**4 + 96*k**3 - 125*k**2. Let v(z) = 25*z**5 + 53*z**4 + 192*z**3 - 249*z**2. Let m(d) = 7*a(d) - 3*v(d). Factor m(c).
2*c**2*(c - 1)*(c + 8)**2
Let q(h) = -h**2 + 24*h + 150. Let w be q(29). Factor 0*s**2 + 7*s**3 - s - 2*s**2 - 3*s - w*s**3.
2*s*(s - 2)*(s + 1)
Suppose 3*u + 9 = -j + 2*j, -4*j + 8 = 2*u. Find w such that j*w**2 - w - 3 + 483*w**3 + 475*w**3 - 957*w**3 = 0.
-3, -1, 1
Let z(j) be the second derivative of j**4/6 + 4*j**3 + 11*j**2 - 1422*j + 1. Find d such that z(d) = 0.
-11, -1
Let z(d) = -16*d - 571. Let l be z(-36). Let i(s) be the third derivative of -1/120*s**6 - 1/60*s**l - 21*s**2 + 1/6*s**4 + 0*s + 0 + 2/3*s**3. Factor i(p).
-(p - 2)*(p + 1)*(p + 2)
Let i = -463 - -471. Suppose -i = 22*f - 23*f. Factor 3/2*y**4 + 15/2*y**2 - 3*y - 4 + f*y**3.
(y + 1)**2*(y + 4)*(3*y - 2)/2
Let l(n) = -3*n**3 - 19*n**2 + 56*n + 76. Let p(d) = -11*d**3 - 58*d**2 + 165*d + 226. Let t(c) = 21*l(c) - 6*p(c). What is s in t(s) = 0?
-1, 8, 10
Suppose 4*u = 9902*y - 9897*y + 21, -3*u + 7 = -20. Factor -11045*h - 235*h**2 - 5/3*h**y - 519115/3.
-5*(h + 47)**3/3
Let s be ((-6)/57)/(355/(-6745)). Factor 0 + 1/7*t**s + 8/7*t.
t*(t + 8)/7
Suppose 80*o = 72*o + 32. Determine x so that -8*x**o + 4*x + 8*x**2 + 0*x**5 + 4*x**3 + 2*x**5 - 7*x - 3*x = 0.
-1, 0, 1, 3
Let i(s) = -s**3 + 128*s**2 + 4930*s + 35. Let x be i(-31). Find c, given that 4/3*c**x + 0 + 8*c - 16/3*c**3 + 4/3*c**2 = 0.
-1, 0, 2, 3
Let u(t) be the second derivative of t**6/15 - 113*t**5/10 - 78*t**4 - 5999*t. Find k such that u(k) = 0.
-4, 0, 117
Suppose 16 = 4*b - 32. Let q = b + -8. Solve -v**4 - 63*v**3 + 4*v**2 - 3*v**4 + q*v + 59*v**3 = 0 for v.
-1, 0, 1
Suppose 184/3 + 464/3*c + 126*c**2 + 2/3*c**4 + 100/3*c**3 = 0. Calculate c.
-46, -2, -1
Let c be (-3)/(-14)*4069/195. Let g = c - 39/10. Factor -2/7*r**2 - 2/7*r**3 + 0 + g*r.
-2*r*(r - 1)*(r + 2)/7
Let u(l) be the first derivative of -l**3/3 - 3303*l**2 - 10909809*l + 13203. Solve u(b) = 0 for b.
-3303
Let q = 30 - 26. Let u = 112 + -56. Solve u*c**2 - 9*c - 5*c + 28*c**3 - 16*c**q + 26*c = 0.
-1, -1/4, 0, 3
Suppose 2*n - 23 = -3*k, -3*n = -5*k + 8 + 5. Determine h so that 12110*h**2 - 12072*h**2 + 0*h**3 - n*h**3 - 2*h**4 + 40*h = 0.
-5, -1, 0, 4
Let v = 350 - 346. Suppose -7*a**v + 627*a**3 - 678*a**3 + 4*a**4 = 0. Calculate a.
-17, 0
Let d be 763/21 - (5 - (-84)/(-18)). Suppose -d*a + 91 - 19 = 0. Factor 2/7*w**a - 2/7*w**4 + 0 + 2/7*w**3 - 2/7*w.
-2*w*(w - 1)**2*(w + 1)/7
Let r(s) be the first derivative of -4/7*s**2 + 0*s - 4/7*s**3 + 2/7*s**4 - 271. Factor r(i).
4*i*(i - 2)*(2*i + 1)/7
Let m(h) = -45718*h - 274300. Let x be m(-6). Determine z so that -15/2*z - x + 1/2*z**2 = 0.
-1, 16
Let t(f) be the first derivative of f**5/20 + f**4/16 - f**3 + 2627. Factor t(s).
s**2*(s - 3)*(s + 4)/4
Let i(p) be the second derivative of 0 + 15*p**2 + 173*p + 14/3*p**3 - 1/6*p**4. Let i(t) = 0. Calculate t.
-1, 15
Let a(c) = 2*c**3 - 30*c**2 + 11*c + 240. Let o be a(14). Factor 1/4*k**5 + 4*k + 6*k**o - 3/2*k**4 + 1/4*k**3 + 0.
k*(k - 4)**2*(k + 1)**2/4
Let v(s) be the third derivative of s**9/15120 - s**8/1400 + 3*s**7/1400 + 24*s**3 + 15*s**2 + 3. Let d(k) be the first derivative of v(k). Factor d(f).
f**3*(f - 3)**2/5
Suppose 4*b - 430 = 2*m, 4*m - m = 5*b - 539. Suppose 4*r - 2*l - b = 0, 8 = -2*l - 2. Factor -p**3 - 14*p - r*p**3 + 36*p**2 + 2 + 16*p**4 - 15*p**3.
2*(p - 1)*(2*p - 1)**3
Let a be 592/2704*13 - 2/(-13). Let p(z) be the second derivative of -9/4*z**4 + 2*z**a + 0 - 1/10*z**6 + 9/10*z**5 + 0*z**2 - 18*z. Factor p(y).
-3*y*(y - 4)*(y - 1)**2
Factor -64*p**3 + 256*p**3 + 8752 - 8752 + 3*p**5 - 60*p**4.
3*p**3*(p - 16)*(p - 4)
Factor -2/3*c**3 + 1628/3*c**2 + 3262/3*c + 544.
-2*(c - 816)*(c + 1)**2/3
Let c = 6241 - 6238. Let a(n) be the first derivative of 19 - 4/3*n**c - 4*n**2 - 4*n. Let a(i) = 0. Calculate i.
-1
Solve -697300 - 728480 - 6*n**2 + n**2 + 5340*n = 0 for n.
534
Factor -198744/5 + 1068/5*o**2 - 45318/5*o - 6/5*o**3.
-6*(o - 91)**2*(o + 4)/5
Let m be (24 - (-876)/(-36))/((-4)/60). Determine l so that 0 - 2*l**4 - 2/3*l**3 + 4/3*l**m - 2/3*l + 2*l**2 = 0.
-1, 0, 1/2, 1
Let 74/5 + 58/5*n**2 + 2148/5*n = 0. Calculate n.
-37, -1/29
Factor -1006/5*s**2 + 127006/5*s + 2/5*s**3 - 126002/5.
2*(s - 251)**2*(s - 1)/5
Let z(d) be the second derivative of d**5/5 + 7*d**4/3 - 80*d**3/3 - 200*d**2 + 11*d + 9. Factor z(q).
4*(q - 5)*(q + 2)*(q + 10)
Let y(d) be the first derivative of -3*d**4/28 - 58*d**3/7 + 177*d**2/14 - 487. Suppose y(m) = 0. Calculate m.
-59, 0, 1
Let l(k) be the third derivative of -3/70*k**7 + 0*k**3 + 71*k**2 - k + 5/8*k**6 + 19/20*k**5 - 9/8*k**4 + 0. Factor l(s).
-3*s*(s - 9)*(s + 1)*(3*s - 1)
Let z(s) = 14*s**4 + 678*s**3 - 2084*s**2 + 1384*s - 8. Let u(o) = -9*o**4 - 452*o**3 + 1389*o**2 - 923*o + 5. Let i(p) = 8*u(p) + 5*z(p). Factor i(c).
-2*c*(c - 2)*(c - 1)*(c + 116)
Let b(j) = -19*j - 98. Let o be b(-6). Factor -7*t**3 - 5*t + o*t**2 - 27*t + 5*t**3.
-2*t*(t - 4)**2
Let p(i) be the first derivative of -i**4/4 + 26*i**3/3 + 25*i**2/2 + 56*i + 484. Let d be p(27). Factor 2/3*b**4 + 0*b + 0 + b**3 + 1/3*b**d.
b**2*(b + 1)*(2*b + 1)/3
Suppose 4*w = -12, -4*w + 14 = -5*r + 66. Determine v so that 17*v**2 + 257*v**3 + 8*v + r*v**4 - 229*v**3 + 11*v**2 = 0.
-2, -1, -1/2, 0
Suppose 10*o = 11*o. Suppose o = -5*z + 4*l - 1, -3*z - 5*l = -2*l - 21. Factor 4*p + 49*p**2 + p**z + 52*p**2 - 93*p**2 + 3*p**3.
4*p*(p + 1)**2
Let t = 2 + 2. Factor -5*p + t*p + 18*p**3 - 17*p**3.
p*(p - 1)*(p + 1)
Suppose 162*j - 137*j = 0. Let c(p) be the third derivative of 0 + 1/45*p**5 + j*p**4 + 2*p**2 + 0*p**3 + 0*p. Factor c(i).
4*i**2/3
Let y be 3*(15/(-6) + 4). Let m = 9385/2 + -4682. Find f such that 3*f**3 + m*f**2 - y + 3*f = 0.
-3, -1, 1/2
Let r = 48 - 19. Solve -40 - 5*x**3 + r*x + 40*x**2 - 53*x + 29*x = 0 for x.
-1, 1, 8
Let v = -42228 + 42232. Determine i, given that 2/11*i**5 + 12/11*i + 2/11*i**2 + 0 - 14/11*i**3 - 2/11*i**v = 0.
-2, -1, 0, 1, 3
Factor -70*f + 0 - 65/3*f**2 - 5/3*f**3.
-5*f*(f + 6)*(f + 7)/3
Let p(v) = -16*v**3 - 1144*v**2 - 276*v - 36. Let r(s) = -2*s**2 - 2. Let m(o) = p(o) - 18*r(o). Factor m(z).
-4*z*(z + 69)*(4*z + 1)
Factor 420*r**4 - 177*r + 415*r**4 - 185*r + 106*r - 476*r**3 - 1144*r**2 - 819*r**4.
4*r*(r - 32)*(r + 2)*(4*r + 1)
Let n(d) be the third derivative of -3/20*d**4 + 0*d + 112*d**2 + 1/50*d**5 - 9/5*d**3 + 1/300*d**6 + 0. Determine h so that n(h) = 0.
-3, 3
Let m(p) be the third derivative of -p**8/84 - 8*p**7/105 + 2*p**6/15 + 16*p**5/15 + 148*p**2 - 4*p. Solve m(v) = 0 for v.
-4, -2, 0, 2
Let k(t) be the first derivative of t**6/3 - 42*t**5 - 109*t**4/2 + 626*t**3/3 + 528*t**2 + 424*t - 3321. Let k(l) = 0. Calculate l.
-1, 2, 106
Let i(v) = 2628*v - 144540. Let k be i(55). Factor k + 20/7*o**2 + 2/7*o**3 - 22/7*o.
2*o*(o - 1)*(o + 11)/7
Let p = -57 + -347. Let u = p + 1220/3. Factor u*b - 2/3*b**3 + 8/3 - 2/3*b**2.
-2*(b - 2)*(b + 1)*(b + 2)/3
Suppose 9*q - 28 = 179. Suppose -4*r + 20 = 4*k, 0 = k - 4*r + q - 3. Factor k*g - 12/7*g**2 + 0 + 2/7*g**3.
2*g**2*(g - 6)/7
Let 5 - i - 6 + 6*i**2 + 0 - 6 = 0. What is i?
-1, 7/6
Let a(z) = -12*z**3 + 13*z**2 + 178*z + 228. Let j(r) = -7*r**3 + 7*r**2 + 90*r + 108. Let f(g) = -3*a(g) + 5*j(g). Solve f(y) = 0 for y.
-6, -2, 12
Let x(t) be the first derivative of -14*t**6/15 - 344*t**5/25 - 101*t**4/5 - 88*t**3/15 + 867. Determine a, given that x(a) = 0.
-11, -1, -2/7, 0
Suppose 2*d + 5*o = 0, -119 = -5*d - 5*o - 104. Let g(y) be the third derivative of -5/4*y**4 - 25/2*y**3 - 1/20*y**d + 0 + 42*y**2 + 0*y. Factor g(q).
-3*(q + 5)**2
Let r(v) = 2*v + 37. Let l be r(-3). Factor 19 - l + 11*y**2 - 5*y**3 - 68 - 51*y**2 - 100*y.
-5*(y + 2)**2*(y + 4)
Let h = -1937/4 - -485. Let j(y) be the first derivative of 48 - 6*y**2 + 0*y - h*y**4 + 4*y**3. Determine d so that j(d) = 0.
0, 2
Let k = -4322/1047 + 8993/2094. Let x(r) = r - 3. Let o be x(5). Factor k*t + 1/6*t**o + 0.
t*(t + 1)/6
Let r(n) = 14*n**5 - 24*n**3 - 20*n**2 + 18*n + 12. Let g = -124 + 116. Let l(d) = -5*d**5 + 8*d**3 + 7*d**2 - 6*d - 4. Let x(p) = g*l(p) - 3*r(p). Factor x(z).
-2*(z - 2)*(z - 1)*(z + 1)**3
Let p(x) = -4*x**4 - 67*x**3 - 8*x**2 - x - 12. Let a(w) = w**4 - w**3 + 10*w**2 - 2*w - 3. Let o(v) = -4*a(v) + p(v). Suppose o(q) = 0. What is q?
-7, -1, 0, 1