e second derivative of 1/2*o**2 + 13/36*o**3 - 47*o + 1/120*o**5 + t*o**4 + 0. Factor x(r).
(r + 1)**2*(r + 6)/6
Let w(s) be the first derivative of -36*s**5/5 - 38*s**4 + 148*s**3/3 + 20*s**2 - 1371. Determine g so that w(g) = 0.
-5, -2/9, 0, 1
Let d = 599 - 1068. Let a = 472 + d. Find u such that -1024/7 - 48/7*u**2 - 384/7*u - 2/7*u**a = 0.
-8
Let c be (387*15/(-405) - -13)/(4/(-6)). Factor -3*p + 0 - 1/2*p**3 - 11/4*p**c.
-p*(p + 4)*(2*p + 3)/4
Let n(d) = -d**2 - 4*d + 60. Suppose -20*h + 182 = 62. Let l be n(h). What is u in -9/8*u**3 + 0*u**2 + l - 3/8*u**4 + 3/2*u = 0?
-2, 0, 1
Let d(n) be the third derivative of 3*n**2 - 1/140*n**5 + 1/280*n**6 + 1/490*n**7 + 12 - 1/56*n**4 + 0*n**3 + 0*n. Factor d(w).
3*w*(w - 1)*(w + 1)**2/7
Let q(m) be the first derivative of -m**5/35 - 7*m**4/2 - 2761*m**3/21 - 1260*m**2 - 32400*m/7 - 3363. Let q(o) = 0. Calculate o.
-45, -4
Let d(n) be the first derivative of n**6/3 + 1326*n**5/5 + 146523*n**4/2 + 21587722*n**3/3 - 1147. Let d(h) = 0. What is h?
-221, 0
Let j be ((-14)/(-10))/(-7) - 38/10. Let r be 11 + 2*-3*2/j. Factor -36*s**2 - 9*s + 38*s**2 - r - 3*s.
2*(s - 7)*(s + 1)
Let u = 7213 + -7213. Let i(q) be the third derivative of u - 18/7*q**3 - 1/140*q**5 + 25*q**2 + 0*q - 3/14*q**4. Factor i(a).
-3*(a + 6)**2/7
Suppose 239*p - 1396 = -440. Let h(n) be the first derivative of -p*n + 28/3*n**3 + 4*n**4 + 14 + 4*n**2. Suppose h(t) = 0. Calculate t.
-1, 1/4
Let c(n) = n**2 - 4*n. Let t(s) = 3*s**2 + 1100*s + 2176. Let q(x) = -c(x) - t(x). Solve q(h) = 0.
-272, -2
Let x be (18/(-225))/((-540)/125 - -4). Determine o so that -1/2*o**2 + x*o**5 - 1/4*o + 0*o**3 + 1/2*o**4 + 0 = 0.
-1, 0, 1
Factor 4312803/5 + 7194/5*j + 3/5*j**2.
3*(j + 1199)**2/5
Let g(q) be the second derivative of 2*q**7/21 - 8*q**6/15 - 8*q**5/5 + 32*q**4/3 + 32*q**3/3 - 128*q**2 + 774*q. What is z in g(z) = 0?
-2, 2, 4
Suppose 4*g + 231 = 3*k + 115, k = 5*g + 13. Let -k*c**4 + 168/5*c - 118/5*c**3 - 10*c**5 + 32/5 + 208/5*c**2 = 0. What is c?
-4, -1, -2/5, 1
Let c = 1488/2717 + -23/247. Let t(v) be the second derivative of -c*v**2 + 0 + 1/66*v**4 + 24*v + 4/33*v**3. Find n such that t(n) = 0.
-5, 1
Let y(b) be the first derivative of 40*b**2 + 84*b - 4/3*b**3 + 232. What is q in y(q) = 0?
-1, 21
Let r = -7890 - -7892. Factor -10 + 15/2*s**r + 0*s - 5/2*s**3.
-5*(s - 2)**2*(s + 1)/2
Find w such that 424*w**2 + 387*w**2 + 420 + 309*w**3 + 698*w + 3*w**5 + 14*w**2 - 115*w + 51*w**4 + 401*w = 0.
-7, -5, -2, -1
Factor -4/15*x**2 - 2/15*x**3 - 4/3 + 26/15*x.
-2*(x - 2)*(x - 1)*(x + 5)/15
Let r(k) = -35*k + 41*k + 48 - 9. Let q be r(-6). Factor -27*p**2 + 0*p**4 - q*p**4 + 18*p**3 + 0*p**2.
-3*p**2*(p - 3)**2
Factor 23/4*n**2 - 4*n**3 + 1/4*n**4 + 75 + 85*n.
(n - 10)**2*(n + 1)*(n + 3)/4
Factor -790/9*f - 88 + 2/9*f**2.
2*(f - 396)*(f + 1)/9
Let d(j) be the first derivative of j**3/6 - 507*j**2 + 514098*j + 3059. Determine q, given that d(q) = 0.
1014
Suppose -5*u + 48 - 2 = 2*b, -5*b = u - 92. Suppose 0 = 3*l - 36 - b. Factor 3*p**4 + l*p - p**3 - 6*p + 7*p**2 + 20*p**2 + 19*p**3.
3*p*(p + 1)**2*(p + 4)
Solve -2/5*d**5 + 1024*d - 896/5*d**2 - 14*d**4 - 684/5*d**3 + 0 = 0.
-16, -5, 0, 2
Solve 44*t**2 - 76 - 18*t**3 - 88*t + 43 + 22*t**3 + 148*t - 75 = 0.
-9, -3, 1
Let w(o) = 0 - 3 + 59*o - 54*o. Let m be w(4). Factor 21*a**4 - 16*a**3 + m*a**4 - 8*a**2 - 28*a**4.
2*a**2*(a - 2)*(5*a + 2)
Let p = 436 + -288. Suppose 7*k + 30*k - p = 0. Factor -2/9*j**3 + 2/9*j**k - 2/9*j**2 + 0 + 2/9*j.
2*j*(j - 1)**2*(j + 1)/9
Suppose -164 = -4*g - 5*c, 14 - 178 = -4*g - 2*c. Let u = 43 - g. Find a, given that -a**4 + 3*a**4 - 2*a**4 - 2*a**4 + 2*a**u = 0.
-1, 0, 1
Factor 6/5*v**3 + 0 + 0*v + 2/5*v**4 - 36/5*v**2.
2*v**2*(v - 3)*(v + 6)/5
Let k = 44 + -39. Factor 121*o**2 + 2*o - k*o + 2*o - 122*o**2.
-o*(o + 1)
Let f be -16*(-8 - 99/(-12)) + 44/5. Solve -2/5*i**3 + f + 6/5*i**2 + 32/5*i = 0.
-2, -1, 6
Let z be ((-150)/12 - -7)*9/(-91 - 8). What is k in 5 + 9/2*k - z*k**2 = 0?
-1, 10
Let t(n) be the second derivative of 3*n**5/140 - 5*n**4/14 - 37*n**3/14 - 39*n**2/7 + 1189*n. Factor t(i).
3*(i - 13)*(i + 1)*(i + 2)/7
Suppose 441*z - 2 = 2*f + 442*z, z + 2 = 0. Let t(x) be the first derivative of f*x + 0*x**3 + 0*x**2 - 5/4*x**4 - x**5 - 3. What is s in t(s) = 0?
-1, 0
Let j(f) be the third derivative of f**6/210 + f**5/7 - 72*f**4/7 + 3968*f**3/21 - 125*f**2 - 1. Factor j(l).
4*(l - 8)**2*(l + 31)/7
Suppose 0 = -4*g + 7*d - 21, 9*g - 15 = 8*g - 5*d. Factor 0 + g*h + 4/7*h**2 - 2/7*h**3.
-2*h**2*(h - 2)/7
Find k such that -k**3 + 21*k - 149*k - 64 + 80*k + 15*k**2 = 0.
-1, 8
Determine w, given that -105*w**2 - 8*w**3 + 648*w + 459*w**2 - 2510262 + 2510078 = 0.
-2, 1/4, 46
Let p(j) be the second derivative of j**7/630 - j**5/30 - 43*j**4/12 + 3*j + 3. Let d(g) be the third derivative of p(g). Suppose d(h) = 0. What is h?
-1, 1
Suppose -14479407*f + 6156*f**2 + 1847295*f + 1467*f**3 + 8640364608 - 1468*f**3 = 0. Calculate f.
2052
Factor -10/7*p + 2/7*p**2 - 24.
2*(p - 12)*(p + 7)/7
Suppose -49 = 7*i + 273. Let w = i + 46. What is s in w*s**2 + 14*s**4 + 2*s**2 - 32*s**4 - 1 + 17*s**4 = 0?
-1, 1
Let r = 215921 - 215919. Suppose -1/4*k**3 - 7/4 + 1/4*k + 7/4*k**r = 0. Calculate k.
-1, 1, 7
Let t(l) = 82*l**2 - 2*l + 2. Let f be t(1). Let y = f + -74. Factor 14 + 0 - 8*w - 2*w**2 + 4 - y*w.
-2*(w - 1)*(w + 9)
Suppose -b + 377 = -1840. Suppose b = 4*p - 999. Solve -343*j**5 - 23*j**2 - 72 - 1636*j**2 - 1499*j**2 - 4935*j**3 - 2352*j**4 - p*j = 0 for j.
-3, -2/7
Suppose -81*j + 3 = -79*j - 5. Let m(l) be the third derivative of -1/8*l**j + 1/60*l**5 + 2*l**2 + 0 + 1/3*l**3 + 0*l. Factor m(c).
(c - 2)*(c - 1)
Let p be (-4)/18*-3*45*26/351. Factor 2/9*r**2 - p*r - 16/3.
2*(r - 12)*(r + 2)/9
Let v(c) = 35*c**3 - 90*c**2 + 15*c + 5. Let a(j) = -18*j**3 + 45*j**2 - 8*j - 2. Let o(k) = 22*k - 17. Let t be o(1). Let n(m) = t*a(m) + 2*v(m). Factor n(d).
-5*d*(d - 2)*(4*d - 1)
Factor 44 + 89/4*s + 1/8*s**2.
(s + 2)*(s + 176)/8
Let a(x) be the third derivative of -4*x + x**2 - 2/3*x**3 + 0 + 3/4*x**4 - 7/30*x**5. Factor a(k).
-2*(k - 1)*(7*k - 2)
Let f(u) be the second derivative of -u**4/48 - 55*u**3/24 - 3*u - 210. Factor f(q).
-q*(q + 55)/4
Let d(a) be the second derivative of 132*a - 1/20*a**5 + 4*a**2 + 7/4*a**4 + 0 - 13/3*a**3 - 1/15*a**6. Solve d(h) = 0.
-4, 1/2, 1, 2
Let h = 180791 + -1265513/7. Factor -h - 36/7*g - 3/7*g**3 - 18/7*g**2.
-3*(g + 2)**3/7
Let x = -618834 + 1856504/3. What is t in -16/3 - x*t**3 + 10/3*t**2 - 4/3*t = 0?
-1, 2, 4
Let w = -231 + 248. Suppose -11*i - 24 = -w*i. What is l in -2*l + i + 1/4*l**2 = 0?
4
Let b be ((-6802)/1253 + (-994)/(-84) + 2/12)/1. Find t, given that 46/7*t**3 + 528/7*t**2 - b*t + 1/7*t**4 - 529/7 = 0.
-23, -1, 1
Suppose 311 = -5*m + 336. Determine g, given that 2*g**4 - 6*g**3 - g**4 + 11*g**3 - 5*g + m*g = 0.
-5, 0
Let z(n) be the third derivative of -7/300*n**6 + 0*n + 0 - 2/5*n**3 - 17/60*n**4 - 1/525*n**7 + 25*n**2 - 17/150*n**5. What is i in z(i) = 0?
-3, -2, -1
Let i be 1200/650*(2/13 - (-327)/156). Determine t, given that -8/13 - i*t**5 + 30/13*t**4 - 198/13*t**2 + 72/13*t + 158/13*t**3 = 0.
-2, 2/9, 1/3, 1
Let d be (15/2 - 0)*(11776/(-360))/(-368). Determine a so that -10952/3 - 296/3*a - d*a**2 = 0.
-74
Let n(x) be the first derivative of x**6/10 + 3*x**5/20 - x**4 - 2*x**3 - 225*x - 166. Let b(p) be the first derivative of n(p). Let b(m) = 0. What is m?
-2, -1, 0, 2
Let c be 1*(-2 + 0) + 4. Suppose 5*l - 3*n + 93 = 93, -20 = -4*n. Factor 7/9*f**4 - 16/9*f**l - 16/9 + 16/9*f + 8/9*f**c - 1/9*f**5.
-(f - 2)**4*(f + 1)/9
Let b(m) be the third derivative of -1/15*m**5 - 5/3*m**4 - 16/3*m**3 + 35*m**2 + 0*m + 1/30*m**6 + 0. Solve b(y) = 0 for y.
-2, -1, 4
Let y(m) be the second derivative of -m**4/78 - 23*m**3/39 - 102*m**2/13 - 122*m - 6. Factor y(l).
-2*(l + 6)*(l + 17)/13
Let t(n) be the third derivative of 6*n**2 + 1/2*n**3 + 1/315*n**5 + 1/3780*n**6 + 0 + 1/84*n**4 + 0*n. Let u(s) be the first derivative of t(s). Factor u(g).
2*(g + 1)*(g + 3)/21
Let a be 184/14 - (26 + -14). Let q be ((-12)/15)/(6/(-15)). Determine n, given that -8/7 + 12/7*n**q - 12/7*n + a*n**3 = 0.
-2, -1/2, 1
Let v(f) be the third derivative of -f**5/210 - 19*f**4/84 + 40*f**3/7 + 1093*f**2. Factor v(a).
-2*(a - 5)*(a + 24)/7
Let z(l