)/4
Let n = -104087/77 - -14879/11. Factor -12*r + 144/7 + n*r**3 - 66/7*r**2.
6*(r - 12)*(r - 1)*(r + 2)/7
Let u be (2 + -2 + 5)/(4 + 0). Let y(i) = -i**2 + 31*i + 224. Let j be y(-6). Factor -2*x**j - 1/4*x**4 + 0 + x + u*x**3.
-x*(x - 2)**2*(x - 1)/4
Let s be 2/9 + (-44)/(-126). Let o = 1842/2737 - -72/391. Factor -2/7*v**2 - o*v - s.
-2*(v + 1)*(v + 2)/7
Let h be (-1276)/232*(-3)/693. Let x(a) be the second derivative of -1/12*a**4 - 5*a + 1/30*a**6 + 0*a**2 - h*a**7 + 0*a**3 + 1/20*a**5 + 0. Factor x(s).
-s**2*(s - 1)**2*(s + 1)
Let u(v) be the first derivative of -45*v**4/14 - 358*v**3/21 - 176*v**2/7 + 8*v/7 + 2443. Determine m, given that u(m) = 0.
-2, 1/45
Let j(k) be the third derivative of -k**6/1020 + k**5/85 + 37*k**4/204 - 30*k**3/17 + 2906*k**2. Suppose j(t) = 0. What is t?
-5, 2, 9
Let s(m) be the first derivative of 40 - 2/15*m**2 + 2/9*m**3 + 0*m. Factor s(h).
2*h*(5*h - 2)/15
Let g(h) be the second derivative of -h**6/105 + 291*h**5/70 - 3504*h**4/7 - 21316*h**3/21 - 175*h + 1. Factor g(l).
-2*l*(l - 146)**2*(l + 1)/7
Let w be (-42)/1 - (-31464)/736. Let 5/2*m**2 - w*m**3 - m - 2 = 0. Calculate m.
-2/3, 2
Let g(a) = -5*a**2 + 5*a - 4. Let s(x) = 11*x**2 - 12*x + 9. Let p = -188 + 192. Let f(i) = p*s(i) + 9*g(i). Find z such that f(z) = 0.
-3, 0
Let f be -26 - (14 - 10 - 10). Let h(u) = -2*u - 40. Let p be h(f). Factor -2/11*w**5 - 4/11*w**4 + p + 0*w**2 + 0*w + 0*w**3.
-2*w**4*(w + 2)/11
Let k = 4/2655 + 71677/5310. Suppose 3/8*t**2 + 9/2*t + k = 0. What is t?
-6
Let o = -1237426 - -1237426. Suppose 1/2*v**4 + 33*v**3 + o*v + 1089/2*v**2 + 0 = 0. Calculate v.
-33, 0
Let m = -24507/170 - -2466/17. Let z(c) be the first derivative of -14/25*c**5 + m*c**4 - 15 + 0*c + 0*c**2 - 4/15*c**3. Find r such that z(r) = 0.
0, 2/7, 1
Suppose -14*h - 18*h - 15*h = -43*h. Let n(s) be the first derivative of 0*s + h*s**3 + 0*s**2 + 3/4*s**4 + 16 + 3/5*s**5. Factor n(i).
3*i**3*(i + 1)
Let d(k) be the first derivative of k**6/960 + 3*k**5/20 + 9*k**4 - k**3/3 - k - 69. Let f(x) be the third derivative of d(x). Let f(t) = 0. Calculate t.
-24
Let i(t) = 2*t**5 + 5*t**4 + t**2 + t - 3. Let q(p) = -p**5 - p**4 - p**2 + 1. Let d be (1/(4 + 9/(-2)))/(-2). Let w(o) = d*i(o) + 3*q(o). Factor w(k).
-k*(k - 1)**3*(k + 1)
Let u(d) be the first derivative of 0*d + 1/210*d**5 - 10 + 5*d**2 - 1/84*d**4 - 2/7*d**3. Let f(w) be the second derivative of u(w). Factor f(v).
2*(v - 3)*(v + 2)/7
Determine z, given that 44/3*z - 434/15*z**2 - 4/15*z**3 + 218/15 = 0.
-109, -1/2, 1
Let l(n) be the second derivative of -n**6/120 + 17*n**5/16 - 403*n**4/48 + 77*n**3/8 + 90*n**2 - 2349*n. Factor l(z).
-(z - 80)*(z - 3)**2*(z + 1)/4
Let u(g) be the first derivative of -21*g**5/5 - 183*g**4/4 + 88*g**3 - 30*g**2 + 886. Let u(v) = 0. What is v?
-10, 0, 2/7, 1
Let j = 332228/45 - 36912/5. Factor 0 + 1/9*r**4 + 2/9*r + 5/9*r**2 + j*r**3.
r*(r + 1)**2*(r + 2)/9
Let l(s) be the first derivative of s**7/252 - s**6/60 - s**5/24 + s**4/24 + s**3/9 - 17*s + 64. Let t(w) be the first derivative of l(w). Factor t(f).
f*(f - 4)*(f - 1)*(f + 1)**2/6
Suppose 56/5*t + 116/5*t**2 - 12/5*t**4 - 32/5 + 16/5*t**3 = 0. Calculate t.
-2, -1, 1/3, 4
Let p(d) be the first derivative of -d**6/540 - d**5/36 + d**4/6 + d**3 - 3*d**2/2 - 33. Let w(u) be the third derivative of p(u). What is m in w(m) = 0?
-6, 1
Let 2048/11*z + 4088/11 + 2/11*z**2 = 0. Calculate z.
-1022, -2
Let m(u) = 40*u**3 + 171*u**2 - 301*u + 160. Let j(k) = 11*k**3 + 57*k**2 - 101*k + 53. Let i(x) = -7*j(x) + 2*m(x). Factor i(q).
3*(q - 17)*(q - 1)**2
Determine z so that 9582*z**3 + 19*z**4 - 104*z**2 - 2*z**5 - 9580*z**3 + 85*z**4 = 0.
-1, 0, 1, 52
Factor 2*b**3 - 108 - 9*b**3 + 60*b - b**4 + 17*b**2 - 5*b**3 + 4*b**3.
-(b - 2)**2*(b + 3)*(b + 9)
Let m = -1593 + 3785. Let f = m + -4383/2. Solve 0 + f*g**2 + 5/2*g = 0 for g.
-5, 0
Let x(o) be the first derivative of o**5/35 + o**4/7 - 62*o**3/21 - 66*o**2/7 + 27*o + 6598. Suppose x(b) = 0. What is b?
-9, -3, 1, 7
Factor 20*a**3 + 18445*a + 4835*a + 6426*a**2 + 2*a**4 + 196*a**3 - 4185*a + 12117*a.
2*a*(a + 6)*(a + 51)**2
Factor 25955750/3*b**3 - 331350*b**2 + 4230*b - 18.
2*(235*b - 3)**3/3
Let z(d) = -2*d**2 - 2506*d - 788744. Let c(w) = -2*w**2 - 2505*w - 788740. Let f(y) = -6*c(y) + 7*z(y). Determine s so that f(s) = 0.
-628
Suppose 21*g + 1/3*g**3 - 19/3*g**2 - 15 = 0. Calculate g.
1, 3, 15
Solve -193844*o**2 + 8 - 111918*o**2 + 9362*o - 42338*o**2 - 72 + 78*o = 0.
4/295
Let w(t) = -t - 13. Let a be w(-15). Let y = 28 - 18. Factor 8*c**3 + 0*c**5 - c**5 - y*c**a - 28*c**3 + 6*c**5 + 15*c + 10*c**4.
5*c*(c - 1)**2*(c + 1)*(c + 3)
Let v(i) = -859*i - 169218. Let p be v(-197). Let 2 + 10/3*x - 4*x**3 + 2/3*x**p - 4/3*x**2 - 2/3*x**4 = 0. What is x?
-1, 1, 3
Let u(t) be the first derivative of -2/15*t**3 + 27 + 1/4*t**2 - 1/5*t + 1/40*t**4. Factor u(d).
(d - 2)*(d - 1)**2/10
Let 1073*q**4 + 142*q**2 + 87*q + 54 - 349*q**2 - 1064*q**4 + 57*q**3 = 0. What is q?
-9, -1/3, 1, 2
Let x(t) be the third derivative of t**8/273 + 418*t**7/1365 - 1189*t**6/780 + 1147*t**5/390 - 439*t**4/156 + 55*t**3/39 + 2373*t**2. What is s in x(s) = 0?
-55, 1/4, 1/2, 1
Determine p, given that -238*p + 485*p + 35*p**2 + 38*p**3 + 176 - 167*p**2 + 160*p**4 - 239*p - 158*p**4 = 0.
-22, -1, 2
Suppose -111*p - 4 = -4. Let z(w) be the third derivative of 4/15*w**5 + 0*w**4 - 1/30*w**6 + 0*w**3 - 7*w**2 + p + 0*w. Find m such that z(m) = 0.
0, 4
What is c in -186*c + 60543 + 1/7*c**2 = 0?
651
Let d(a) be the first derivative of 100/21*a**2 - 2/63*a**3 - 5000/21*a + 105. Factor d(j).
-2*(j - 50)**2/21
Let m(n) be the first derivative of n**4/6 + 3*n**3 - 10*n**2 + 157*n + 15. Let a(w) be the first derivative of m(w). Suppose a(o) = 0. What is o?
-10, 1
Factor -282*y - 3*y**3 + 285*y**2 + 39605592 - 39605592.
-3*y*(y - 94)*(y - 1)
Let k = 35948 + -1078439/30. Let f(a) be the second derivative of -26*a + 9/5*a**2 + 0 - 8/15*a**3 - k*a**4. Factor f(y).
-2*(y - 1)*(y + 9)/5
Let t(a) be the third derivative of 3*a**2 + 17*a + 0 + 1/140*a**5 - 3/56*a**4 + 0*a**3. Determine r, given that t(r) = 0.
0, 3
What is u in -2/9*u**2 + 14/9*u - 4/3 = 0?
1, 6
Suppose 2*k + 12 = 72. Let r = k + -27. Suppose 135 + 2*q**2 - 64 + 2*q**r - 71 = 0. What is q?
-1, 0
Let t be (90/(-300))/((-6)/(-176)). Let u = t + 182/15. Factor u*o - 5 + 5/3*o**2.
5*(o - 1)*(o + 3)/3
Let t be 2*(-2)/(-8)*(-24 - 22). Let r = t - -23. Factor 0 + 3/4*q**4 + 0*q + r*q**2 + 3/2*q**3.
3*q**3*(q + 2)/4
Let m = -172 - -689/4. Let u(i) = 90*i - 268. Let w be u(3). Factor -3/4*h + 0 + m*h**w.
h*(h - 3)/4
Factor -82/3*j - 2/3*j**2 - 192.
-2*(j + 9)*(j + 32)/3
Let 15 + 95/4*w**2 + 5/4*w**4 - 315/4*w**3 + 110*w + 35/4*w**5 = 0. What is w?
-3, -1, -1/7, 2
Determine c, given that 11*c**2 - 13*c**2 - 2983*c + 1183*c - 405000 = 0.
-450
Suppose -4*i - 12 = -4*m, -m - 2*i + 125 = 131. Let o(y) be the second derivative of 1/12*y**4 - 5/2*y**2 - 2/3*y**3 + m + 35*y. Find h, given that o(h) = 0.
-1, 5
Let m(x) be the second derivative of x**5/50 + 7*x**4/15 - 416*x**3/15 + 384*x**2 + 1099*x. Factor m(h).
2*(h - 8)**2*(h + 30)/5
Let d(p) be the first derivative of -18 - 100/3*p**3 + 0*p - 105/2*p**2 + 5/4*p**4. Factor d(z).
5*z*(z - 21)*(z + 1)
Suppose 0 - 2/3*u**2 + 102*u = 0. What is u?
0, 153
Let x(t) be the second derivative of -t**6/45 - t**5/10 + 67*t**4/18 - 71*t**3/3 + 66*t**2 - 16*t + 16. Solve x(m) = 0 for m.
-11, 2, 3
Let w be (-11)/(22/(-28)) + (-39)/(156/40). Let 12*u**w + 8*u**2 + 220/7*u**3 - 32/7 - 16*u = 0. Calculate u.
-2, -1, -2/7, 2/3
Let z = 2460/19 - 18771/38. Let x = z + 372. Factor 3/4 + 9/4*v**4 + 9*v**2 + x*v**3 + 9/2*v.
3*(v + 1)**3*(3*v + 1)/4
Let v(b) be the second derivative of 5 - 1/40*b**6 - 3/8*b**2 + 0*b**5 + 0*b**3 + 1/8*b**4 + b. Solve v(i) = 0.
-1, 1
Suppose -10*b + 34 = 4. Factor 46*d - 3*d**3 + 30*d - d**b - 16*d**2 - 36 - 20.
-4*(d - 2)*(d - 1)*(d + 7)
Let -3/5*y**3 - 3/5*y**2 - 168/5 + 102/5*y = 0. What is y?
-7, 2, 4
Let d(o) be the third derivative of -o**7/1050 + 287*o**6/150 - 36672*o**5/25 + 7077314*o**4/15 - 55742968*o**3/15 + 3949*o**2 + o. Solve d(z) = 0 for z.
2, 382
Let m be (-626)/(-80) - 96/(-120). Let i(h) be the first derivative of 9/2*h - m*h**2 + 7/4*h**3 - 2. Find u such that i(u) = 0.
2/7, 3
Let i(v) be the 