5*f + f**3 + 2*f. Let w(o) = g*p(o) + i(o). Factor w(l).
-2*l*(l - 1)*(l + 1)**2
Suppose 0 = 129*w - 77*w. Let c(x) be the second derivative of w - 15/2*x**2 - 25/6*x**3 + 1/4*x**5 + 9*x - 5/12*x**4. Solve c(v) = 0.
-1, 3
Let j(g) be the third derivative of g**8/1512 - 2*g**7/135 - 31*g**6/540 - 8*g**5/135 - 305*g**2. Suppose j(z) = 0. Calculate z.
-1, 0, 16
Let g(k) be the first derivative of k**6/27 + 28*k**5/45 + 49*k**4/18 - 32*k**3/27 - 176*k**2/9 + 256*k/9 + 14120. Find w such that g(w) = 0.
-8, -4, 1
Let o(h) = 10*h**2 - 214*h + 28. Let p(r) = -9*r**2 + 215*r - 26. Let n(i) = 13*o(i) + 14*p(i). Factor n(g).
4*g*(g + 57)
Let y(r) = r**3 + 29*r**2 + 3. Let l be y(-29). Factor 20 - 11*b**2 + 21 - 41 - b**l.
-b**2*(b + 11)
Let i(j) = 2*j**3 - 32*j**2 - 7*j + 1239. Let r be i(12). Solve -15/7*f + 9/7 + 3/7*f**2 + 3/7*f**r = 0 for f.
-3, 1
Factor 1208*m**2 + 25/3*m**4 + 0 - 724/3*m - 1515*m**3.
m*(m - 181)*(5*m - 2)**2/3
Factor -7304 + 7304 - 3*s**2 - 3*s**4 - 12*s**3 + 18*s.
-3*s*(s - 1)*(s + 2)*(s + 3)
Solve -465/2 + 1/4*n**2 + 463/4*n = 0.
-465, 2
Let o be ((-16)/24)/((-3)/2637). Factor 8*u + u**2 + 8 - 3*u**2 + o*u**3 - 588*u**3.
-2*(u - 2)*(u + 1)*(u + 2)
Let q = -29 + 33. Let u(m) = -31*m**2 + 371*m + 106. Let s(t) = 30*t**2 - 370*t - 105. Let v(z) = q*s(z) + 5*u(z). Suppose v(c) = 0. Calculate c.
-2/7, 11
Let v(c) be the second derivative of -5*c**4/12 + 40*c**3/3 + 285*c**2/2 - 4*c - 149. Let v(w) = 0. What is w?
-3, 19
Let k = 12482 - 37430/3. Factor k*a + 10/3 - 4/3*a**3 + 2/3*a**2.
-2*(a + 1)**2*(2*a - 5)/3
Let n(v) be the third derivative of -v**5/12 - 35*v**4/24 + 20*v**3/3 + 77*v**2 - 10*v. Suppose n(u) = 0. Calculate u.
-8, 1
Let a(y) be the second derivative of -y**7/35 - 56*y**6/225 - 31*y**5/50 + y**4/5 + 116*y**3/45 + 8*y**2/5 + 13*y + 63. Determine o so that a(o) = 0.
-3, -2, -2/9, 1
Solve 2/3*f**5 - 44/3*f**2 + 14/3*f + 0 + 16*f**3 - 20/3*f**4 = 0 for f.
0, 1, 7
Solve -75/2 - 115/2*p - 5/2*p**3 - 45/2*p**2 = 0.
-5, -3, -1
Let i(q) be the second derivative of 23/30*q**6 + 0*q**2 - 1/3*q**3 + 0 + 27/20*q**5 - 25/42*q**7 - 23/12*q**4 + 163*q. Suppose i(g) = 0. What is g?
-1, -2/25, 0, 1
Let q(n) = 5*n**4 - 487*n**3 + 11828*n**2 - 84498*n - 3. Let u(o) = -10*o**4 + 975*o**3 - 23660*o**2 + 168990*o + 5. Let l(y) = -5*q(y) - 3*u(y). Factor l(r).
5*r*(r - 66)*(r - 16)**2
Let v(l) be the first derivative of -3*l**4 + 64/3*l**3 + 134*l**2 + 262 - 96*l. Suppose v(d) = 0. Calculate d.
-3, 1/3, 8
Let s be 28/(-98) + 37/7. Let p(t) be the first derivative of 0*t**3 - 3/25*t**s + 0*t**4 + 0*t + 15 + 0*t**2 - 1/30*t**6. Suppose p(b) = 0. What is b?
-3, 0
Let j = -3289/3 - -9881/9. Let a(f) be the first derivative of 1/9*f**6 + j*f**3 + 19 + 3/2*f**4 + 0*f + 2/3*f**2 + 2/3*f**5. Factor a(o).
2*o*(o + 1)**3*(o + 2)/3
What is o in 1/2*o**2 + 49/2*o + 272 = 0?
-32, -17
Let q(a) = -4*a + 3. Let b be q(-14). Solve -159 + 104*p**2 - b*p - 50*p**3 + 163 + p = 0.
2/25, 1
Let i(r) be the first derivative of r**3 - 402*r**2 + 1178. Factor i(o).
3*o*(o - 268)
Factor -78*q + 0 + 1/2*q**3 + 10*q**2.
q*(q - 6)*(q + 26)/2
Let h(w) be the first derivative of -1/4*w**4 + 3*w**3 - 9*w + 1/2*w**2 + 194. Find v such that h(v) = 0.
-1, 1, 9
Let y = -61459 + 61464. Factor 8/7 + 6/7*r**3 + 6*r - y*r**2.
(r - 4)*(r - 2)*(6*r + 1)/7
Let h(x) be the first derivative of -x**9/7560 + 17*x**8/4200 - 4*x**7/525 - 59*x**3/3 + 120. Let g(i) be the third derivative of h(i). Factor g(y).
-2*y**3*(y - 16)*(y - 1)/5
Let z(f) be the second derivative of 0*f**2 - 1/170*f**5 + 70*f - 1 + 1/34*f**4 + 0*f**3. Determine y, given that z(y) = 0.
0, 3
Let -182/3*j**3 + 418/9*j**2 - 560/9*j**4 - 46/3 + 274/9*j - 8/9*j**5 = 0. What is j?
-69, -1, 1/2
Let x(t) be the second derivative of 10*t**3 - 1/20*t**5 + t**4 - 149*t + 32*t**2 + 2. Factor x(q).
-(q - 16)*(q + 2)**2
Let i = -4097829/69220 + 1/13844. Let a = -4982/85 - i. Factor 22/17*z + 14/17*z**2 + a + 2/17*z**3.
2*(z + 1)**2*(z + 5)/17
Let h(x) = -11*x**3 - 175*x**2 - 1605*x + 12583. Let r(n) = 7*n**3 + 116*n**2 + 1072*n - 8390. Let d(v) = -5*h(v) - 8*r(v). Factor d(q).
-(q - 5)*(q + 29)**2
Let x(h) be the second derivative of 15*h + 97/4*h**4 - 2303/2*h**3 - 7203/2*h**2 - 3/20*h**5 - 2. Find s such that x(s) = 0.
-1, 49
Let s(j) be the third derivative of 1/60*j**6 + 0*j + 1/9*j**4 + 1/630*j**7 + 1/15*j**5 + 0*j**3 - 9*j**2 + 3. Factor s(i).
i*(i + 2)**3/3
Let n(c) be the second derivative of -11/30*c**3 - 8 - 1/60*c**4 - c - c**2. Factor n(m).
-(m + 1)*(m + 10)/5
Let u(w) be the first derivative of -w**3/9 + 217*w**2/6 + 146*w - 3911. Factor u(x).
-(x - 219)*(x + 2)/3
Factor 99*x**4 + 94*x**4 + 4*x**2 - 192*x**4 - 4*x**3.
x**2*(x - 2)**2
Factor 2/9*q**3 - 926/3*q + 232 + 688/9*q**2.
2*(q - 3)*(q - 1)*(q + 348)/9
Let t(j) = -3*j**2 - 2232*j + 9. Let h(s) = 3*s**2 + 2217*s - 12. Let m(p) = 3*h(p) + 4*t(p). Determine z, given that m(z) = 0.
-759, 0
Let i = 149 - 111. Factor -256*v**2 - 80*v - 56*v**4 - i*v**4 + 58*v**4 - 228*v**3.
-4*v*(v + 5)*(3*v + 2)**2
Let a = -500 + 741. Suppose 2*y + 31 - a = 0. Factor 3*u**3 - 5*u**2 - 4*u**2 - 2*u**2 - 22*u**2 + y*u - 75.
3*(u - 5)**2*(u - 1)
Let y(i) be the third derivative of i**5/15 + 397*i**4/3 + 315218*i**3/3 + 1623*i**2. Let y(f) = 0. Calculate f.
-397
Let o(y) be the second derivative of y**5/10 - 37*y**4/6 - y**3/3 + 37*y**2 + 5418*y + 2. Suppose o(x) = 0. Calculate x.
-1, 1, 37
Let l(w) be the second derivative of w**4/36 + 5*w**3/18 + 906*w. Factor l(a).
a*(a + 5)/3
Let x = 291 + -289. Find i, given that -i**2 - 2*i**x - 60 + 39*i + i - 2*i**2 = 0.
2, 6
Let q(w) be the second derivative of -5 + 0*w**3 + 1/6*w**5 - 3*w + 0*w**2 + 2/9*w**4. Solve q(v) = 0 for v.
-4/5, 0
Let c(o) = -o**5 + o**3 - o**2 + 1. Suppose 1386*w - 1389*w = 36. Let b(m) = -2*m**5 + 2*m**4 - 3*m**2 + 3. Let j(x) = w*c(x) + 4*b(x). Solve j(f) = 0 for f.
-3, 0, 1
Let s be (1 - -1)*1 + 2. Suppose -56 = -39*q + 31*q. Determine o, given that -5*o - q*o + 0*o - 7*o**2 + s = 0.
-2, 2/7
Let s = 1/4 + -3/28. Let a be 3945/(-11046)*16/(-10). Factor -s*r**4 + 3/7 + 4/7*r**3 - 2/7*r**2 - a*r.
-(r - 3)*(r - 1)**2*(r + 1)/7
Factor -790 + 1335 - 673 + 48*x - 4*x**2.
-4*(x - 8)*(x - 4)
Let h(q) be the first derivative of 0*q + 1/90*q**6 - 1/15*q**5 - 13/3*q**3 + 1/6*q**4 - 8 + 0*q**2. Let b(n) be the third derivative of h(n). Factor b(m).
4*(m - 1)**2
Let h = -4843006 + 658653405/136. Let l = h - 269/8. Determine r so that 8/17*r**2 + l*r**3 + 0*r + 0 = 0.
-4, 0
Let k = 772/3 + -256. Suppose -2*g**3 - 2/3*g**4 + k*g**2 + 16/3 + 8*g = 0. What is g?
-2, -1, 2
Let h(d) = 205*d + 2667. Let b be h(-13). What is x in 6 + 0*x - 26/3*x**b - 8/3*x**3 = 0?
-3, -1, 3/4
Let r(n) = 33*n + 18. Let f be r(-8). Let w be (-213)/(-355) - (f/10)/1. Determine j, given that 109/5*j**2 - w*j**3 + 4/5 + 49/5*j**4 - 36/5*j = 0.
2/7, 1
Suppose -4*j + 80 = d, -5*j + 28 = 3. Let p = 1 - -1. Suppose 80 - 10*t**2 + 5*t**3 - d*t + 10*t**p = 0. Calculate t.
-4, 2
Factor -203/6*x**2 - 65/6*x**4 + 1/6*x**5 + 0 - 34/3*x - 67/2*x**3.
x*(x - 68)*(x + 1)**3/6
Let x(a) = a**2 - 8*a - 21. Let b be x(9). Let l = 15 + b. Factor 87*i**3 - 171*i**3 - i + 85*i**l.
i*(i - 1)*(i + 1)
Let t(l) = 6*l - 2. Let f(m) be the first derivative of -4*m + 3 + 13/2*m**2 + 1/3*m**3. Let b(j) = -2*f(j) + 5*t(j). Factor b(a).
-2*(a - 1)**2
Let f be (450/(-250))/(6/(-10)). Factor 13*y**f - 30*y - 2*y**4 - 3 + 3 - 14*y**2 + y**3 + 0.
-2*y*(y - 5)*(y - 3)*(y + 1)
Let b(g) be the third derivative of g**5/15 - 343*g**4/6 - 688*g**3/3 + 22*g**2 + 2*g - 59. Factor b(a).
4*(a - 344)*(a + 1)
Let c = -165092 - -821923/5. Let p = -707 - c. What is h in -4/15*h + 2/15*h**3 - p*h**2 + 2/15*h**5 + 0 + 2/5*h**4 = 0?
-2, -1, 0, 1
Let r(j) be the third derivative of j**7/560 - j**6/160 - j**5/32 + 3*j**4/32 - 70*j**2. Factor r(b).
3*b*(b - 3)*(b - 1)*(b + 2)/8
Let p be 390/(-33) + ((-24)/(-66))/(-2). Let k be ((-8)/p)/((-77)/(-66)). Factor 10/7*l**2 + 0 + 6/7*l**3 + k*l.
2*l*(l + 1)*(3*l + 2)/7
Let c be 3 - (-2 + -1) - (-184)/(-128)*4. Let z(q) be the first derivative of 1/4*q**2 + 1/12*q**3 + 13 + c*q. Factor z(v).
(v + 1)**2/4
Let a(y) = -3*y**3 - y**2 + 96*y + 450. Let d be a(-5). Let s(o) be the first derivative of -d*o - 10 + 40*o**2 - 5/3*o**3. Factor s(t).
-5*(t - 8)**2
Let z(h) be the 