f(k) be the first derivative of -1/5*k**2 + 4 + 2/5*k - 2/15*k**3 + 1/10*k**4. Let f(d) = 0. What is d?
-1, 1
Let n(t) be the third derivative of t**5/24 + 45*t**4/16 + 275*t**3/6 - 227*t**2. Factor n(o).
5*(o + 5)*(o + 22)/2
Let o(a) be the first derivative of -5*a**4/4 + 20*a**3/3 - 25*a**2/2 + 10*a + 69. Find s, given that o(s) = 0.
1, 2
Let j(i) = -4*i**3 - 6*i - 5. Let t(n) = 3*n**3 + n**2 + 5*n + 4. Let c(h) = 2*j(h) + 3*t(h). Let s(d) be the first derivative of c(d). Factor s(g).
3*(g + 1)**2
Let a be (-9)/((-720)/256) - 1/5. Let s(h) be the second derivative of -1/12*h**4 + 0 + 5*h - 2/3*h**a + 0*h**2. Factor s(w).
-w*(w + 4)
Let x = 8875 + -35499/4. Factor x + 1/4*p - 1/4*p**2 - 1/4*p**3.
-(p - 1)*(p + 1)**2/4
Let f(s) be the third derivative of -s**5/180 + 13*s**4/72 + 167*s**2. Factor f(j).
-j*(j - 13)/3
Let x be (10/3)/(21/(-252)*-24). Determine v so that 1/3 - x*v + 4/3*v**2 = 0.
1/4, 1
Let i(j) = -8*j**4 + 12*j**3 + 40*j**2 - 96*j + 36. Let q(c) = c**4 - c**2 + c + 3. Let z(p) = i(p) + 4*q(p). Factor z(u).
-4*(u - 4)*(u - 1)**2*(u + 3)
Let d(i) = -9*i**3 - 176*i**2 - 2128*i - 7840. Let s(w) = 8*w**3 + 177*w**2 + 2121*w + 7840. Let u(o) = -3*d(o) - 4*s(o). What is y in u(y) = 0?
-14, -8
Factor 8*h**5 + 7032*h**3 - 4*h**5 - 2270 + 3844 + 324*h**4 + 19192*h**2 + 5200*h + 4510 + 13364*h.
4*(h + 1)**3*(h + 39)**2
Let k(g) = 298*g - 2678. Let b be k(9). Factor 0 - 8/9*t**3 + 0*t**2 + 2/9*t**b + 0*t.
2*t**3*(t - 4)/9
Let w(m) be the second derivative of -m**6/55 - 3*m**5/22 - 3*m**4/22 + 9*m**3/11 + 45*m. Factor w(v).
-6*v*(v - 1)*(v + 3)**2/11
Let v(a) = 10*a**3 - 26*a**2 + 2*a + 44. Let x(q) = q**3 - q**2 - q + 2. Let i(n) = -v(n) + 6*x(n). Factor i(s).
-4*(s - 4)*(s - 2)*(s + 1)
Let x = -9017 + 9022. Factor -38/3*m**3 - 32/3*m - 2/3*m**x + 8/3 + 14/3*m**4 + 50/3*m**2.
-2*(m - 2)**2*(m - 1)**3/3
Let g(s) be the third derivative of s**8/1008 - s**7/315 - 13*s**6/360 - s**5/18 - 412*s**2. Suppose g(v) = 0. Calculate v.
-2, -1, 0, 5
Suppose 0 = 4*j + 2*h - 10, 1 = 2*h - 9. Let q(t) be the first derivative of 1/2*t**2 + 1/20*t**5 - 3/16*t**4 + j*t + 0*t**3 - 6. Find o such that q(o) = 0.
-1, 0, 2
Let j(z) be the first derivative of -z**5/10 + 2*z**4 - 71*z**3/6 + 14*z**2 + 72*z + 377. Factor j(c).
-(c - 9)*(c - 4)**2*(c + 1)/2
Let n(r) be the first derivative of r**4/26 + 10*r**3/39 + 8*r**2/13 + 8*r/13 + 166. Factor n(q).
2*(q + 1)*(q + 2)**2/13
Let f(y) = 8*y - 75. Let k be f(10). Suppose k*b = 3*g - 0*g - 60, -4*g + 54 = 2*b. Let -g - 95/3*n**2 - 55*n - 5*n**3 = 0. What is n?
-3, -1/3
Let n = 357 - -213. Let j be (-2)/(-19) + 282/n. Factor 3/5*g**2 - 3/5*g**3 + j*g**5 + 0 + 0*g - 3/5*g**4.
3*g**2*(g - 1)**2*(g + 1)/5
Let v(p) be the third derivative of 0 + 1/6*p**3 + 5/48*p**4 + 1/60*p**5 + 0*p + 13*p**2. Factor v(x).
(x + 2)*(2*x + 1)/2
Let k = 117 - 57. Let l be (-24)/240 - (-206)/k. Let 4/3*y - 2*y**2 + 0 - l*y**3 = 0. What is y?
-1, 0, 2/5
Suppose 50 - 80 = -15*j. Let p(y) be the third derivative of 2/315*y**7 - 2*y**j + 0*y**3 + 0*y**4 - 1/90*y**6 + 0*y + 0 - 2/45*y**5. Factor p(d).
4*d**2*(d - 2)*(d + 1)/3
Let j(b) be the second derivative of -b**6/120 + 61*b**5/80 - 899*b**4/48 - 961*b**3/24 + 345*b. Factor j(k).
-k*(k - 31)**2*(k + 1)/4
Let u(r) be the third derivative of 0*r**4 + 1/1620*r**6 - 1/6*r**3 + 1/270*r**5 - 2*r**2 + 0 + 0*r. Let l(d) be the first derivative of u(d). Factor l(h).
2*h*(h + 2)/9
Let o(z) = -z**3 - 5*z**2 + 7*z + 8. Let a be o(-6). Solve 18*i - a*i**2 + 0*i**2 - 3*i**2 + 12*i - 25 = 0.
1, 5
Suppose -h - 22 = 2*b + 89, -45 = b - 3*h. Let c be 15*(b/(-90))/(2/4). Find s, given that -27*s**5 - 6 + c*s + 153/2*s**4 + 9/2*s**2 - 66*s**3 = 0.
-1/2, 2/3, 1
Let s(l) = -12*l**2 + 2*l - 5. Let o = -41 + 57. Let m(r) = -36*r**2 + 6*r - 16. Let f(p) = o*s(p) - 5*m(p). Let f(g) = 0. Calculate g.
0, 1/6
Let r(o) = -2*o**4 + 4*o**3 + 8*o**2 - 6. Let m(s) = -s**2 + 29 - 12 - s**3 - 16. Let v(h) = 4*m(h) + r(h). Factor v(z).
-2*(z - 1)**2*(z + 1)**2
Find i such that -60*i**3 - 30*i**2 - 15*i**4 + 49*i**3 - 3 - 19*i**3 - 15*i - 3*i**5 = 0.
-1
Let m(a) = -2*a**2 + 6*a + 22. Let r be m(5). Suppose 97*i**3 + 15*i**4 - 92*i**3 - 58*i**2 - i**5 + 23*i**r - 4*i**5 + 20 = 0. What is i?
-1, 1, 2
Let x = -43 - -48. Suppose -4*r**4 + 3*r**4 + r**x - 2*r**4 + 2*r**5 = 0. What is r?
0, 1
Let r(w) be the third derivative of w**6/540 + w**5/135 - 7*w**4/108 + 4*w**3/27 + 84*w**2. Solve r(o) = 0.
-4, 1
Let b(r) = 6*r**3 + 94*r**2 + 104*r - 197. Let i(x) = 10*x**3 + 156*x**2 + 174*x - 328. Let k(g) = 12*b(g) - 7*i(g). Solve k(w) = 0 for w.
-17, -2, 1
Let u(s) = s**2 - 4*s - 1. Let c(l) = 1. Let d(x) = -12*c(x) - 3*u(x). Factor d(w).
-3*(w - 3)*(w - 1)
Let c(j) be the first derivative of -2/3*j + 2/9*j**3 - 3/2*j**2 + 3/4*j**4 + 19. Solve c(f) = 0 for f.
-1, -2/9, 1
Factor 47*o + 2990 + 33*o + 4*o**2 - 3166.
4*(o - 2)*(o + 22)
Let z = -2991 + 8974/3. Suppose -2/3*r + 0 + z*r**2 + 2/3*r**3 - 1/3*r**4 = 0. Calculate r.
-1, 0, 1, 2
Let p(m) be the third derivative of -11*m**7/70 - 9*m**6/40 + 23*m**5/10 + 9*m**4/2 - 4*m**3 + 5*m**2 + 13. Determine d, given that p(d) = 0.
-2, -1, 2/11, 2
Let o(a) be the first derivative of -1/22*a**4 + 0*a - 11 + 2/11*a**2 + 2/33*a**3. Determine g, given that o(g) = 0.
-1, 0, 2
Factor 92/9*w**3 + 1226/9*w**2 + 1288/3*w + 392 + 2/9*w**4.
2*(w + 2)**2*(w + 21)**2/9
Let x(r) = -r + 4. Let u be x(5). Let t be (0 - (-2 - -2))/u. Determine g so that -2*g**2 + 8 + g + t*g - 3*g - 4 = 0.
-2, 1
Let m(i) = 48*i**3 - 20*i**2 - 17*i + 1. Let x(t) = t**2 + t + 1. Suppose 16 - 8 = 2*r. Let n(w) = r*x(w) - m(w). Determine a, given that n(a) = 0.
-1/4, 1
Let l(o) be the first derivative of o**7/5880 - o**6/420 + o**5/105 - 44*o**3/3 - 13. Let n(a) be the third derivative of l(a). Suppose n(j) = 0. What is j?
0, 2, 4
Let t = 71 + -69. Suppose 4*k + 9 = t*q + 7, q - 1 = -2*k. Factor 0*a + k + 2/9*a**2 + 0*a**3 - 2/9*a**4.
-2*a**2*(a - 1)*(a + 1)/9
Let 1/2*a**2 - a + 0 = 0. What is a?
0, 2
Let g be (-13 + 20)*(1 + 4). Suppose -2*f + 2*w = 6, 2*f + 5*w - g = -3*f. Factor a**2 - 9*a**3 + a**4 + 2*a**4 + 5*a**f.
3*a**2*(a - 2)*(a - 1)
Let i be 115/9 + 4/18. Let k = i + -7. Factor -k*u**3 + 2*u**3 + 6*u**3 + 2*u**2.
2*u**2*(u + 1)
Let f(l) be the first derivative of -l**7/280 + l**6/48 + 3*l**5/80 + 29*l**3/3 + 30. Let q(v) be the third derivative of f(v). Factor q(j).
-3*j*(j - 3)*(2*j + 1)/2
Let p be (-7)/(-3) + (-2)/(-3). Suppose -f + 28 = 4*f + 2*n, -p*n = 5*f - 32. Factor 21*v**2 + f - 3 + 3 - 5 + v - 45*v**3.
-(3*v - 1)**2*(5*v + 1)
Let k(t) be the third derivative of -t**10/604800 - t**9/120960 - t**8/80640 - 23*t**5/60 - 5*t**2. Let h(c) be the third derivative of k(c). Factor h(g).
-g**2*(g + 1)**2/4
Suppose -224/11*s + 0 - 2/11*s**3 - 116/11*s**2 = 0. What is s?
-56, -2, 0
Let a be ((1 - -3)/20)/(2/(-66)). Let w = 261/35 + a. Factor -w*y**2 + 4/7*y + 2/7.
-2*(y - 1)*(3*y + 1)/7
Let q(p) be the first derivative of p**4/9 - 8*p**3/27 - 26*p**2/9 - 40*p/9 + 136. Suppose q(t) = 0. Calculate t.
-2, -1, 5
Let c(i) be the first derivative of 0*i**4 - 4/5*i - 5 + 8/15*i**3 - 4/25*i**5 + 0*i**2. Factor c(f).
-4*(f - 1)**2*(f + 1)**2/5
Let q(u) be the third derivative of u**7/105 - 7*u**6/60 + 11*u**5/30 - 5*u**4/12 - 4*u**2 - 6. Factor q(p).
2*p*(p - 5)*(p - 1)**2
Let s(i) be the second derivative of i**7/1050 + i**6/45 + 17*i**5/150 + 4*i**4/15 - 16*i**3/3 + i - 18. Let f(y) be the second derivative of s(y). Factor f(n).
4*(n + 1)**2*(n + 8)/5
Let q be -13*3/6 - 3/2. Let h be (q + 3 + 4)*2/(-11). Find s, given that 2/11*s**2 - 2/11*s - h*s**4 + 2/11*s**3 + 0 = 0.
-1, 0, 1
Let v be 1 + (2/(-6))/((-6)/54). What is a in -4 - 15*a**v + 5*a**4 + 8*a**2 + 6*a**4 = 0?
-1, 1
Factor 376*h**2 + 93*h - 16 + 817*h + 38*h**3 - 84.
2*(h + 5)**2*(19*h - 2)
Suppose 29 - 34 = -z. Suppose 6*s + 0*s = -z*s. Factor 0 - 9/4*a**2 + 3/4*a**3 + s*a.
3*a**2*(a - 3)/4
Let u = 23 + -20. Factor 6 + 34*c**u + c**4 - 4*c**2 - 4*c**4 + 8*c + c**4 - 42*c**3.
-2*(c - 1)*(c + 1)**2*(c + 3)
Let a(b) = -6*b - 2*b**2 + 3*b**2 - 1 - 1. Let i be a(7). Suppose 4*q**2 - 2*q**4 - 3*q**5 - 3*q**i + 0*q**4 - 2*q**4 + 6*q**3 = 0. What is q?
-1, -2/3, 0, 1
Let f = -1/3554 - -3559/17770. Factor -1/5*q**3 + 0*q**2 - 1/10 + f*q + 1/10*q**4.
(q - 1)**3*(q + 1)/10
Let o(b) b