7252. Let s(m) be the first derivative of 0*m + 1/6*m**2 - f*m**3 - 9. Factor s(t).
-t*(t - 1)/3
Let s(d) = -33*d - 5*d**2 - 41*d + 9*d. Let p(y) be the first derivative of y**3/3 + 11*y**2/2 + 29. Let g(l) = 35*p(l) + 6*s(l). Find w such that g(w) = 0.
0, 1
Let 31*r**4 + 8*r**3 + 17409*r**5 - 72*r - 17406*r**5 + 61*r**3 - 141*r**2 + 2*r**4 + 108 = 0. What is r?
-6, -1, 1
Let f(k) be the first derivative of -k**4/12 - 47*k**3/3 + 707*k**2/2 - 7595*k/3 + 7688. Let f(u) = 0. What is u?
-155, 7
Let k(d) be the third derivative of -5/78*d**4 + 19*d**2 + 1/1365*d**7 + 0*d - 7/390*d**5 + 0 + 1/195*d**6 + 0*d**3. Determine q so that k(q) = 0.
-5, -1, 0, 2
Let l(h) be the second derivative of -1/78*h**4 + 0 + 57*h + 0*h**3 + 0*h**2. Factor l(o).
-2*o**2/13
Let o(q) be the first derivative of -q**7/3360 + q**6/240 + 7*q**5/480 - 49*q**3/3 + 3*q + 76. Let l(r) be the third derivative of o(r). Factor l(n).
-n*(n - 7)*(n + 1)/4
Suppose 592*j - 735 = 20 + 429. Suppose 7/2*f**j + 1/2*f**3 - 90 - 12*f = 0. Calculate f.
-6, 5
Let c = 116 + -241. Let m be (330/c)/(-11)*5/3. Factor 0*w + 2/5*w**4 + 0 - m*w**3 - 2/5*w**2 + 2/5*w**5.
2*w**2*(w - 1)*(w + 1)**2/5
Suppose 0 = 4*w + 29 + 55. Let h = -16 - w. Factor 5*g**5 - 35*g**2 - 222*g + 252*g + 4*g**3 - h*g**3 + 15*g**4 - 14*g**3.
5*g*(g - 1)**2*(g + 2)*(g + 3)
Suppose 0 = -4*c + 24, -3*c - 112 = 3*g - 142. Let j(v) be the first derivative of 7/15*v**3 + 12/5*v - 8/5*v**2 - 1/20*v**g + 9. Factor j(p).
-(p - 3)*(p - 2)**2/5
Let s = 205 - 201. Factor 3 - 6*p**3 - 4*p - 7*p + s*p - 3*p**2 + 13*p.
-3*(p - 1)*(p + 1)*(2*p + 1)
Let r(t) = t**3 + 82*t**2 - 217*t - 4113. Let b be r(-84). Factor 0 + 21/5*k**b - 42/5*k**2 + 24/5*k - 3/5*k**4.
-3*k*(k - 4)*(k - 2)*(k - 1)/5
Let n(b) = -17*b**3 + 148*b**2 - 310*b + 139. Let a(c) = 24*c**3 - 221*c**2 + 461*c - 208. Let l(x) = -5*a(x) - 7*n(x). Factor l(d).
-(d - 67)*(d - 1)**2
Factor 1/4*q**3 + 4224*q + 129/2*q**2 + 8192.
(q + 2)*(q + 128)**2/4
Solve -6*l + 3/5*l**2 + 63/5 = 0.
3, 7
Let k(t) be the third derivative of -t**10/302400 + t**9/120960 + t**8/6720 + 7*t**5/2 - 2*t**2 + 54. Let c(a) be the third derivative of k(a). Factor c(y).
-y**2*(y - 3)*(y + 2)/2
Let p(o) be the second derivative of o**6/660 - 2*o**5/11 + 100*o**4/11 + 133*o**3/6 + 22*o - 5. Let h(g) be the second derivative of p(g). Factor h(w).
6*(w - 20)**2/11
Let f be (3 + -17)/(-2) - -173. Factor 29*z**4 + 55*z**3 - 7*z**4 + f*z**2 - 17*z**4 + 80*z - 320.
5*(z - 1)*(z + 4)**3
Let x(h) be the first derivative of 2*h**3/3 + 421*h**2 - 4260*h - 8643. Find l such that x(l) = 0.
-426, 5
Let s be (-8)/(-12)*-3*-1. Suppose -31 - 20 = -3*c. Suppose -13*g**3 + c*g**3 - 3*g**2 + 3*g**s - 2*g**4 = 0. Calculate g.
0, 2
Let m = 16 - 11. Let t(v) = v**3 - v**2 + 2*v + 5. Let x be t(0). Factor 0*o**x + 2*o**5 - o**m.
o**5
Let u(y) be the third derivative of -55/6*y**4 + 6*y + 0 - 11*y**2 - 11/4*y**5 - 1/42*y**7 - 50/3*y**3 - 5/12*y**6. Factor u(z).
-5*(z + 1)*(z + 2)**2*(z + 5)
Let a(k) be the third derivative of 5*k**7/42 + k**6/2 + 47*k**5/60 + k**4/2 + 69*k**2 - 5. Factor a(p).
p*(p + 1)*(5*p + 3)*(5*p + 4)
What is l in -148*l**2 - 143*l**2 + 139*l + 264*l**2 - 20 = 0?
4/27, 5
Let s be 1 - 25/(25/(-4))*(-1)/(-4). Let l(t) be the first derivative of -5 - 9*t**2 + 1/2*t**4 - s*t**3 - 10*t. Factor l(h).
2*(h - 5)*(h + 1)**2
Let s = -89 + 718. Let a = 633 - s. Factor 5/4*i**2 - 1/2*i + 0 + 1/4*i**a - i**3.
i*(i - 2)*(i - 1)**2/4
Let y = 20218 + -60650/3. Factor -i - 1/3*i**2 + y.
-(i - 1)*(i + 4)/3
Factor -224/15*v**2 + 2/15*v**3 - 454/15*v - 76/5.
2*(v - 114)*(v + 1)**2/15
Let n(g) be the second derivative of -g**8/50400 - g**7/9450 - g**6/5400 + g**4/2 + g**2 - 2*g - 41. Let c(y) be the third derivative of n(y). Factor c(u).
-2*u*(u + 1)**2/15
Solve 32*n**2 - 2*n**2 + 51 - 2*n**3 - 858 - 193 = 0 for n.
-5, 10
Let q be -84*10/(-270) + 11/(-99). Find g such that 0 + 3/2*g - 1/2*g**q + g**2 = 0.
-1, 0, 3
Let o(d) = -23*d**3 - 37*d**2 + 648. Let p(a) = -17*a**2 - 3*a**3 - 5*a**3 + 2*a**2 + 3*a**2 + 216. Let h(r) = 6*o(r) - 17*p(r). Factor h(k).
-2*(k - 3)*(k + 6)**2
Let d(n) be the third derivative of 5*n**8/1344 - n**7/28 + 11*n**6/96 - n**5/24 - 5*n**4/8 + 5*n**3/3 + 2289*n**2. Let d(k) = 0. What is k?
-1, 1, 2
Find n, given that 133*n**2 - n**4 - 9*n**3 - 2*n**3 + 142*n**2 - 305*n**2 = 0.
-6, -5, 0
Let f(b) = -4*b**3 + 390*b**2 + 200*b - 392. Let y be f(98). Factor 2/11*p**3 + 0*p**4 + y*p**2 - 2/11*p**5 + 0*p + 0.
-2*p**3*(p - 1)*(p + 1)/11
Let x(t) = -11*t**2 + 241*t - 102. Let i(f) = 12*f**2 - 243*f + 107. Let k(o) = -3*i(o) - 4*x(o). Factor k(p).
(p - 29)*(8*p - 3)
Factor -230*l + 14*l**2 - 4*l**2 + 130*l**3 - 64*l**3 - 61*l**3 - 240 + 5*l**2.
5*(l - 6)*(l + 1)*(l + 8)
Let z = -277 + 280. Factor -43*l**z + 0*l**5 + 0*l**2 - l**5 + 38*l**3 + 0*l**2 + 6*l**4.
-l**3*(l - 5)*(l - 1)
Suppose 5*f = -a + 7 - 1, -7*f + 2*a = 12. Let r(y) be the first derivative of f*y + 4/3*y**3 + 0*y**2 + 30 + 1/3*y**4. Solve r(o) = 0 for o.
-3, 0
Let r be 13/15 + 1/(-5). Suppose -76*t + 94 + 134 = 0. Factor 8/3*b**t - r*b**4 - 2/3 - 4*b**2 + 8/3*b.
-2*(b - 1)**4/3
Let g(l) = 162*l + 150. Let r be g(-1). Let k be 111/22 - r/(-22). Factor 3/4*o**2 - 15/4*o - k.
3*(o - 6)*(o + 1)/4
Suppose 3*p = 59 - 17. Suppose 6*c + c = p. Factor n - n**2 - 6*n + c*n**2.
n*(n - 5)
Suppose -5474 = 121*i - 128*i. Factor -1565*l**4 - 17 - 15*l**3 + 780*l**4 + 9*l**2 - 13 + i*l**4 + 39*l.
-3*(l - 1)**2*(l + 2)*(l + 5)
Let k(b) = -2*b**3 + 37*b**2 + 89*b + 50. Let l(s) = -5*s**3 + 75*s**2 + 180*s + 100. Let v = -131 + 136. Let n(j) = v*k(j) - 3*l(j). Factor n(w).
5*(w - 10)*(w + 1)**2
Suppose 27*a + 699 = -678. Let i be (a/(-34))/((-1)/(-2)). Factor 1/3*m**i + 1/2 - 7/6*m**2 + 1/3*m.
(m - 3)*(m - 1)*(2*m + 1)/6
Let a be (-2233)/(-35) + 18/15. Let a + 41 - 5*h**2 + 26 - 87 = 0. Calculate h.
-3, 3
Let d(h) be the first derivative of h**4/9 + 628*h**3/27 - 651. Factor d(x).
4*x**2*(x + 157)/9
Let i(u) be the second derivative of -u**5/30 - 587*u**4/6 - 344569*u**3/3 - 202262003*u**2/3 + 4077*u + 2. Factor i(t).
-2*(t + 587)**3/3
Let q(z) be the first derivative of z**4/4 - 23*z**3/6 - 13*z**2 + 225*z + 58. Let h(f) be the first derivative of q(f). Solve h(s) = 0 for s.
-1, 26/3
Factor -68/9 + 68/9*g**2 - 2/9*g + 2/9*g**3.
2*(g - 1)*(g + 1)*(g + 34)/9
Factor 1/2*w**2 - 129*w + 765/2.
(w - 255)*(w - 3)/2
Let m(j) be the first derivative of j**3/5 - 441*j**2/10 + 3972. Factor m(s).
3*s*(s - 147)/5
Let j(v) be the second derivative of -2*v**7/21 - 3*v**6/5 + 8*v**5/15 + 89*v**2 + 20*v. Let b(t) be the first derivative of j(t). Factor b(z).
-4*z**2*(z + 4)*(5*z - 2)
Let f be (-4)/5 - 0 - (-109538)/(-390). Let x = f - -285. Factor -22/3*z**2 + 4/3 - 8/3*z**3 - x*z.
-2*(z + 1)*(z + 2)*(4*z - 1)/3
Let g = -1 - -3. Let q(h) = -h + 4. Let v be q(g). Find b, given that -80*b**v + 78*b**2 + 2*b**4 + 0*b**5 - 2*b**5 + 2*b**3 = 0.
-1, 0, 1
Suppose 25*n - 23*n = 4. Determine l so that -104*l**5 + 422*l**n - 1262*l**2 - 190*l**5 - 384*l - 24*l**3 + 861*l**4 - 48 = 0.
-1/2, -2/7, 2
Suppose 42/5*y + 0 - 129/5*y**2 - 51/5*y**4 + 3/5*y**5 + 27*y**3 = 0. What is y?
0, 1, 14
Let m = -18 - -20. Suppose -m*y - 4*y + 12 = 0. Let c(h) = 2*h**2 - 2*h. Let b(j) = -j**2 - j. Let s(k) = y*b(k) + 2*c(k). Factor s(w).
2*w*(w - 3)
Let o(d) = -139*d**3 - 149*d**2 + 400*d - 35. Let w(m) = 69*m**3 + 75*m**2 - 204*m + 18. Let u(c) = 6*o(c) + 11*w(c). Factor u(b).
-3*(b - 1)*(b + 2)*(25*b - 2)
Let m(p) be the second derivative of -2 + 85/4*p**2 - 20/3*p**3 + 32*p - 5/24*p**4. Factor m(j).
-5*(j - 1)*(j + 17)/2
Find m such that -12/7*m**5 + 177/7*m**3 + 45/7*m**2 + 0*m + 24*m**4 + 0 = 0.
-1/2, 0, 15
Factor -689 - 416 + 1417 + 0*o**2 + 315*o + 3*o**2.
3*(o + 1)*(o + 104)
Let h(x) be the first derivative of -5*x**3/3 + 135*x**2/2 - 900*x + 1209. Find w, given that h(w) = 0.
12, 15
Suppose 0 = d - 1 - 9. Let k be ((-5)/(-3))/(10/12). Suppose g**4 - 7*g**2 - d*g**2 + 16*g**k = 0. What is g?
-1, 0, 1
Let r(t) = 30*t**2 - 171*t + 147. Let z(l) = -7*l**2 + 40*l - 37. Let p(j) = 5*r(j) + 21*z(j). Factor p(q).
3*(q - 7)*(q + 2)
Suppose 51*m - 47 = 157. Let y(b) be the first derivative of 0*b + 4/25*b**5 + 4/15*b**3 - 1/10*b**2 - 1/30*b**6 - 7 - 3/10*b**m. Factor y(c).
-c*(c - 1)**4/5
Let m(b) be the second 