20829 - 45*q**3 + 145*q**2 + 285*q**2 - 20829. Let s(f) = -35*d(f) - 4*n(f). Factor s(m).
5*m*(m - 6)*(m - 2)
Let c be 256/120 + (-1536)/(-576). Determine i, given that -12/5*i**4 - 15*i**3 - c - 132/5*i - 162/5*i**2 = 0.
-2, -1/4
Suppose -54 = -18*v - 0*v. Suppose -3*i = -d - 2*i + 10, -d - v*i + 10 = 0. Solve 15*g - 4*g**2 + 8*g**2 - 965*g**3 + 5*g**5 + 945*g**3 + 6*g**2 - d = 0.
-2, -1, 1
Let c(k) be the first derivative of -k**4/10 - 22*k**3/3 - 54*k**2/5 + 5452. Find j such that c(j) = 0.
-54, -1, 0
Suppose -6*k = 5*k + 308. Let u be 119/k + 5/1. Factor u*t**3 - 9/4*t + 3/2*t**2 + 0.
3*t*(t - 1)*(t + 3)/4
Let r(g) be the first derivative of -g**3/12 - 1517*g**2/4 + 8821. Factor r(b).
-b*(b + 3034)/4
Let n = 1493098/99 - -85352/33. Factor -2/9*c**3 - 3698/3*c + 86/3*c**2 + n.
-2*(c - 43)**3/9
Determine p so that -4*p**2 - 45*p + 46*p**2 - 16*p + 1792 - 46*p**2 + 13*p = 0.
-28, 16
What is a in -46/3*a - 281/9*a**3 + 73/9*a**4 + 347/9*a**2 + 0 - 1/9*a**5 = 0?
0, 1, 2, 69
Let k(x) be the second derivative of 7/6*x**3 + 17/5*x**2 + 0 + 1/60*x**4 - 93*x. Factor k(q).
(q + 1)*(q + 34)/5
Let m(v) be the second derivative of v**7/63 + v**6/45 - v**5/15 - v**4/9 + v**3/9 + v**2/3 - 577*v + 2. Factor m(t).
2*(t - 1)**2*(t + 1)**3/3
Let l(x) be the second derivative of x**5/600 - 13*x**4/120 + 5*x**3/12 - 60*x**2 + 115*x. Let a(h) be the first derivative of l(h). Solve a(s) = 0.
1, 25
Let m(n) be the first derivative of -1/5*n**5 + 2/5*n**4 + 1/15*n**3 + 1/60*n**6 - 154 + 4/5*n - 17/20*n**2. Solve m(b) = 0.
-1, 1, 8
Factor 12/5*s + 0 + 2*s**2 + 2/5*s**3.
2*s*(s + 2)*(s + 3)/5
Let x be 1/3 + (-14)/(-12). Suppose 52 = 4*b, 74*n + 5*b - 65 = 79*n. Factor -3/2*z + n + 3/4*z**2 - 3/4*z**4 + x*z**3.
-3*z*(z - 2)*(z - 1)*(z + 1)/4
Suppose -2*x = 2*x - 20. Suppose -3*v + 3*b = -60, -x*v - 45 = -7*v - 3*b. Determine t, given that 6*t**2 + v*t**3 + 14*t**4 - 7*t**5 - 8*t**4 - 2*t**5 = 0.
-1, -1/3, 0, 2
Let x(s) be the first derivative of -s**6/40 - 11*s**5/20 + 25*s**4/8 - 13*s**3/2 + 43*s**2/2 - 60. Let r(d) be the second derivative of x(d). Factor r(z).
-3*(z - 1)**2*(z + 13)
Find i such that 2958 + 1630 + 11388 - 1396 + 2830*i**2 + 5*i**3 - 2965*i**2 = 0.
-9, 18
Let l = 14893/3 + -44621/9. Factor -6*q**2 + 2/9*q**4 - 20/9 + l*q + 14/9*q**3.
2*(q - 1)**3*(q + 10)/9
Let q(m) be the second derivative of -m**4/30 + 664*m**3/15 + 17*m - 96. Factor q(t).
-2*t*(t - 664)/5
Let y(o) = -15*o**4 + 44*o**3 + 295*o**2 + 501*o + 351. Let l(c) = 2*c**4 - c**3 - 7*c**2 + c - 1. Let g(s) = -35*l(s) - 5*y(s). Determine j so that g(j) = 0.
-2, 43
Let i(f) be the first derivative of f**4/18 - 14*f**3/27 + 3858. Factor i(h).
2*h**2*(h - 7)/9
Let h(o) = -2*o**3 + 12*o**2 - 18*o - 4. Let k(p) = -3*p**3 + 13*p**2 - 16*p - 3. Let s(r) = -3*h(r) + 4*k(r). Suppose s(j) = 0. Calculate j.
0, 1, 5/3
Let w(h) be the first derivative of 0*h - 13/3*h**2 + 24 - 2/9*h**3. Determine d so that w(d) = 0.
-13, 0
Let c(b) be the first derivative of b**4/16 + b**3/2 + 9*b**2/8 - 502. Suppose c(n) = 0. What is n?
-3, 0
Let w(a) be the first derivative of -a**6/42 + 153*a**5/35 - 3033*a**4/14 + 15530*a**3/21 + 7125*a**2/2 + 28125*a/7 - 1429. Find y such that w(y) = 0.
-1, 5, 75
Let g(y) be the second derivative of y**7/63 + 4*y**6/15 - 9*y**5/10 + 7*y**4/9 - 10*y. Factor g(b).
2*b**2*(b - 1)**2*(b + 14)/3
Let y be (-1)/(70/(-30) + 2). Factor -4*o**3 + 6*o**3 - 2*o**3 + 5*o**y - 2*o**5 - 3*o**3.
-2*o**3*(o - 1)*(o + 1)
Let s be 104/(-260) + ((-777)/90)/(-7). What is c in -1/6*c**2 + 0 + s*c = 0?
0, 5
Suppose 3*u + 187 - 19 = 0. Let l = 60 + u. Solve -4*g**4 - g + l - 64*g**3 + 20*g**3 - 3*g - 36*g**2 - 12*g**4 = 0 for g.
-1, 1/4
Let s = -176 - -179. Let q(u) = -u**2 + 182*u + 8102. Let c(p) = -2*p**2 + 183*p + 8103. Let v(x) = s*q(x) - 2*c(x). Factor v(h).
(h + 90)**2
Let t(h) be the second derivative of -h**9/9072 - h**8/56 - 15*h**7/14 - 25*h**6 - 29*h**3/3 + h + 75. Let q(j) be the second derivative of t(j). Factor q(m).
-m**2*(m + 30)**3/3
Let t(a) be the second derivative of a**5/100 + 5*a**4/12 + 53*a**3/10 + 27*a**2/2 - 155*a - 7. Solve t(z) = 0 for z.
-15, -9, -1
Let h = -500 - -592. Suppose -110 + h = -9*m. Factor 1/4*j**3 + 1/4 + 3/4*j**m + 3/4*j.
(j + 1)**3/4
Let 1/2*q**3 + 23/2*q**2 + 0 + 51*q = 0. Calculate q.
-17, -6, 0
Let o = -47 + 51. Factor 0*w**o - 1024 - 4*w**4 + 30118*w - 772*w**2 - 32038*w + 120*w**3.
-4*(w - 16)**2*(w + 1)**2
Let j(k) = -2*k**2 + 12*k - 8. Let i = -65 - -69. Suppose -12 = 4*s - i. Let l(h) = h. Let c(g) = s*l(g) + j(g). Factor c(x).
-2*(x - 4)*(x - 1)
Let v(f) be the first derivative of -f**5/300 - 43*f**4/240 - 7*f**3/20 - 11*f**2 - 37. Let t(d) be the second derivative of v(d). Factor t(k).
-(k + 21)*(2*k + 1)/10
Let x(r) be the second derivative of r**6/6 + 3*r**5/2 - 15*r**4/4 - 35*r**3/3 - 2*r - 93. Factor x(n).
5*n*(n - 2)*(n + 1)*(n + 7)
Let q(u) be the third derivative of u**5/20 - 3*u**4/2 - 133*u**3/2 + 430*u**2. Let q(i) = 0. What is i?
-7, 19
Let j = -6683 - -6685. Let w(s) = -21*s**3 - 25*s**2 + 3*s + 7. Let o(l) = -1 + l + l**3 + 4*l**2 - 3*l**2 - 2*l. Let g(u) = j*w(u) + 14*o(u). Factor g(q).
-4*q*(q + 1)*(7*q + 2)
Let r = 80 + -75. Factor -w**r - 5*w**3 - 3*w**2 - 20*w**3 + 30*w**3 - w**4.
-w**2*(w - 1)**2*(w + 3)
Let -17*l**5 + 40*l**2 + 47*l**2 + 6*l - 60*l + 33*l**5 + 45*l**3 - 87*l**4 - 7*l**5 = 0. What is l?
-1, 0, 2/3, 1, 9
Let u(d) = d**3 - 5. Let z(l) = -14*l**3 + 48*l**2 - 92*l + 65. Let y(k) = 52*u(k) + 4*z(k). Factor y(a).
-4*a*(a - 46)*(a - 2)
Let s(t) be the first derivative of t**6/24 - 5*t**5/12 + 5*t**4/6 + 11*t**2/2 + 7*t + 110. Let r(g) be the second derivative of s(g). Factor r(v).
5*v*(v - 4)*(v - 1)
Let s(g) = 28*g**2 + 622*g - 48. Let u(j) = 13*j**2 - j + 1. Let k(m) = -s(m) + 4*u(m). Find c such that k(c) = 0.
1/12, 26
Let r(c) be the third derivative of -1/200*c**6 + 0*c + 0 + 2/5*c**3 + 73*c**2 + 3/50*c**5 - 9/40*c**4. Factor r(t).
-3*(t - 4)*(t - 1)**2/5
Let w(r) = -r**3 + 11*r**2 - 19*r + 26. Let f be w(7). Solve f*s - 16 + 16*s + 71 + 25 - 3*s**2 + 28 = 0.
-1, 36
Factor 18*m**2 + 0 - 243/4*m + 3/4*m**3.
3*m*(m - 3)*(m + 27)/4
Suppose 76*q = -2*q + 7644. Suppose r = 50*r - q. Factor 1/2*y**r - 2*y + 3/2.
(y - 3)*(y - 1)/2
Factor -322/3*q**2 - 968/9*q + 0 + 2/9*q**3.
2*q*(q - 484)*(q + 1)/9
Let d(u) be the first derivative of -u**8/2240 + u**7/560 - u**6/480 - 4*u**3/3 + 3*u**2/2 + 86. Let m(j) be the third derivative of d(j). Factor m(h).
-3*h**2*(h - 1)**2/4
Let o be 6075/729*(-120)/(-250). Find w such that 3/8*w - 3/8*w**o - 9/4 - 3/8*w**3 + 21/8*w**2 = 0.
-3, -1, 1, 2
Let a(o) = -2*o**2 - 2*o - 9. Let n(t) = -22*t**2 + 242*t - 90. Let g(y) = -10*a(y) + n(y). Factor g(j).
-2*j*(j - 131)
Let k be (-32)/(-32) + (2 - 0). What is d in 19*d + 2106 - 14*d**2 - 7*d**4 + 28*d**k - 73*d**2 - 2092 + 33*d**3 = 0?
-2/7, 1, 7
Let q(x) be the first derivative of 1/6*x**4 + x**3 - 1/30*x**5 + 9*x**2 - 2 + 0*x. Let l(u) be the second derivative of q(u). Factor l(b).
-2*(b - 3)*(b + 1)
Find w such that -12*w + w**4 + 2677 - 2677 - w**2 + 12*w**3 = 0.
-12, -1, 0, 1
Suppose 8*o = -33*o - 395 + 1010. Factor -33/5*g**3 + 21*g**2 + 3/5*g**4 - o*g + 0.
3*g*(g - 5)**2*(g - 1)/5
Let n(l) be the first derivative of -2*l**3 + 4 + 4*l**2 + 1/5*l**5 + 0*l**4 - 3*l. Let u(c) be the first derivative of n(c). What is w in u(w) = 0?
-2, 1
Let t be -3*2*(-2)/4. Factor i + 10*i - 4*i - i**t - 3*i.
-i*(i - 2)*(i + 2)
Let t be -1770*-23*22/13915. Factor -6/11*h**2 - t*h - 20886/11.
-6*(h + 59)**2/11
Let b(c) be the second derivative of c**5/30 + 23*c**4/36 - 73*c**3/18 - 7*c**2 - 2*c + 2379. Factor b(r).
(r - 3)*(r + 14)*(2*r + 1)/3
Let p(l) be the second derivative of 1/21*l**7 - 2*l + 3/4*l**3 + 0*l**2 + 61/40*l**5 + 52 - 7/15*l**6 - 7/4*l**4. Let p(c) = 0. Calculate c.
0, 1/2, 3
Let x be (861/420)/(-41)*(-6 + 6). Factor 2/3*f**3 + x + 46/3*f**2 - 16*f.
2*f*(f - 1)*(f + 24)/3
Let k(d) be the first derivative of -1156/21*d**3 - 1/7*d - 34/7*d**2 - 45. Factor k(c).
-(34*c + 1)**2/7
Suppose 0 = -4*s - 16, u - 2*u = -s - 7. Determine r so that u*r**3 + 20242*r**2 + 2*r - r**5 + 1 - 20237*r**2 - 1 - r**4 = 0.
-1, 0, 2
Let d be (-24)/14*(-1071)/408. Factor 3/2 - d*b**3 + 21/2*b**2 + 17/2*b.
-(b - 3)*(3*b + 1)**2/2
Suppose -135*c = -133*c + 30. Let n be