-f**4 + f**3 - 2*f**2. Let k(a) = -10*s(a) + 2*t(a). Factor k(n).
4*n**2*(n - 5)*(n + 1)*(n + 6)
Let q(y) = 8*y**2 - 713*y + 7680. Let x(v) = 5*v**2 - 475*v + 5120. Let m(k) = -5*q(k) + 7*x(k). Let m(a) = 0. What is a?
16, 32
Let s(p) = -p**3 + 10*p**2 + 9*p - 9. Let z be s(9). Determine n so that -25*n**2 - z + 55*n + 3 - 40*n - 400*n = 0.
-15, -2/5
Let k(m) be the second derivative of m**4/21 + 22*m**3/21 + 15*m - 22. Factor k(s).
4*s*(s + 11)/7
Suppose -432*s + 433*s = 2*z + 236, 5*s = -6*z + 1212. Factor s + 3/5*j**2 - 24*j.
3*(j - 20)**2/5
Let n(c) be the first derivative of -3*c**5 + 63/2*c**4 + 53 + 243*c - 108*c**3 + 81*c**2. Factor n(i).
-3*(i - 3)**3*(5*i + 3)
Let d(h) be the second derivative of -h**6/6 - 463*h**5/4 + 2335*h**4/2 - 14050*h**3/3 + 9380*h**2 + 254*h + 1. Determine l, given that d(l) = 0.
-469, 2
Factor -5*c**2 - 225*c - 218*c - 227*c + 660*c.
-5*c*(c + 2)
Factor -135 + 180*w**2 - 135*w + 130*w**3 + 5*w**5 - 46*w**2 - 44*w**2 + 45*w**4.
5*(w - 1)*(w + 1)*(w + 3)**3
Let l(w) be the first derivative of -2*w**3/15 + 584*w**2/5 - 170528*w/5 + 3074. Find j, given that l(j) = 0.
292
Let w(u) be the third derivative of 0*u + 99*u**2 + 0 - 1/9*u**3 - 1/36*u**4 + 1/180*u**6 + 1/90*u**5. Solve w(o) = 0.
-1, 1
Suppose -28 = -254*c + 250*c + i, 2*c - 42 = 4*i. Factor 16/7*k**2 + 0*k - 4/7*k**c + 0 + 0*k**3 - 12/7*k**4.
-4*k**2*(k - 1)*(k + 2)**2/7
Let o(n) = 33*n**2 - 152*n - 13. Let g(h) = -100*h**2 + 452*h + 40. Suppose 1115*k + 12 = 1111*k. Let j(q) = k*g(q) - 8*o(q). What is c in j(c) = 0?
-1/9, 4
Suppose 2*a = -2*o - 3 + 1, -4*o - a = 7. Let i be -13 - 536/(-40) - o/(-10). Factor 2/5*p - i*p**2 + 0.
-p*(p - 2)/5
Suppose 48*b + 281 = 377. Let y(h) be the second derivative of -3/5*h**b - 9/100*h**5 + 1/10*h**4 + 3/10*h**3 - 8*h + 0. What is n in y(n) = 0?
-1, 2/3, 1
Determine l so that -116/13*l + 118/13 - 2/13*l**2 = 0.
-59, 1
Let z = -49 + 51. Let d(q) = 3*q - 9. Let s be d(4). Let -37*i**2 - 2*i**4 + i**s + 37*i**z + 0*i**3 + i**5 = 0. What is i?
0, 1
Let i = -113928 - -683569/6. Factor 0*m - i*m**5 + 0*m**2 - 1/6*m**3 + 1/3*m**4 + 0.
-m**3*(m - 1)**2/6
Let j = 1295/596 + 6/1043. Let r = j - 7/4. Solve 0*c**2 - r*c**4 + 0 - 9/7*c**3 + 0*c = 0 for c.
-3, 0
Let t(p) = -15*p**4 - 2506*p**3 - 5040*p**2 + 7470*p + 7. Let y(r) = -10*r**4 - 1670*r**3 - 3365*r**2 + 4980*r + 5. Let k(a) = -5*t(a) + 7*y(a). Factor k(o).
5*o*(o - 1)*(o + 3)*(o + 166)
Let q(l) be the first derivative of -1/18*l**4 - 1/3*l**3 + 18 + 0*l - 1/270*l**5 + 6*l**2. Let c(o) be the second derivative of q(o). Solve c(n) = 0 for n.
-3
Let -27/2*s + 3/2*s**2 + 27 = 0. What is s?
3, 6
Let v be 8/18*1308/168. Let d = v - 26/9. Let 16/7 + 12/7*h**4 + 4/7*h**3 + 0*h - d*h**5 - 4*h**2 = 0. What is h?
-1, 1, 2
Suppose 5*q + o - 5 = 0, 5 = -5*q - 7*o + 4*o. Find r such that -5120 - 5*r**q - 264*r - 50*r - 6*r = 0.
-32
Suppose r + 32*a - 29*a = -20, -4*r + a = 15. Let n(i) = -45*i - 225. Let z be n(r). Solve -1/3*h + z - 1/2*h**3 - 5/6*h**2 = 0 for h.
-1, -2/3, 0
Determine x so that 5*x**5 + 16569*x + 900*x**2 + 245*x**4 + 920*x**3 - 33134*x + 16565*x = 0.
-45, -2, 0
Let -3*k**4 + 353*k + 105*k**2 - 3*k**3 - 54006 + 0*k**4 + 54384 + 34*k = 0. Calculate k.
-3, -2, 7
Let j = -6396561/7 - -913815. Find o, given that 20/7*o**2 - 2/7*o**5 + 30/7*o**3 - j - 120/7*o + 0*o**4 = 0.
-2, 3
Let a(k) be the third derivative of k**5/420 + 15*k**4/56 + 82*k**3/21 - 639*k**2. Solve a(u) = 0 for u.
-41, -4
Factor 0 - 676/7*s - 2/7*s**3 + 678/7*s**2.
-2*s*(s - 338)*(s - 1)/7
Let r(y) = 2*y**2 - y - 4. Let l be r(5). Let m = -6834 + 6899. Find i such that -108*i**3 + 15*i**4 + m - 116*i - l + 180*i**2 + 5*i**4 = 0.
2/5, 1, 3
Suppose 0 = 9*n + 4500 - 1584. Let h = -319 - n. Determine y, given that 46/3*y**2 + 2/3*y**3 - 7/3*y**4 - 1/3*y**h - 65/3*y + 25/3 = 0.
-5, 1
Let i = 125 - 123. Factor 6*m + 3*m**2 - 6*m**i + 9 + 0*m**2.
-3*(m - 3)*(m + 1)
Suppose 2*i + 3*i = 25. Determine m, given that -43 - 31 + 60*m + i*m**2 + 9 = 0.
-13, 1
Suppose 12*v = 2*v + 20. Factor -4*p + 33 + 0*p**2 - 33 + v*p**3 + 2*p**2.
2*p*(p - 1)*(p + 2)
Let w = -168738 + 674961/4. Factor w + 121/4*g**2 - 33/2*g.
(11*g - 3)**2/4
Let i(y) = -2*y**4 - 16*y**3 + 14*y**2 - 36*y + 8. Let s(b) = -b**3 - b**2 - 3*b + 1. Let l(o) = i(o) - 8*s(o). Factor l(n).
-2*n*(n - 1)**2*(n + 6)
Let y(n) be the first derivative of 3/4*n**2 + 3/4*n**4 + 0*n**5 + 0*n - 1/12*n**6 - 29 - 4/3*n**3. Factor y(k).
-k*(k - 1)**3*(k + 3)/2
Let z(g) be the third derivative of g**9/181440 + g**8/30240 - g**7/3780 - g**6/270 + g**5/30 + 40*g**2. Let t(r) be the third derivative of z(r). Factor t(d).
(d - 2)*(d + 2)**2/3
Let m(s) be the third derivative of s**8/448 - 23*s**7/70 + 1011*s**6/80 + 1081*s**5/20 + 2209*s**4/32 + 6688*s**2. Factor m(w).
3*w*(w - 47)**2*(w + 1)**2/4
Let r = 126 - 117. Let d(t) = -t**2 + 5*t + 46. Let n be d(r). Factor -36*w + 5*w**4 + 3*w**5 - 3*w**3 + 4*w**4 - 20*w**2 - 2 - n - 13*w**2.
3*(w - 2)*(w + 1)**3*(w + 2)
Let d = -2008440/13 + 154498. Let -2/13*u**2 - 32/13*u + d = 0. Calculate u.
-17, 1
Determine n so that 354 + 7/2*n**3 + 369/2*n**2 - 1292*n = 0.
-59, 2/7, 6
Let r(v) = v**4 + 11*v**3 - v**2 + 1. Let k(c) = 6*c**4 + 78*c**3 + 144*c**2 + 171*c + 69. Let w(x) = -k(x) + 3*r(x). Let w(p) = 0. What is p?
-11, -2, -1
Let c(o) be the second derivative of -5/33*o**3 + 3 + 0*o**2 + 1/22*o**5 - 6*o - 1/66*o**4 + 1/165*o**6. Factor c(q).
2*q*(q - 1)*(q + 1)*(q + 5)/11
Let b(y) be the third derivative of 5*y**8/336 + 7*y**7/6 + 61*y**6/8 + 45*y**5/4 - 2933*y**2. Determine f so that b(f) = 0.
-45, -3, -1, 0
Suppose -5*h + 11 = -29. Factor h + 290*b**2 - 259*b**3 - 59*b**5 - 191*b**3 - 80*b + 270*b**4 + 5*b**5.
-2*(b - 2)**2*(3*b - 1)**3
Let p = -975 - -2927/3. Let t = 60 - 58. Factor 2*q + 0 + p*q**t.
2*q*(q + 3)/3
Suppose 26*w - 225 = -21*w - 37. Let z(j) be the first derivative of -2 - 14/3*j**3 - 18*j - 1/2*j**w - 15*j**2. Let z(x) = 0. Calculate x.
-3, -1
Let s(z) be the first derivative of 2*z**3/21 + 20*z**2/7 + 951. Determine i, given that s(i) = 0.
-20, 0
Suppose 5*x + 2*z = -0*z + 123, -5*z = -4*x + 72. Let g(i) = -2*i + 49. Let f be g(x). Factor -16*u**2 + 3*u**5 - 18*u**4 + u**3 + 3*u**3 - 8*u**2 + 32*u**f.
3*u**2*(u - 2)**3
Let k(f) be the first derivative of -13 - 2/3*f**3 + f**2 + 3*f. Let u(o) = -o**2 - o - 1. Let s(r) = k(r) - u(r). Find l, given that s(l) = 0.
-1, 4
Let o(j) = -34*j**4 + 84*j**3 + 83*j**2 - 22*j + 1. Let c(l) = -33*l**4 + 84*l**3 + 83*l**2 - 16*l. Let y(k) = 2*c(k) - 3*o(k). Factor y(q).
(q - 3)*(q + 1)*(6*q - 1)**2
Factor -307*h + 3*h**2 - h**2 + 455 + 505*h + 305.
2*(h + 4)*(h + 95)
Suppose -3*m**3 - 21*m + 1/4*m**4 + 25/2*m**2 + 45/4 = 0. What is m?
1, 3, 5
Factor -168/17 + 1346/17*a - 16/17*a**2.
-2*(a - 84)*(8*a - 1)/17
Let v = 335537/56 + -5992. Let o = 269/168 + v. Let -4*k**3 + 4*k - 4/3*k**4 + o*k**2 + 0 = 0. Calculate k.
-3, -1, 0, 1
Let c(o) be the first derivative of -5*o**3/3 - 4105*o**2 - 3370205*o + 7284. Factor c(b).
-5*(b + 821)**2
Factor 172*k + 146*k**2 + 127 + 69 + 143*k**2 + 164 - 293*k**2.
-4*(k - 45)*(k + 2)
Factor -5/8*u**3 - 3*u + 0 + 23/8*u**2.
-u*(u - 3)*(5*u - 8)/8
Let u(c) be the second derivative of -2*c + 8/3*c**3 + 5 + 1/12*c**4 - 1/20*c**5 - 8*c**2. Factor u(l).
-(l - 4)*(l - 1)*(l + 4)
Let c(a) be the second derivative of -7*a**7/9 - 4333*a**6/45 + 684*a**5 - 14444*a**4/9 + 11888*a**3/9 - 496*a**2 - 12396*a. Suppose c(f) = 0. Calculate f.
-93, 2/7, 2
Let b = 49 + -47. Determine u so that -3*u**2 + 110*u + 111*u + 0*u**b + 3*u**4 - 3*u**3 - 218*u = 0.
-1, 0, 1
Let g(j) = 2*j**3 + 13*j**2 + 5*j - 6. Let q(c) = c**3 + 7*c**2 + 2*c - 4. Let n(x) = 3*g(x) - 5*q(x). Solve n(s) = 0 for s.
-2, -1
Let a(v) = -3*v**2 - 13*v + 5. Let x be a(5). Let m = x + 138. Let 3 - 2*g**2 - 8 - m + 10*g = 0. What is g?
1, 4
Factor -382*u - 10*u**3 - 396 - 3*u**3 + 14*u**3 - 8*u**3 + 9*u**3 + 16*u**2.
2*(u - 11)*(u + 1)*(u + 18)
Suppose -1704*p + 35402 + 73645 = 17031. Factor 3*o**2 - 45/2*o - p + 3/2*o**3.
3*(o - 4)*(o + 3)**2/2
Let y(b) = 12*b**2 + 37*b - 890. Let j(m) = -17*m**2 - 55*m + 1339. Let t(o) = -5*j(o) - 7*y(o). Factor t(z).
(z - 15)*(z + 31)
Let l(o) be the first derivative of 9/28*o**4 + 35 + 22/21*o**3 - 24/7*o - 10/7*o**2 + 1/42*o**6 - 8/35*o**5. Determine c so tha