*w - 16/13*j - 10/13*j**3.
-2*j*(j + 4)*(5*j + 2)/13
Let r(g) be the first derivative of -110 - 4/7*g**2 + 2/21*g**3 - 24/7*g. Factor r(l).
2*(l - 6)*(l + 2)/7
Let u(z) = 2*z**2 + 18*z - 41. Let i be u(-10). Let m be i/35 + 0 + 1. Determine v, given that -3/5 + 4/5*v**2 - 1/5*v**4 + m*v - 2/5*v**3 = 0.
-3, -1, 1
Let v(o) be the second derivative of -o**7/21 + 93*o**6 - 97719*o**5/2 + 1457425*o**4/6 - 484880*o**3 + 484416*o**2 - 12*o - 309. Factor v(u).
-2*(u - 696)**2*(u - 1)**3
Let b(o) be the third derivative of -3*o**6/80 + 11*o**5/5 - 167*o**4/16 + 41*o**3/2 + o**2 + 718*o. Factor b(h).
-3*(h - 1)**2*(3*h - 82)/2
Let k = 199 + -231. Let g be (-56)/k + -2 + (-1)/(-4). Factor 6/5*x**2 + 3/5*x**4 + g + 0*x + 9/5*x**3.
3*x**2*(x + 1)*(x + 2)/5
Let m(p) be the third derivative of p**5/300 + 17*p**4/120 - 2*p**3 + 2*p**2 + 694. Factor m(g).
(g - 3)*(g + 20)/5
Let o(g) be the second derivative of -g**6/120 + 249*g**5/20 - 62001*g**4/8 + 5146083*g**3/2 - 3844124001*g**2/8 + 2868*g. Find x such that o(x) = 0.
249
Let d(p) be the third derivative of 0*p**3 + 4*p**2 - 6 + 0*p + 1/105*p**7 + 0*p**5 + 0*p**4 + 1/10*p**6 - 1/168*p**8. Factor d(f).
-2*f**3*(f - 3)*(f + 2)
Factor 27*l - 3/4*l**2 + 57.
-3*(l - 38)*(l + 2)/4
Let v(k) = k**2 - 13*k - 54. Let q be v(19). Find r such that -82*r**5 + 85*r**3 + 19*r**5 + 68*r**5 + 200 + q*r**4 - 180*r - 170*r**2 = 0.
-10, -2, 1
Suppose 61 = -2*t + 57. Let a be 26/18 + t/(-18)*2. Factor 4/3*i + 0 - 4*i**2 + a*i**3.
i*(i - 2)*(5*i - 2)/3
Let d(y) be the first derivative of -y**6/120 - y**5/16 + 7*y**4/24 - 54*y + 86. Let w(u) be the first derivative of d(u). Factor w(r).
-r**2*(r - 2)*(r + 7)/4
Let u(a) = 6*a**2 - 4*a - 4. Let h be u(-1). Suppose -f = h*f + f. Find d such that -2/3*d + f - 8*d**3 - 17/3*d**4 - 4/3*d**5 - 13/3*d**2 = 0.
-2, -1, -1/4, 0
Factor -53*j - 12 - 61/3*j**2 - 4/3*j**3.
-(j + 3)*(j + 12)*(4*j + 1)/3
What is p in -269 - 159*p**2 - 29*p**3 + 665 - p**4 + 409*p - 616 = 0?
-20, -11, 1
Let m(t) be the second derivative of 0*t**2 + 4 - 6*t - 21/16*t**3 - 83/32*t**4 + 3/40*t**5. Find p such that m(p) = 0.
-1/4, 0, 21
Let j(q) be the first derivative of 191 + 3/40*q**5 + 33/16*q**4 + 15/2*q**3 + 87/8*q**2 + 57/8*q. Factor j(c).
3*(c + 1)**3*(c + 19)/8
Factor 2573*z + 2573*z - 70*z**3 - 5*z**4 + 105*z**2 - 5526*z + 350*z**2.
-5*z*(z - 4)*(z - 1)*(z + 19)
Let h = -37615 - -37615. Suppose 0*r**2 + 0*r - 3/8*r**4 + 3/8*r**5 - 3/4*r**3 + h = 0. What is r?
-1, 0, 2
Let w = -71 - -77. Suppose -81 = -21*l - w*l. Determine k so that 0 - 1/4*k**l - 1/4*k**2 + 0*k = 0.
-1, 0
Let h(u) = -8*u**2 + 55*u - 255. Let y(d) = 17*d**2 - 109*d + 563. Let b(t) = -7*h(t) - 3*y(t). Factor b(w).
(w - 2)*(5*w - 48)
Let i(z) = -115*z**4 - 40*z**3 - 145*z**2 + 720*z - 500. Let w(g) = -6*g**4 + g**2 + g. Let b(l) = -i(l) + 20*w(l). Solve b(t) = 0 for t.
-5, 1, 2, 10
Let k(o) = o**2 - 42*o - 135. Let y be k(45). Suppose -3*i + y + 13 = -2*v, 3*i - 4*v = 17. Factor -3/2 + 3/2*w**4 + 0*w**2 + i*w - 3*w**3.
3*(w - 1)**3*(w + 1)/2
Let d(o) be the second derivative of o**5/120 - o**4/4 + 3*o**3 + 15*o**2/2 - 2*o + 10. Let m(n) be the first derivative of d(n). Find t such that m(t) = 0.
6
Let o = 258737 - 258732. Let -22/15*s + 28/15*s**4 - 16/5*s**o - 4/15 - 4/5*s**2 + 58/15*s**3 = 0. What is s?
-2/3, -1/2, -1/4, 1
Let j be (2 + (-22)/8)*(-1764)/126*40/56. Let u = 1037 - 4127/4. Factor u*l + 3/4*l**2 + j.
3*(l + 2)*(l + 5)/4
Let x(g) = 15*g**5 + 43*g**4 - 105*g**3 - 93*g**2 + 40*g. Let m = -364 - -367. Let j(z) = z**4 - z**2. Let o(y) = m*j(y) - x(y). Solve o(c) = 0 for c.
-4, -1, 0, 1/3, 2
Let b(a) be the second derivative of 0*a**2 + 3/5*a**5 - 25/6*a**3 + 1/210*a**7 - 47*a + 0 - 7/75*a**6 - 5/6*a**4. Solve b(m) = 0.
-1, 0, 5
Factor 4624/5 - 132/5*m**2 - 2/5*m**3 - 408*m.
-2*(m - 2)*(m + 34)**2/5
Let c(r) be the second derivative of 4/3*r**3 - 6*r**2 + 11/36*r**4 + 1/60*r**5 - 72*r + 0. Solve c(f) = 0 for f.
-6, 1
Let j be (-112)/(30 - 14) + (18 - 2). Let l(b) be the second derivative of 0*b**2 + 1/15*b**4 + 0 + j*b - 1/100*b**5 - 2/15*b**3. Solve l(c) = 0.
0, 2
Factor -11/3*q**2 - 16/3 + 9*q.
-(q - 1)*(11*q - 16)/3
Let q(k) be the second derivative of k**4/30 - 43*k**3/3 - 389*k. Factor q(o).
2*o*(o - 215)/5
Let c = 108271/15 - 7218. Let a(p) be the second derivative of 1/100*p**5 + 0*p**2 + 0 + c*p**4 - 11*p + 0*p**3. Suppose a(k) = 0. Calculate k.
-4, 0
Find r, given that -54/7 + 78/7*r + 2/7*r**3 - 26/7*r**2 = 0.
1, 3, 9
Let k(w) be the second derivative of -w**5/130 + 191*w**4/78 - 9215*w**3/39 + 9025*w**2/13 + 187*w. Factor k(u).
-2*(u - 95)**2*(u - 1)/13
Suppose 4*t - 4*o = 232, o = 3*t - 15 - 163. Let j = 62 - t. Factor -4/11*k + 0 - 2/11*k**j + 6/11*k**3.
2*k*(k - 1)*(3*k + 2)/11
Let u(o) be the second derivative of -1/54*o**4 - 14*o + 1 - 1/3*o**2 - 4/27*o**3. Determine k, given that u(k) = 0.
-3, -1
Suppose 180 = 11*p + 26. Let t be -3 + ((-120)/84)/((-4)/p). Factor 1/6*u**t + 0*u + 0.
u**2/6
Let v(d) be the first derivative of -d**6/36 + 81*d**5/10 - 5041*d**4/8 + 43921*d**3/18 - 3620*d**2 + 2400*d + 431. Factor v(n).
-(n - 120)**2*(n - 1)**3/6
Factor -3/8*k**4 - 14283/8*k**2 - 207/4*k**3 + 0 + 0*k.
-3*k**2*(k + 69)**2/8
Let k(u) be the second derivative of -u**9/52920 - u**8/2940 + 107*u**4/12 - 2*u - 2. Let y(j) be the third derivative of k(j). What is m in y(m) = 0?
-8, 0
Suppose 0 = -113*o - 29*o - 0. Let z(i) be the third derivative of o - 5/8*i**4 - 1/12*i**5 + 0*i - 5/3*i**3 + 6*i**2. Determine j, given that z(j) = 0.
-2, -1
Let d(m) be the third derivative of m**7/840 - m**6/36 + 3*m**5/40 + 11*m**3/3 - 8*m**2 - 3*m. Let b(o) be the first derivative of d(o). What is j in b(j) = 0?
0, 1, 9
Factor 139/7*u**3 - 1/7*u**4 - 5280/7*u**2 + 0 + 4356*u.
-u*(u - 66)**2*(u - 7)/7
Let q(s) be the first derivative of 24*s**2 - 45/8*s**4 + 13/2*s**3 + 6*s + 21. Find l such that q(l) = 0.
-1, -2/15, 2
Let x(t) = -4*t - 42. Let q be x(-3). Let m be (-180)/q + (-6)/1. Solve m + 2/7*g**2 + 0*g - 2/7*g**4 - 2/7*g**3 + 2/7*g**5 = 0.
-1, 0, 1
Let n = 593027/8 + -74128. Solve 3*p**3 - n*p**4 + 9/2*p + 0 - 57/8*p**2 = 0.
0, 1, 3, 4
Let w = -233 + 236. Factor w*m - 274*m**2 - 23*m + 269*m**2.
-5*m*(m + 4)
Let v(f) = 2 + f**3 + f**2 + f**3 - 6 - 1 + 8 - 10*f. Let q be v(0). Solve 3/4*y**4 - 9*y + 39/4*y**2 - 9/2*y**3 + q = 0.
1, 2
Let d be 38/4 + ((-1254)/(-11))/(-57). Factor 9/2*v + 1/2*v**4 + 0 + d*v**2 + 7/2*v**3.
v*(v + 1)*(v + 3)**2/2
Let l = 3/7267 - -116257/36335. Find j such that l - 4/5*j**2 + 0*j = 0.
-2, 2
Let c(r) be the first derivative of r**3/18 - 35*r**2/12 - 19*r + 5398. Factor c(z).
(z - 38)*(z + 3)/6
Let y = -4/401 - 1432/17243. Let u = y - -200/301. Factor 8/7*q - u*q**3 - 2/7*q**4 - 8/7 + 6/7*q**2.
-2*(q - 1)**2*(q + 2)**2/7
Let y(s) be the second derivative of -s**4/12 + 47*s**3/6 + 130*s**2 + 30*s - 41. Determine i so that y(i) = 0.
-5, 52
Let b(r) = -r**4 + 20*r**3 - 49*r**2 + 24*r - 9. Let x(s) = 2*s**4 - 21*s**3 + 47*s**2 - 27*s + 9. Let h(g) = 4*b(g) + 6*x(g). Factor h(i).
2*(i - 3)*(i - 1)**2*(4*i - 3)
Let r(v) be the third derivative of -7*v**6/360 - v**5/45 + 29*v**4/72 - v**3 + 2*v**2 - 180*v - 1. Factor r(i).
-(i - 1)**2*(7*i + 18)/3
Let x(u) = -u**3 - u**2 - 5*u - 30. Let k(n) = -15*n**3 - 160*n**2 + 145*n - 210. Let c(i) = -k(i) + 20*x(i). Find s such that c(s) = 0.
-1, 3, 26
Let i be (3/(-3) - -1)*115/(-230). Let r(h) be the third derivative of 0 - 1/720*h**6 + 1/360*h**5 + i*h - 41*h**2 + 0*h**3 + 0*h**4. Factor r(w).
-w**2*(w - 1)/6
Let j be 174/5394*(10 + 83). Determine n, given that -66/7*n**4 + 10/7*n**5 - 10*n**2 + 16/7 + 122/7*n**j - 12/7*n = 0.
-2/5, 1, 4
Let l(h) be the third derivative of 1/51*h**4 + 0*h - 16/51*h**3 - 1/1020*h**6 + 0 - 64*h**2 + 2/255*h**5. Let l(k) = 0. Calculate k.
-2, 2, 4
Let t = 1153/33690 + -1/1123. Let s(i) be the second derivative of 1/42*i**7 - 26*i + 0 - 1/6*i**4 + 1/2*i**2 + t*i**6 - 1/10*i**5 + 1/6*i**3. Factor s(j).
(j - 1)**2*(j + 1)**3
Let a(f) be the third derivative of -f**8/2688 + f**7/280 + f**6/240 - 7*f**5/60 + 8*f**3/3 - 82*f**2. Solve a(k) = 0 for k.
-2, 2, 4
Let j = 20344/113 - 135176/791. What is y in j*y + 24/7 + 10/7*y**2 = 0?
-6, -2/5
Find t such that -11/4*t**2 + 185/4*t + 17/2 = 0.
-2/11, 17
Let y(i) be the second derivative of -i**4/9 + 61