et x be 357/85 + (-31)/5 + 46*(-1)/(-14). Find j such that 0 - 30/7*j**2 + 0*j + 12/7*j**4 + x*j**3 = 0.
-2, 0, 5/4
Let c = -21457 + 21460. Let f(t) be the first derivative of 1/4*t**2 + 18 - 1/3*t - 1/18*t**c. What is y in f(y) = 0?
1, 2
Let l(d) be the first derivative of -17*d**5/345 - d**4/276 - 99*d**2/2 - 76. Let r(t) be the second derivative of l(t). Solve r(v) = 0 for v.
-1/34, 0
Let i(f) = -41*f**2 - 206*f - 2197. Let k(p) = 50*p**2 + 205*p + 2195. Let c(d) = -5*i(d) - 4*k(d). Determine z, given that c(z) = 0.
-21
Let h(n) be the second derivative of 27*n**5/20 - 97*n**4/4 - 128*n**3 - 78*n**2 - 912*n. Suppose h(p) = 0. Calculate p.
-2, -2/9, 13
Let s(c) be the second derivative of -c**6/90 + c**5/10 - c**4/3 + 4*c**3/9 - c - 452. Factor s(m).
-m*(m - 2)**3/3
Suppose 35 - 23 = 3*s. Let -16*o**2 + o**4 - 4*o**5 + 20*o**4 - 17*o**s + 16*o**3 = 0. Calculate o.
-2, 0, 1, 2
Let j be (-6)/(-8) - 59211/(-1836). Factor j*y + 69/2 - 3/2*y**2.
-3*(y - 23)*(y + 1)/2
Let w(r) be the first derivative of -3*r**5/5 + 243*r**4/4 - 234*r**3 - 845. Factor w(p).
-3*p**2*(p - 78)*(p - 3)
Suppose -275/2*w**4 + 0*w**2 + 0 + 273/2*w**5 + 0*w + w**3 = 0. What is w?
0, 2/273, 1
Solve 5285*c**2 - 3629520*c - 400*c**3 + 395*c**3 - 13805*c**2 = 0 for c.
-852, 0
Let r(q) be the third derivative of -1/420*q**6 - 1/210*q**5 + 0*q**3 + 0*q**4 - 121*q**2 + 0 + 0*q. Determine p so that r(p) = 0.
-1, 0
Let i be (-94 + 89)*(-4)/5. Let t(w) be the first derivative of -4 - 4/7*w + 0*w**2 - 1/28*w**i + 1/7*w**3. Find l such that t(l) = 0.
-1, 2
Let r(i) be the first derivative of -23 - 2/9*i**3 + 0*i**2 + 0*i - 1/9*i**6 - 2/5*i**5 - 1/2*i**4. Determine z, given that r(z) = 0.
-1, 0
Let u = 70221/7 + -10031. Let l(c) be the first derivative of -u*c**2 + 0*c + 0*c**3 + 3/14*c**4 + 2/35*c**5 + 2. Solve l(t) = 0.
-2, 0, 1
Let i(o) be the first derivative of 2*o**3/3 + 27*o**2 + 100*o - 458. Factor i(t).
2*(t + 2)*(t + 25)
Let i(k) be the third derivative of -k**8/126 + 53*k**7/315 - 97*k**6/180 - 31*k**5/90 + 101*k**4/36 - 22*k**3/9 + 151*k**2 + 7*k. Solve i(x) = 0.
-1, 1/4, 1, 2, 11
Let t = 2211 - 1226. Factor -3*r**2 - 917*r + t*r + r**2 - 578.
-2*(r - 17)**2
Let f be 41/(-7) - ((-228)/(-28) + -8). Let x be f - ((-140)/65 - 4). Factor -x*a**2 + 8/13*a + 10/13.
-2*(a - 5)*(a + 1)/13
Let n = 1717817/6936 + -1/6936. Let o = n + -247. Factor 8/9*q + 2/9*q**2 + o.
2*(q + 1)*(q + 3)/9
Let c = 17742/11267 + -372/593. Suppose 0 + 2/19*k**5 - c*k + 12/19*k**2 - 12/19*k**4 + 16/19*k**3 = 0. Calculate k.
-1, 0, 1, 3
Let k be (-1)/25*(10*1)/(478/(-717)). Let l be 95/(-25) - (0 - 4). Factor k*s - l - 3/5*s**3 + 1/5*s**2.
-(s - 1)*(s + 1)*(3*s - 1)/5
Let p(b) be the second derivative of -b**6/720 - b**5/80 + 7*b**4/12 - 85*b**3/3 - b**2 + b - 8. Let h(y) be the second derivative of p(y). Solve h(l) = 0.
-7, 4
Let d(h) = h**3 - 3*h**2 - 4*h - 10. Let u be d(5). Suppose u = -5*n + 35. What is w in -4*w**3 + 2*w**5 - 9*w**n - 6*w**4 + 10*w**3 - 5*w**5 = 0?
-1, 0
Let z(t) = -856*t**2 + 780*t - 180. Suppose 67 = 3*w - 3*g - 8, -4*w + 85 = g. Let k(y) = -171*y**2 + 156*y - 36. Let d(a) = w*k(a) - 4*z(a). Factor d(s).
-2*(13*s - 6)**2
Suppose 4*w - 2*k = w + 112, 4*w - 141 = k. Let z = w - 30. Let -53*y**3 + 9*y**3 - 22*y**2 + y**5 - z*y - 38*y**4 - 7*y**5 - 6*y**5 = 0. What is y?
-1, -2/3, -1/2, 0
Suppose -7907*o**2 - o**3 + 18069*o**2 - 7913*o**2 = 0. What is o?
0, 2249
Let i(p) be the third derivative of p**6/90 - 145*p**5/3 + 525625*p**4/6 - 762156250*p**3/9 + 11*p**2 + 52*p. Factor i(l).
4*(l - 725)**3/3
Factor -b**2 + 41*b - 234*b + 215 - 215.
-b*(b + 193)
Solve -2/5*t**2 - 4/5*t + 32 = 0 for t.
-10, 8
Suppose -3*t - 5 - 1 = -4*z, 4*t - 5*z + 7 = 0. Factor -11*a**3 - 4*a**t - 2*a**3 - 3*a + 3*a + 9*a**3.
-4*a**2*(a + 1)
Let q(p) = 5*p**3 + 470*p**2 + 11066*p. Let f(x) = -3*x. Let z(d) = 7*f(d) + q(d). Factor z(s).
5*s*(s + 47)**2
Let t(c) be the second derivative of 2 + 3/100*c**5 + 2/5*c**4 + 3/2*c**3 + 0*c**2 + 4*c. Factor t(s).
3*s*(s + 3)*(s + 5)/5
Suppose 12*n - 30 = -12*n + 9*n. Let t(g) be the third derivative of 1/40*g**5 + 1/8*g**4 + 0*g - 29*g**n + 1/3*g**3 + 0 + 1/480*g**6. Factor t(p).
(p + 2)**3/4
Let w(t) be the second derivative of -5*t**4/12 - 35*t**3/3 + 180*t**2 + 2*t - 407. Find q such that w(q) = 0.
-18, 4
Let k(i) be the first derivative of -83 + 1/25*i**5 + 13/20*i**4 + 0*i**3 + 0*i + 0*i**2. Let k(f) = 0. What is f?
-13, 0
Let d(p) be the first derivative of 2*p**3/27 + 115*p**2/9 - 232*p/9 + 4736. Factor d(r).
2*(r - 1)*(r + 116)/9
Let a(k) = 3*k**2 - k + 1. Let h(q) = -363*q**3 + 85092*q**2 - 30906*q + 2814. Let i(j) = 6*a(j) - h(j). Factor i(f).
3*(f - 234)*(11*f - 2)**2
Determine t so that -t**2 - 127/3 - 382/3*t = 0.
-127, -1/3
Suppose -12*m + 40 = 8*m. Let -331*h**5 + 35*h**m + 665*h**5 - 98*h**3 + 13*h**3 - 354*h**5 + 45 - 80*h**4 + 105*h = 0. Calculate h.
-3/2, -1, 1
Let d = -515/3 - -3614/21. Let f(q) be the first derivative of -2/21*q**3 - 21 + d*q**2 - 4/7*q. Determine o so that f(o) = 0.
1, 2
Let g(x) be the third derivative of 61*x**8/462 + 81*x**7/385 - 49*x**6/132 - 81*x**5/110 + x**4/132 - 7172*x**2. Let g(r) = 0. What is r?
-1, 0, 1/244, 1
Suppose -m + 4 - 7 = 0. Let a be (1/2)/(5*(-3)/(-30)). Let o(u) = -u**2 - 1. Let g(d) = -6*d**2 - 3*d + 3. Let f(x) = a*g(x) + m*o(x). Factor f(k).
-3*(k - 1)*(k + 2)
Suppose 5*a = 15*a - 250. Solve -3*g**3 - a*g**2 + 60 - 40*g + 2*g**3 + 6*g**3 = 0 for g.
-2, 1, 6
Let s(b) = 17*b**3 + 225*b**2 - 234*b - 451. Let i(m) = 115*m**3 + 1575*m**2 - 1640*m - 3160. Let p(k) = -3*i(k) + 20*s(k). Let p(q) = 0. Calculate q.
-46, -1, 2
Let q(g) be the third derivative of g**9/181440 - g**8/6720 + g**7/1080 - 15*g**5/4 + 17*g**2 - 2. Let b(m) be the third derivative of q(m). Factor b(j).
j*(j - 7)*(j - 2)/3
Let o(g) be the first derivative of 9585000*g**2 + 33450*g**4 + 25/6*g**6 + 598*g**5 - 60 + 882000*g**3 - 8100000*g. Solve o(y) = 0 for y.
-30, 2/5
Let m(s) be the second derivative of -4*s**4/3 + 86*s**3/3 - 126*s**2 - 1452*s. Solve m(x) = 0.
7/4, 9
Find w, given that 132*w**3 - 15*w**4 - 101*w**5 - 36*w**3 + 164*w**3 - 300*w**2 + 80*w + 76*w**5 = 0.
-4, 0, 2/5, 1, 2
Let f(j) be the first derivative of -j**6/600 - 2*j**5/5 - 40*j**4 - 71*j**3 + 217. Let u(x) be the third derivative of f(x). Solve u(q) = 0 for q.
-40
Let y be (6 - (-155)/(-25) - (-154)/(-105))/(40/(-16)). What is v in y*v**4 - 64*v + 10*v**3 - 256/3 + 92/3*v**2 = 0?
-8, -1, 2
Let -6468*z**2 - 148/3*z**4 + 2/3*z**5 + 1088*z**3 + 10890*z + 0 = 0. Calculate z.
0, 3, 5, 33
Solve -g**2 + 431*g - 235*g - 204*g - 178*g = 0.
-186, 0
Let s(n) be the first derivative of -14*n - 1/10*n**6 + 0*n**2 - 1/2*n**4 + 0*n**3 + 1 - 9/20*n**5. Let y(m) be the first derivative of s(m). Solve y(c) = 0.
-2, -1, 0
Let v be ((-270)/264)/((-299)/3289). Factor 39/4*p + 63/4*p**2 + v*p**3 + 3*p**4 + 9/4.
3*(p + 1)**3*(4*p + 3)/4
Let n(h) be the first derivative of h**7/2100 + h**6/50 + h**5/5 + 14*h**4/15 - 76*h**3/3 + h**2/2 - 96. Let z(o) be the third derivative of n(o). Factor z(q).
2*(q + 2)**2*(q + 14)/5
Let l be ((-17243)/215 + 83)/(2/10). Factor -l - 8/3*f + 2/3*f**2.
2*(f - 7)*(f + 3)/3
Let b(d) = -d**3 - 596*d**2 - 10412*d + 8. Let h(a) = -198*a**2 - 3471*a + 3. Let u = 271 + -263. Let o(g) = u*h(g) - 3*b(g). Factor o(k).
3*k*(k + 34)**2
Let h(t) be the second derivative of -2*t**5/5 - 35*t**4/2 - 42*t**3 - 25*t**2 + 504*t - 9. Let h(d) = 0. Calculate d.
-25, -1, -1/4
Let f = -391714 - -391717. Find x, given that 206/3*x**2 - 700/3*x**5 + 8 - 1210/3*x**4 - 144*x**f + 152/3*x = 0.
-1, -3/7, -2/5, 1/2
Let s be 13/(-5) - -3 - 154/385. Let z(m) be the third derivative of 0*m**3 - 9*m**2 - 1/210*m**5 + s + 0*m + 1/840*m**6 + 1/168*m**4. Factor z(x).
x*(x - 1)**2/7
Let b be (8/30)/(3409/14610). Find q, given that -b + 12/7*q**4 + 48/7*q - 38/7*q**3 + 6/7*q**2 = 0.
-1, 1/6, 2
Let f(h) be the third derivative of 13*h**5/18 + 713*h**4/36 - 22*h**3/9 + 3585*h**2. Determine d so that f(d) = 0.
-11, 2/65
Factor -374/3 + 5/3*w + 1/3*w**2.
(w - 17)*(w + 22)/3
Suppose u - 91 = -5*t + 2*t, 419 = 4*u + t. Let h be 212/u - ((-11)/(-6) + 0). Let -1/6 + 1/3*x**3 + h*x**4 - 1/3*x + 0*x**2 = 0. Calculate x.
-1, 1
Let y = 316855 - 316855. Factor -1/2*v**4 + 0*v**2 + y*v + 0 - 11/2*v**3.
-v**3*(v