= 0. What is n?
1, 8
Let r(d) be the first derivative of 11*d**3/3 - d**2 + 11*d - 1. Let g(n) = -9*n**2 + 3*n - 10. Let t(m) = -5*g(m) - 4*r(m). Factor t(k).
(k - 6)*(k - 1)
Let m = -1/4624 + 73987/13872. Let x(v) be the first derivative of 13 + 4/3*v**2 - 1/6*v**4 - m*v + 4/9*v**3. Factor x(w).
-2*(w - 2)**2*(w + 2)/3
Let f = -1/339865 - -8156767/2379055. Suppose -20/7 - f*l - 4/7*l**2 = 0. Calculate l.
-5, -1
Let t(a) be the third derivative of -1/2*a**5 + 0*a + 2/21*a**7 + 0*a**4 - a**2 + 5/336*a**8 - 3 + 1/24*a**6 + 0*a**3. Factor t(j).
5*j**2*(j - 1)*(j + 2)*(j + 3)
Let t(j) = -95*j - 90. Suppose -25*m = -111*m - 86. Let l be t(m). Factor -18/5*h**4 - 32/5 + 96/5*h - 112/5*h**2 + 2/5*h**l + 64/5*h**3.
2*(h - 2)**4*(h - 1)/5
Let 187*u**3 - 50*u**2 + 136*u**3 - 378*u**3 - 5*u**4 = 0. Calculate u.
-10, -1, 0
Let u(p) be the first derivative of 2/45*p**5 - 239 - 28/9*p**2 + 130/9*p**3 - 392/9*p + 14/9*p**4. Determine f, given that u(f) = 0.
-14, -1, 1
Let 84*w**2 - 2/3*w**5 + 106/3*w**3 - 4*w**4 - 80 - 104/3*w = 0. Calculate w.
-10, -2, -1, 1, 6
Let r(f) be the third derivative of f**5/60 + 119*f**4/6 + 28322*f**3/3 - 9*f**2 - 143*f + 1. Factor r(c).
(c + 238)**2
Suppose -12*y = -15*y + 18. Factor -3*w**2 - 24*w + 634 - 613 + y*w**2.
3*(w - 7)*(w - 1)
Let h(n) be the second derivative of n**6/150 - 348*n**5/25 + 60552*n**4/5 - 28096128*n**3/5 + 7333089408*n**2/5 - 696*n. Factor h(t).
(t - 348)**4/5
Let j(r) = -9*r**2 - 132*r - 1581. Let v(m) = -33*m + 17*m + 17*m + 1 - m**2 + 0. Let b(c) = j(c) - 6*v(c). Factor b(t).
-3*(t + 23)**2
Let x = -3500 + 3500. Let j(d) be the first derivative of 2/35*d**5 + 0*d + x*d**4 + 0*d**3 - 15 + 0*d**2. Find u, given that j(u) = 0.
0
Let x(v) = -38*v**2 + 224*v - 336. Let j(f) = f**3 + 75*f**2 - 448*f + 648. Let n(d) = 2*j(d) + 5*x(d). Factor n(w).
2*(w - 12)*(w - 4)**2
Let z(m) be the third derivative of m**7/1260 - 119*m**6/720 + 1739*m**5/180 + 80*m**4/3 - 200*m**3 + 2*m**2 - 109*m. Factor z(y).
(y - 60)**2*(y - 1)*(y + 2)/6
Let i(c) be the third derivative of 1/40*c**5 + 0*c + 0 + 11/16*c**4 - 11/80*c**6 - 1/140*c**7 - 37*c**2 + 0*c**3. What is u in i(u) = 0?
-11, -1, 0, 1
Let c(q) = -12*q**2 - 46*q + 28. Let l(h) = h**2 + 2*h. Let a = 161 + -151. Let p(g) = a*l(g) + c(g). Factor p(s).
-2*(s - 1)*(s + 14)
Let j(l) be the first derivative of 5*l**6/6 + 11*l**5/5 - 29*l**4/2 + 58*l**3/3 - 11*l**2/2 - 5*l + 2729. Let j(f) = 0. Calculate f.
-5, -1/5, 1
Let f = 87 - 62. Let s = f - 23. Find j such that 4*j**3 - 6*j**3 + 4*j**3 - 2*j + j**s - j**4 + 0*j**4 = 0.
-1, 0, 1, 2
Let a(u) = 35*u**3 + 145*u**2 + 40*u - 310. Let c(o) = o**3 + 3*o**2 - o + 3. Let w(s) = -a(s) + 30*c(s). Factor w(p).
-5*(p - 2)*(p + 5)*(p + 8)
Let q(t) be the second derivative of -t**7/21 - 2*t**6/5 - 13*t**5/10 - 2*t**4 - 4*t**3/3 + 13057*t. Factor q(i).
-2*i*(i + 1)**2*(i + 2)**2
Determine b so that 3/5*b**2 - 18/5 + 3/5*b = 0.
-3, 2
Factor 0*y + 0 - 5/4*y**4 + 1545/2*y**2 - 3085/4*y**3.
-5*y**2*(y - 1)*(y + 618)/4
Let x(c) be the third derivative of 5*c**8/336 + c**7/14 - 5*c**6/3 + 5942*c**2. Factor x(k).
5*k**3*(k - 5)*(k + 8)
Factor -8284*q**3 + 8248*q**3 - 2*q**4 + 9248*q - 3 + 3 + 510*q**2.
-2*q*(q - 16)*(q + 17)**2
Solve q**4 - 114*q - 33*q + 49*q**2 + 16*q - 162 - 10*q + 29*q**3 = 0 for q.
-27, -3, -1, 2
Suppose -4*b + 3*z + 77 = -2*z, 3*b + 2*z - 29 = 0. Factor -g**2 - 11*g + 24*g + 7 - b*g - 6*g.
-(g - 1)*(g + 7)
Let f(j) be the first derivative of j**5/15 - 11*j**4/6 - 51*j**2 - 40. Let g(p) be the second derivative of f(p). Factor g(q).
4*q*(q - 11)
Let v(a) = -a**3 + 12*a**2 - 11*a + 31. Let y be v(11). Let r = -29 + y. Find j, given that 4*j**2 - 9*j**2 + 3*j**r + 6*j**2 = 0.
0
Let h(r) be the second derivative of -r**7/2016 - r**6/960 + r**5/60 - 83*r**4/12 - 14*r + 3. Let s(x) be the third derivative of h(x). Solve s(d) = 0 for d.
-8/5, 1
Find u, given that -74/7*u + 72/7 + 2*u**2 = 0.
9/7, 4
Let s be (51/15 - (15/(-25) + 1)) + (-58 - -57). Factor 2/9*k + 2/9*k**3 + 4/3 - 8/9*k**s.
2*(k - 3)*(k - 2)*(k + 1)/9
Let -1/2*d**5 + 0*d - 184*d**2 - 100*d**3 + 0 - 31/2*d**4 = 0. What is d?
-23, -4, 0
Let l = 54267 + -54263. Determine a, given that -14/9*a**3 + 10/3*a**2 - 26/9*a + 8/9 + 2/9*a**l = 0.
1, 4
Let h be (-216)/(-144)*(-32)/(-24). Factor 0 + 8/3*t + 4/3*t**3 - 6*t**h.
2*t*(t - 4)*(2*t - 1)/3
Let g = 10634737/2578120 + 1/322265. Solve g*y + 21/8*y**2 + 15/8 + 3/8*y**3 = 0 for y.
-5, -1
Let w(f) be the second derivative of 1/10*f**5 - 171*f - 1/3*f**3 - 1/3*f**4 + 1/10*f**6 + 1/2*f**2 + 1. Find m, given that w(m) = 0.
-1, 1/3, 1
Let v(z) be the first derivative of -4*z**3 - 210 + 0*z - 15/2*z**2 + 3/4*z**4. Factor v(h).
3*h*(h - 5)*(h + 1)
Let x(f) be the first derivative of f**4/24 - f**3/3 + f**2 - 69*f - 25. Let t(d) be the first derivative of x(d). What is s in t(s) = 0?
2
Let v(y) = 7*y - 30. Let f be v(5). Suppose -f*b + b = -k - 62, -5*k = 3*b - 35. Solve 19*u**4 + 15*u**3 + 19*u**4 + b*u**2 + 14*u**4 - 47*u**4 + 5*u = 0 for u.
-1, 0
Let i(s) be the second derivative of s**6/135 - 2*s**5/5 + 133*s**4/54 - 6*s**3 + 64*s**2/9 - 10*s + 69. Suppose i(v) = 0. Calculate v.
1, 2, 32
Let y(w) = 3*w**2 + 12*w + 26. Let c be y(-5). Determine k, given that -2*k + 40 - 4*k**2 - 12*k + c*k + 9*k = 0.
-1, 10
Let o(v) be the first derivative of -4*v**3/3 + 68*v**2 - 480*v + 624. Solve o(b) = 0.
4, 30
Suppose -2*s - 3*s = 385. Let d = -73 - s. Suppose 7*z**2 - 2*z**2 - 10*z + 2*z**4 - 6*z**d - z**4 + 10*z**3 = 0. Calculate z.
-1, 0, 1, 2
Let m(n) be the third derivative of n**5/60 - 7*n**4/12 + 8*n**3 + 5556*n**2. Find g, given that m(g) = 0.
6, 8
Let l = 1647 + -1636. Let j be -6 + (-99)/21 + l. Determine x so that -j*x + 1/7*x**5 - 3/7*x**2 + 3/7*x**4 + 0 + 1/7*x**3 = 0.
-2, -1, 0, 1
Let g = -1 + 4. Let o(r) = -8*r**2 + 58*r - 11. Let i be o(7). Suppose -w**i + w**g + 0*w**3 - 5*w**3 = 0. What is w?
0
Suppose -16*d - 55*d = -32*d - 195. Find o, given that 4*o**2 + 12/7*o**3 - 2/7*o**4 + 6/7 + 22/7*o - 2/7*o**d = 0.
-1, 3
Solve -16*v**2 - 73*v - 105*v + 24*v**2 + 22*v - 11*v**2 = 0 for v.
-52, 0
Let 97001*f + 0*f**4 - 177*f**3 - f**4 - 97361*f + 538*f**2 = 0. What is f?
-180, 0, 1, 2
Let b(a) = 11*a**2 - 20. Let r = -5 - -14. Let h(z) = 3*z**2 + 9*z + 1. Let k(s) = 3*s + 2. Let g(n) = h(n) - 3*k(n). Let c(j) = r*g(j) - 2*b(j). Factor c(y).
5*(y - 1)*(y + 1)
Let x be (401/(-3609))/((-425)/(-90) - 5). Suppose 18/5*u + 12/5*u**2 + x*u**3 + 0 = 0. What is u?
-3, 0
Let k be (-112)/(-58) + (-766)/(-11107). Find g, given that -6/7*g**k + 3/7*g + 0 + 3/7*g**3 = 0.
0, 1
Suppose -152 = -5*y - 4*c + 87, -y - 3*c = -39. Suppose -7*r = -24*r + y. Find n, given that 6/7*n**4 + 0 + 4/7*n - 2/7*n**r - 2/7*n**5 - 6/7*n**2 = 0.
-1, 0, 1, 2
Solve 6639*z**2 - 6642*z**2 - 42*z - 84*z = 0.
-42, 0
Let v = 518 - 483. Let m be (20/v)/((-132)/(-14) + -4). Solve 12/19*q - 18/19 - m*q**2 = 0 for q.
3
Suppose 8 = -a + 5*a. Suppose -710 = -3*m - 740, 2*q - 4*m = 46. Find v such that -1 + v**q - 3/2*v + 3/2*v**a = 0.
-2, -1/2, 1
Let o(g) = -15*g**3 + 110*g**2 + 125*g. Let t = -136 + 156. Let j(i) = -2*i**3 + 16*i**2 + 18*i. Let v(b) = t*j(b) - 3*o(b). Factor v(h).
5*h*(h - 3)*(h + 1)
Suppose 13*l - 28*l = -10*l. Let x(w) be the third derivative of 1/720*w**6 - 1/1260*w**7 + 0*w**3 + 7*w**2 - 1/36*w**4 + 1/90*w**5 + 0*w + l. Factor x(o).
-o*(o - 2)*(o - 1)*(o + 2)/6
Let j be (-150)/(-175)*(-7)/(-2). Suppose 2*u + 69*u - 36*u**2 + 100 - 11*u + 4*u**3 + 0*u**j = 0. Calculate u.
-1, 5
Let v = 1 + 18. Let n = -13 + v. Let 0 + 0*z - 6 + 3*z + n*z**2 + 6*z = 0. Calculate z.
-2, 1/2
Factor -1130*b + 96*b + 2*b**2 + 634*b + 20000.
2*(b - 100)**2
Let h(w) = 9*w**2 + 37*w - 67. Let f(j) = 12*j**2 + 56*j - 101. Let p(x) = -5*f(x) + 7*h(x). Factor p(r).
3*(r - 4)*(r - 3)
Let i be 178/(-15) - (-22)/11*102/17. Solve 0*s**3 + 0 - i*s**5 + 0*s**4 + 0*s**2 + 0*s = 0.
0
Suppose -6*h + 12 = -3*h + 5*c, -2*h - 5*c + 8 = 0. Determine f so that -183*f**2 + 6*f**5 + 309*f**2 + 132*f**h + 246*f**2 - 368*f**3 - 22*f**5 - 72*f = 0.
0, 1/4, 2, 3
Suppose 20 = -22*l + 26*l. Factor 5*b**5 - 5*b**l + 10*b**3 - 4*b**4 - 11*b**4 + 5*b**5.
5*b**3*(b - 2)*(b - 1)
Let u(i) be the third derivative of 1/360*i**6 + 0*i + 3/160*i**5 - 11/2*i**3 + 0 - 13*i**2 + 5/96*i**4. Let c(g) be the first 