122)*(-23 + 24). What is w in n*w**5 - 4/3*w**2 - 8/9*w - 2/9*w**3 + 0 + 1/3*w**4 = 0?
-2, -1, 0, 2
Let h(g) be the first derivative of g**3 + 39*g**2 - 576*g + 2924. Factor h(v).
3*(v - 6)*(v + 32)
Let 4/3*d**3 - 136/3*d**2 + 504 - 460*d = 0. What is d?
-9, 1, 42
Suppose -2*u + 3*u - 2*q = -4, u = -5*q + 17. Let g(b) be the second derivative of 1/9*b**4 + 0 + 0*b**2 - 1/9*b**3 - u*b - 1/30*b**5. Factor g(h).
-2*h*(h - 1)**2/3
Factor -475/6*y + 1 - 53/2*y**2.
-(y + 3)*(159*y - 2)/6
Let x(p) = -10*p**3 + 76*p**2 + 74*p. Let n(z) = -z**3. Let d = -161 - -160. Let w(u) = d*x(u) + 12*n(u). Factor w(f).
-2*f*(f + 1)*(f + 37)
Let v(x) be the second derivative of -551/3*x**4 - 1/135*x**6 + 86/45*x**5 - 11*x - 20577*x**2 + 7220*x**3 + 5. Find y such that v(y) = 0.
1, 57
Let u(f) be the third derivative of -f**8/6048 - f**7/5670 + f**6/648 + f**5/270 - 15*f**4/8 + 149*f**2. Let a(d) be the second derivative of u(d). Factor a(v).
-2*(v - 1)*(v + 1)*(5*v + 2)/9
Factor 0*s + 0 + 2/3*s**3 + 1726/3*s**2.
2*s**2*(s + 863)/3
Factor 38*q**2 - 60 - 20*q + 5*q**3 + 42*q**2 - 20*q**4 + 0*q + 60.
-5*q*(q - 2)*(q + 2)*(4*q - 1)
Let d(y) be the first derivative of 1/2*y**3 - 42*y - 9*y**2 + 142. What is o in d(o) = 0?
-2, 14
Let k be (-2016)/294*(-49)/63. Solve 328/3*n + 2318/3*n**3 + k + 636*n**2 + 722/3*n**4 = 0.
-2, -1, -2/19
Let m(f) be the first derivative of 2*f**3/9 - 69*f**2 + 820*f/3 + 402. Find a such that m(a) = 0.
2, 205
Let s = 414227/9 + -46025. Find w, given that 0*w + 0*w**3 + 0 + 2/9*w**2 - s*w**4 = 0.
-1, 0, 1
Let n(v) be the second derivative of 1/10*v**5 + 1/60*v**6 + 2 - 13*v + 1/24*v**4 - 1/2*v**3 + 0*v**2. Factor n(r).
r*(r - 1)*(r + 2)*(r + 3)/2
Let m(a) be the first derivative of a**4/3 - 8*a**3/3 + 8*a**2 - 24*a - 17. Let s(l) be the first derivative of m(l). Find y, given that s(y) = 0.
2
Suppose -4*l - 4*d = 2 + 2, 4*l = 4*d + 28. Suppose -5*s + 33*i = 31*i - 29, 2*s - 2*i = 14. Find g, given that -581*g**3 - l*g**4 + 581*g**3 + 3*g**s = 0.
0, 1
Suppose 202*a = 206*a - 3*u + 4, a - 21 = -2*u. Suppose -2 - 4*x**3 + 1/2*x**a + x**2 + 7/2*x + x**4 = 0. Calculate x.
-4, -1, 1
Let n(c) be the first derivative of c**4/14 + 62*c**3/21 + 95*c**2/7 - 722*c + 1446. Factor n(g).
2*(g - 7)*(g + 19)**2/7
Let o(n) be the second derivative of 34/27*n**4 + 16/27*n**3 - 1/5*n**5 + 0 + 0*n**2 + 16*n. Solve o(p) = 0.
-2/9, 0, 4
Let p = 4823 + -4817. Let l(z) be the second derivative of 0*z**2 + 0*z**3 - p*z - 8/5*z**5 + 0 + 1/3*z**4 + 32/15*z**6. Solve l(k) = 0 for k.
0, 1/4
Let t(c) be the first derivative of c**5/300 + c**4/12 + 3*c**3/10 + 147*c**2 - 305. Let a(d) be the second derivative of t(d). Factor a(w).
(w + 1)*(w + 9)/5
Let m(v) be the second derivative of -v**6/90 + 13*v**5/30 - 11*v**4/3 - 20*v**3 + 432*v**2 - v + 650. Find z, given that m(z) = 0.
-4, 6, 18
Let p(n) = n**2 + 4*n + 1. Let u(h) = 2*h**2 + 9*h + 1. Let z(c) = 13*p(c) - 6*u(c). Let k be z(4). Factor -k*l - 26*l - 5*l**2 + 50*l - 24*l.
-5*l*(l + 3)
Suppose -88 = -14*t + 66. Suppose 15*n**2 + 29*n**2 + 5*n**2 - 12 - 38*n - t*n**2 - 8*n**3 = 0. What is n?
-1/4, 2, 3
Suppose 3*x = x + 6. Let c = 287/10 + -283/10. Find d such that -c*d**4 + 0 - 4/5*d**2 + 0*d + 6/5*d**x = 0.
0, 1, 2
Let k(y) be the second derivative of -4*y**7/21 + y**5/40 + 2*y + 8. Determine i, given that k(i) = 0.
-1/4, 0, 1/4
Suppose 6 = -l, l = -4*n + 40 + 14. Let g(v) be the first derivative of -1/4*v**4 + 1/5*v**5 - 3/2*v**2 - n + 0*v - 5/3*v**3. Solve g(x) = 0 for x.
-1, 0, 3
Let u = 210007/630012 - 1/210004. Find g such that -4/3 + 4/3*g - u*g**2 = 0.
2
Factor 0*p + 1/5*p**4 + 12/5*p**3 + 0 + 36/5*p**2.
p**2*(p + 6)**2/5
Let y be (404/(-707))/((-6)/203) - 19. Let y*w**4 + 0 + 5/3*w**2 + 2/3*w + 4/3*w**3 = 0. What is w?
-2, -1, 0
Determine z so that -1/5*z**2 - 256*z - 81920 = 0.
-640
Let x(k) be the second derivative of -91/4*k**5 + 90*k**2 + 80*k**3 - 15/14*k**7 + 125/12*k**4 + 0 + 80*k - 19/2*k**6. Determine p so that x(p) = 0.
-3, -2/3, 1
Let m(i) be the second derivative of -1/14*i**4 + 1/294*i**7 - 2*i + 57 + 1/35*i**6 + 0*i**2 - 1/140*i**5 + 0*i**3. Factor m(s).
s**2*(s - 1)*(s + 1)*(s + 6)/7
Let h(c) be the third derivative of -c**5/180 - 17*c**4/3 - 407*c**3/18 - 3*c**2 - 365. Factor h(w).
-(w + 1)*(w + 407)/3
Let k(y) be the third derivative of -2*y**7/105 + 51*y**5/5 + 162*y**4 + 1080*y**3 + 2144*y**2 + 2. Factor k(n).
-4*(n - 15)*(n + 3)*(n + 6)**2
Let a(w) = -2*w**3 - 60*w**2 - 177*w - 405. Let v be a(-27). Let 16/7*s + 20/7*s**3 - 32/7*s**2 + v - 4/7*s**4 = 0. Calculate s.
0, 1, 2
Suppose 75*y = 4*n + 76*y - 8, 2*n - y = -8. Let b be 35/28 - 1/2. Solve 1/4*u**4 + n + 3/4*u - b*u**3 - 1/4*u**2 = 0 for u.
-1, 0, 1, 3
Let p(s) be the third derivative of s**7/42 - 5*s**6/24 + s**5/2 + 1089*s**2. Factor p(m).
5*m**2*(m - 3)*(m - 2)
Let r(t) be the third derivative of 0*t + 1/6*t**5 + 0*t**3 - 4/21*t**7 - 172*t**2 - 5/84*t**8 + 5/24*t**4 - 1/8*t**6 + 0. Determine p, given that r(p) = 0.
-1, -1/2, 0, 1/2
Let v(h) = h**3 - 16*h**2 + 14*h + 17. Suppose q + 75 = 5*p, -p + 2*q + 15 = q. Let m be v(p). Factor -560*t - 4*t**3 + 16 - 3*t**2 - t**m + 576*t.
-4*(t - 2)*(t + 1)*(t + 2)
Let q(n) be the first derivative of 1/6*n**5 - 3/2*n**2 + 10/3*n**3 + 0*n - 3 + 1/24*n**6 - 35/24*n**4. Let a(b) be the second derivative of q(b). Factor a(l).
5*(l - 1)**2*(l + 4)
Let h = -86 + 70. Let f be 5/5 + h/(-2). Factor m**3 + 9*m**2 + 0*m**2 - 9*m + 8*m + f*m.
m*(m + 1)*(m + 8)
Let b(m) = -3*m - m + 108 - 18*m + 3*m + m. Let k be b(6). Factor k*i - 3/2*i**2 + 0 + 3/2*i**3.
3*i**2*(i - 1)/2
Let y be (-5 - (-44)/8)*17654. Factor -2*b**3 - 4*b**2 - 1617*b + y - 3339 + 25*b**2 + 441*b + 63*b**2.
-2*(b - 14)**3
Suppose 2*t - 28 = -2*g, 4*g - 3*t = -6*t + 57. Suppose -p - g = -20. Solve -10*k**5 + 205 + 212 + p*k**3 - 417 + 15*k**4 - 15*k**2 + 5*k = 0 for k.
-1, 0, 1/2, 1
Let a = 2661/2 - 15961/12. Let p(v) be the second derivative of -10/3*v**3 + 0 + a*v**4 + 6*v + 0*v**2. Factor p(n).
5*n*(n - 4)
Factor 0 - 64/5*o - 4/5*o**3 - 32/5*o**2.
-4*o*(o + 4)**2/5
Let 2/7*y**3 + 1124934/7*y - 162365474/7 - 2598/7*y**2 = 0. Calculate y.
433
Let q(l) be the third derivative of 1/6*l**6 + 0*l**3 + 0*l + 0 + 2/15*l**5 - 2/35*l**7 + 0*l**4 - 47*l**2. Factor q(i).
-4*i**2*(i - 2)*(3*i + 1)
Let u(x) be the second derivative of x**4/42 - x**3 + 110*x**2/7 - 1174*x. What is t in u(t) = 0?
10, 11
Let i = 1797 + -1784. Let g(s) = s**3 - 15*s**2 + 28*s - 26. Let j be g(i). Factor -6/5*c**3 - 2*c**2 + j + 4/5*c.
-2*c*(c + 2)*(3*c - 1)/5
Suppose 20*z = -52*z + 59*z. Factor -2/11*n**5 + 0 + z*n**2 + 0*n - 20/11*n**3 - 2*n**4.
-2*n**3*(n + 1)*(n + 10)/11
Let x(j) = j**3 + 4*j**2 + 248*j + 2242. Let b be x(-8). Factor 0*n - 2*n**b + 2/3*n**4 + 0 + 4/3*n**3.
2*n**2*(n - 1)*(n + 3)/3
Let n = -2573/126 - -1297/63. Factor -1/2*h - 1/2*h**2 - n - 1/6*h**3.
-(h + 1)**3/6
Let b be 1*(-8)/(-180)*5. Let n be 20/11 + ((-4)/(-66))/((-40)/(-120)). Factor b + 4/9*c**3 - 2/9*c**4 + 0*c**n - 4/9*c.
-2*(c - 1)**3*(c + 1)/9
Let s = 14 - 6. Let d = 3 - s. Let w(n) = -3*n**5 + 3*n**3 - 3*n**2. Let v(j) = 6*j**5 - j**4 - 5*j**3 + 5*j**2. Let l(k) = d*w(k) - 3*v(k). Factor l(f).
-3*f**4*(f - 1)
Let g(x) be the second derivative of -69/140*x**5 - 1/7*x**6 + 0*x**3 + 21 + 1/98*x**7 + 3*x + 0*x**2 - 3/7*x**4. Suppose g(b) = 0. Calculate b.
-1, 0, 12
Suppose 23 = -13*h - 55. Let o = -1 - h. Factor 0 + 5/2*g**4 - 4*g**3 + 2*g**2 - 1/2*g**o + 0*g.
-g**2*(g - 2)**2*(g - 1)/2
Find k such that 5/2*k**4 + 78 - 19*k**3 - 371/2*k**2 + 124*k = 0.
-6, -2/5, 1, 13
Let g(h) be the second derivative of -104*h**7/189 + 14*h**6/45 + 154*h**5/45 + 41*h**4/27 - 8*h**3/3 + 8*h**2/9 - 1113*h - 1. Suppose g(x) = 0. Calculate x.
-1, 2/13, 1/4, 2
Let h(v) be the first derivative of -36/25*v**5 - 147*v**2 + 1/15*v**6 + 43/5*v**4 + 12 - 1372/5*v + 112/15*v**3. Solve h(n) = 0 for n.
-2, -1, 7
Let t(s) be the third derivative of -6 - 1/112*s**8 - 13*s**2 - 2/35*s**7 + 0*s**3 - 1/10*s**5 + 0*s**4 + 0*s - 1/8*s**6. Factor t(q).
-3*q**2*(q + 1)**2*(q + 2)
L