 - 35/3*k.
(k - 33)*(k - 1)*(k + 2)/3
Let a(f) be the second derivative of -f**5/2 + 425*f**4/4 - 635*f**3/6 + 72*f + 6. Factor a(u).
-5*u*(u - 127)*(2*u - 1)
Factor 0 + 3/5*f**3 + 36*f - 51/5*f**2.
3*f*(f - 12)*(f - 5)/5
Let q(s) be the second derivative of -17 - 1/3*s**3 + s - 4/7*s**2 - 1/14*s**4. Suppose q(u) = 0. What is u?
-4/3, -1
Let y(v) be the second derivative of -v**5/140 - 3*v**4/28 + 8*v**3/7 + 32*v**2 + 8*v + 12. Find n, given that y(n) = 0.
-8, 7
Let k(t) be the first derivative of -3*t**3 + 537*t**2 - 2457*t + 2433. Factor k(n).
-3*(n - 117)*(3*n - 7)
Suppose 0 = 5*y + 5*o - 110, -48*o + 46*o + 62 = 3*y. Let b(w) be the first derivative of 5/4*w**2 - 15/4*w + 5/12*w**3 + y. Solve b(u) = 0 for u.
-3, 1
Factor 474/7*g**2 - 2/7*g**3 + 0 + 68*g.
-2*g*(g - 238)*(g + 1)/7
Let r(w) be the third derivative of -w**8/840 + 193*w**7/525 + 391*w**6/150 + 589*w**5/75 + 787*w**4/60 + 197*w**3/15 - 2526*w**2. Factor r(j).
-2*(j - 197)*(j + 1)**4/5
Determine g so that 7/2*g**4 + 129981*g**2 + 37636 + 2707/2*g**3 - 168974*g = 0.
-194, 2/7, 1
Let k(f) be the third derivative of 0 + 7/2*f**4 - 10*f**3 + 3/20*f**5 - 54*f**2 + 0*f. Find s, given that k(s) = 0.
-10, 2/3
Let z(l) = 2*l**2 + 6*l + 18. Let d be z(-6). Let c = 56 - d. Factor 75*m - 12*m**c - 5*m**5 + 47*m**2 + 50*m**3 + 80*m**2 - 15*m**2 + 20.
-5*(m - 4)*(m + 1)**4
Let s(q) be the third derivative of -q**8/28 + 2*q**7/15 - q**6/10 - q**5/5 + q**4/3 + 2*q**2 - 124*q. Solve s(j) = 0.
-2/3, 0, 1
Suppose 3*f = 3*z + 54, 52 = 4*f - 48*z + 49*z. Let n be (-6)/f + (-198)/(-168). Solve n*r**3 + 0*r**2 + 0*r + 0 - 1/4*r**4 = 0 for r.
0, 3
Let p = 4646111/7 - 663727. Solve 6/7*r**3 + 66/7*r**2 + 12/7 - 62/7*r - p*r**4 = 0.
-2, 3/11, 1
Let y(n) = 470*n**2 - 1880*n + 3. Let b be y(4). Factor 8/9*u**2 - 2/9*u**b - 2/9*u**4 + 0 + 8/9*u.
-2*u*(u - 2)*(u + 1)*(u + 2)/9
Suppose -13*c - 5*w - 23 = -12*c, -2*c = w + 1. Let g(z) be the second derivative of 17*z - 1/48*z**4 + 0 + 1/2*z**c + 0*z**3. Factor g(m).
-(m - 2)*(m + 2)/4
Suppose -8*i + 2*i = -12. Suppose i*k = 183 - 179. Factor -2/3*p**k - 5/6*p - 1/6.
-(p + 1)*(4*p + 1)/6
Factor 5/4*c**2 - 205*c + 8405.
5*(c - 82)**2/4
Let q(f) be the first derivative of -f**8/168 + f**7/35 - f**6/30 + 39*f**2/2 - 59. Let z(b) be the second derivative of q(b). Determine x, given that z(x) = 0.
0, 1, 2
Let a(k) be the first derivative of -k**7/231 + 4*k**6/165 + k**5/110 - 2*k**4/33 - 71*k - 9. Let n(g) be the first derivative of a(g). Let n(m) = 0. What is m?
-1, 0, 1, 4
Let w(i) = -2*i + 40. Let f be w(19). Suppose 84*r + 8*r**2 - 12*r**2 + f*r**2 - 28 - 114*r = 0. What is r?
-14, -1
Let -51*j**3 - 72*j**2 - 216*j - j**4 + 67*j**2 - 148*j**2 + 21*j**3 = 0. Calculate j.
-24, -3, 0
Let q be -1*((-2)/8 - (-115)/(-20)). Factor -q*p + p**2 + 73 + 13*p - 67.
(p + 1)*(p + 6)
Suppose 294*t - 469 - 1295 = 0. Let z(q) be the second derivative of -20/3*q**3 - 1/15*q**t - 8*q**2 - 3*q**4 - 16*q - 7/10*q**5 + 0. Factor z(s).
-2*(s + 1)*(s + 2)**3
Let -12326187/8 + 6081/4*j - 3/8*j**2 = 0. What is j?
2027
Let c(j) be the first derivative of -j**5/10 + 5*j**4/6 - 8*j**3/3 + 4*j**2 - 47*j - 44. Let t(x) be the first derivative of c(x). Factor t(n).
-2*(n - 2)**2*(n - 1)
Find w such that -5/4*w**4 + 360*w**3 - 894645/4 - 53955/2*w**2 + 152280*w = 0.
3, 141
Let g(d) be the second derivative of -2*d**5/5 - 45*d**4/2 - 182*d**3 + 145*d**2 + 3775*d. Let g(i) = 0. Calculate i.
-29, -5, 1/4
Let a(r) be the third derivative of 0 + 0*r - 1/140*r**5 - 3/4*r**4 - 63/2*r**3 - 53*r**2. Determine w, given that a(w) = 0.
-21
Let w = 4831706/7 + -690218. Suppose 3/7*s**2 + 2700/7 + w*s = 0. What is s?
-30
Let u(y) be the first derivative of y**6/8 - 3*y**5/4 - 1095*y**4/16 - 135*y**3/4 + 14580*y**2 + 139968*y - 2316. Factor u(n).
3*(n - 16)**2*(n + 9)**3/4
Let q be (21680/(-4878))/(3/(-9)). Determine s, given that 0 - q*s**2 - 2/3*s = 0.
-1/20, 0
Let h(j) be the second derivative of j**7/9 + 187*j**6/45 + 673*j**5/15 + 1018*j**4/9 - 1576*j**3/3 + 384*j**2 - 2122*j. What is v in h(v) = 0?
-16, -6, 2/7, 1
Determine h, given that -62/13*h**3 - 58/13*h**2 + 128/13*h - 8/13 = 0.
-2, 2/31, 1
Let c be 827/5 - 4/(-20)*-2. Let o be (18/c)/(57/190). Factor -2/11*j**3 + 2/11*j - 4/11*j**2 + o.
-2*(j - 1)*(j + 1)*(j + 2)/11
Let l(k) = 2*k**3 - 222*k**2 + 904*k - 888. Let x(f) = -2*f**3 + 224*f**2 - 902*f + 888. Let v(p) = -3*l(p) - 4*x(p). Factor v(w).
2*(w - 111)*(w - 2)**2
Let l(x) be the first derivative of -3/25*x**5 + 0*x**2 + 0*x - 45 + 3/5*x**3 - 3/10*x**4. Suppose l(w) = 0. What is w?
-3, 0, 1
Let q(h) be the first derivative of 0*h - 3*h**3 + 24/5*h**2 + 188 - 3/20*h**4. Factor q(l).
-3*l*(l - 1)*(l + 16)/5
Find u such that -40*u**3 + 660*u**3 - 157 - 28*u**4 - 2216*u**2 - 131 + 2320*u = 0.
1/7, 2, 18
Let l = -1623321 + 1623325. Factor 28/9*g**3 + 8*g**2 + 22/9 + 68/9*g + 2/9*g**l.
2*(g + 1)**3*(g + 11)/9
Let c(d) be the second derivative of d**4/3 + 52*d**3 + 154*d**2 - 30*d + 19. Factor c(o).
4*(o + 1)*(o + 77)
Determine s so that -4808/7*s**2 - 2/7*s**3 - 2889608/7*s + 0 = 0.
-1202, 0
Let u(w) = -4*w**2 + 67*w - 249. Let z be u(11). Let m(b) be the third derivative of 1/20*b**5 + 0*b + 1/8*b**z - b**3 - 15*b**2 + 0. What is y in m(y) = 0?
-2, 1
Factor 395/4*i + 1/8*i**2 + 789/8.
(i + 1)*(i + 789)/8
Let c = 44401/8 + -5550. Let t(b) be the first derivative of 0*b**3 + 0*b - c*b**4 + 6 + b**2. Let t(a) = 0. What is a?
-2, 0, 2
Suppose -13135 = -5*f + 4*l, 5*f - 17855 + 4720 = -3*l. Solve 48*s**4 - 41*s**3 - 205*s + 95*s**3 - 89*s - f + 252*s**2 - 45*s**4 - 460 = 0.
-7, 3
Let x(k) be the second derivative of -1/120*k**6 - 55*k + 0*k**3 + 0 + 0*k**2 - 1/12*k**4 - 1/20*k**5. Factor x(r).
-r**2*(r + 2)**2/4
Let y be (-2 - (-24)/3)/((-9)/(-6)). Solve -y*u - 2*u**2 + 23*u**3 - 11*u**2 - 26*u**3 = 0 for u.
-4, -1/3, 0
Let p(w) be the first derivative of 7*w**5/60 + 3*w**4/8 + w**3/3 - 69*w**2 - 78. Let o(s) be the second derivative of p(s). Factor o(x).
(x + 1)*(7*x + 2)
Let u = -536 + 538. Let 4*c**3 + u*c**5 + 6*c**4 - 103825*c - 6*c**2 - 2*c**3 + 103821*c = 0. Calculate c.
-2, -1, 0, 1
Let o(j) = 30*j**3 - 46*j**2 + 208*j - 284. Let u(f) = 37*f**3 - 48*f**2 + 208*f - 285. Let w(t) = 5*o(t) - 4*u(t). Let w(l) = 0. Calculate l.
2, 7, 10
Let l be 10 - -127 - (2 + 0/(-2)). Let t be (1 - 8/(-10)) + (-18)/l. Let 4/3 + 1/3*m**2 + t*m = 0. What is m?
-4, -1
Let k(m) = -2*m**3 - 27*m**2 + 19*m + 62. Let z be k(-14). Let g be 20/z*(-18)/15. Factor -35/4*i**4 - 55/2*i**2 - 15/4 + 5/4*i**5 + 65/4*i + 45/2*i**g.
5*(i - 3)*(i - 1)**4/4
Let c = 4 + -1. Let l(m) = 2*m**2 - 5*m + 7. Let r be l(c). Factor r*g**3 + 4*g - 14*g + 79 + 5*g**2 - 5*g**4 - 79.
-5*g*(g - 2)*(g - 1)*(g + 1)
Let u(h) be the third derivative of h**7/168 + 5*h**6/24 + 47*h**5/24 + 55*h**4/8 + 14*h**3 - 4*h**2 - 6. Let a(w) be the first derivative of u(w). Factor a(y).
5*(y + 1)*(y + 3)*(y + 11)
Factor -268/13 - 10/13*t**2 - 674/13*t.
-2*(t + 67)*(5*t + 2)/13
Let b be (16/4)/((-84)/(-105)). Let h(t) be the first derivative of -4*t**2 + 4/3*t**3 + 25 + 0*t + 5*t**4 + 8/5*t**b. Let h(j) = 0. Calculate j.
-2, -1, 0, 1/2
Factor 268*c**2 - 1696 + 258*c**2 + 272*c**2 - 795*c**2 - 254 + 3*c.
3*(c - 25)*(c + 26)
Factor -4/3*i - 70/3 + 2/3*i**2.
2*(i - 7)*(i + 5)/3
Let p(u) be the third derivative of 21/5*u**3 + 0 - 21/50*u**5 - 14*u + 1/200*u**6 - 3*u**2 - 1/40*u**4. Factor p(a).
3*(a - 42)*(a - 1)*(a + 1)/5
Solve 2120/9 - 4/9*z**2 + 1052/9*z = 0 for z.
-2, 265
What is h in 7/3*h**2 - 17/6*h - 5 + 1/6*h**3 = 0?
-15, -1, 2
Let q = 2825/24 + -53339/456. Solve -100/19 - 110/19*r + q*r**3 - 2/19*r**4 + 6/19*r**2 = 0 for r.
-2, -1, 5
Let l(t) be the second derivative of -50/21*t**7 + 0 - 46/5*t**5 - 2/3*t**4 + 26/3*t**6 + 38*t + 14/3*t**3 + 2*t**2. Factor l(g).
-4*(g - 1)**3*(5*g + 1)**2
Suppose 8*c = -14*c + 396. Let p be (c/27*-12)/(-4). Factor -14/9*t**p + 20/9 - 22/3*t.
-2*(t + 5)*(7*t - 2)/9
Let b(x) be the second derivative of -x**6/150 + 83*x**5/100 + 169*x**4/60 + 17*x**3/6 - 1299*x. Factor b(i).
-i*(i - 85)*(i + 1)**2/5
Let a(d) be the third derivative of d**8/504 - d**7/315 - d**6/180 + d**5/90 - 544*d**2 - 2*d. Factor a(t).
2*t**2*(t - 1)**2*(t + 1)/3
Factor -870 + 3485*f + 1736*f**2 + 1731*f**2 - 3487*f**2.
-5*(f - 174)*(4*f - 1)
Factor -4602