Let m(i) be the first derivative of i**2/2 - 16*i + 9. Let k be m(18). Determine d so that -3*d**5 + k*d**5 + 5*d**4 - 369*d**2 - 6*d**3 + 365*d**2 + 8*d = 0.
-1, 0, 2
Let a(c) be the first derivative of c**6/12 + 37*c**5/10 + 35*c**4/4 - c**3/3 - 71*c**2/4 - 35*c/2 + 209. Factor a(p).
(p - 1)*(p + 1)**3*(p + 35)/2
Factor -373926*g**3 + 373921*g**3 + 320 + 3*g**2 + 7*g**2 + 200*g.
-5*(g - 8)*(g + 2)*(g + 4)
Factor 346445*m**3 - 4*m**4 - m + 19*m**2 + 29*m**2 - 346453*m**3 - 128 + 33*m.
-4*(m - 2)**2*(m + 2)*(m + 4)
Let s = 3395 + -30554/9. Let x(m) be the third derivative of 1/360*m**5 + 0*m - s*m**3 + 0*m**4 + 0 - 27*m**2. Factor x(f).
(f - 2)*(f + 2)/6
Factor -2/7*v**3 - 5282*v - 115926/7 + 550/7*v**2.
-2*(v - 139)**2*(v + 3)/7
Let h(u) be the first derivative of -u**6/21 + 26*u**5/35 + 23*u**4/7 + 64*u**3/21 + 850. Find m, given that h(m) = 0.
-2, -1, 0, 16
Let c(u) be the first derivative of u**4/16 + 4*u**3/3 - 123*u**2/8 + 99*u/2 - 8832. Solve c(j) = 0.
-22, 3
Let o(i) be the third derivative of -i**8/336 - 22*i**7/35 - 4613*i**6/120 - 8513*i**5/30 - 864*i**4 - 4096*i**3/3 + 49*i**2 + 6. Suppose o(j) = 0. What is j?
-64, -2, -1
Suppose -3*v + 132 = 5*s - 262, 0 = -2*s + 10. Let d be (1/2)/(v/12 - 10). Factor 2*k**d - 2*k + 1/2*k**3 + 0 - 1/2*k**4.
-k*(k - 2)*(k - 1)*(k + 2)/2
Let y(o) = 57*o + 401. Let w be y(-7). Let r(z) be the second derivative of -1/36*z**4 + 0*z**3 + 1/12*z**5 - 2/45*z**6 + 0 + 0*z**w - 6*z. Factor r(l).
-l**2*(l - 1)*(4*l - 1)/3
Suppose 28*q + 272 = 30*q. Find r such that 0*r - 191 + 116*r**3 - 59 - q*r**3 + 3*r**5 - 40*r**4 - 8*r**5 + 25*r + 290*r**2 = 0.
-5, -1, 1, 2
Let z(f) = -3*f**4 + 36*f**3 + 11*f**2 - 48*f - 56. Let j(i) = 6*i**4 - 78*i**3 - 18*i**2 + 96*i + 111. Let u(k) = -4*j(k) - 9*z(k). Solve u(o) = 0 for o.
-2, -1, 2, 5
Let a be (-1128)/(-1880) - (-64)/10. Let w(l) be the second derivative of 16*l + 0*l**4 + 0*l**2 + 0 - 1/8*l**3 + 3/40*l**5 - 1/56*l**a + 0*l**6. Factor w(i).
-3*i*(i - 1)**2*(i + 1)**2/4
Solve 5075*c**3 - 5071*c**3 + 5586 + 6958 + 3120*c**2 - 12528*c = 0 for c.
-784, 2
Let v(a) be the second derivative of 27/170*a**5 - 1 - 6/85*a**6 - 34*a - 15/17*a**2 + 1/3*a**3 + 77/102*a**4. Suppose v(q) = 0. Calculate q.
-1, -5/6, 1/3, 3
Let s(a) be the first derivative of 35*a**6/8 + 97*a**5/4 - 1725*a**4/16 + 275*a**3/12 + 90*a**2 + 35*a + 5238. Find t, given that s(t) = 0.
-7, -1/3, -2/7, 1, 2
Let m be 1*483/216 + (-2420)/2178. Determine j, given that -m*j - 3/2 + 3/8*j**2 = 0.
-1, 4
Let n(x) be the second derivative of -x**4/12 + 10*x**3/3 + 47*x**2/2 + 4*x. Let l be n(22). Find q, given that 15*q**3 - 33*q**l + 17*q**3 - q**4 = 0.
-1, 0
Let m = 5603/42 - 667/5. Let n(p) be the second derivative of 1/140*p**5 + 0*p**2 - m*p**6 - 34*p - 1/42*p**3 + 0 + 1/84*p**4. Factor n(a).
-a*(a - 1)**2*(a + 1)/7
Let w be ((-9)/(-6) - 1) + (-660)/(-72) + -9. Factor 0 + w*s**2 - 4*s + 2/3*s**4 + 8/3*s**3.
2*s*(s - 1)*(s + 2)*(s + 3)/3
Let a(y) be the first derivative of 75 - 1/5*y**5 - 5*y**3 - 17/2*y**2 + 16*y + 17/4*y**4. Determine v, given that a(v) = 0.
-1, 1, 16
Let u = 42016/3 + -294103/21. Factor 6*j**4 + 0 - u*j**5 - 384/7*j - 216/7*j**3 + 480/7*j**2.
-3*j*(j - 4)**3*(j - 2)/7
Suppose 0 = 4*q - 2*a - 52, -q = 3*q + 5*a - 38. Factor -q*l**2 + 140 - 22*l**2 + 39*l**2 + 80*l.
5*(l + 2)*(l + 14)
Let q(n) be the second derivative of 61*n**4/3 + 120*n**3 - 18*n**2 + 47*n + 5. What is m in q(m) = 0?
-3, 3/61
Let n(h) be the third derivative of -h**7/315 - 2*h**6/15 - 14*h**5/15 - 20*h**4/9 - 515*h**2 - 2. Factor n(p).
-2*p*(p + 2)**2*(p + 20)/3
Let c(u) = 5*u**3 - 7*u**2 + 7*u + 4. Suppose 47 + 53 = 50*b. Let d be c(b). Factor -150 - d*r - 3/2*r**2.
-3*(r + 10)**2/2
Let o(m) be the third derivative of -m**8/168 + 8*m**7/5 - 7217*m**6/60 + 6553*m**5/15 + 2407*m**4 - 55112*m**3/3 - 8739*m**2. Solve o(g) = 0 for g.
-2, 2, 83
Find j such that -52*j**2 + 2/3*j**3 + 102*j - 152/3 = 0.
1, 76
Let f(t) be the second derivative of -t**7/252 + 2*t**6/45 - 11*t**5/60 + t**4/3 - t**3/4 + 1332*t. What is z in f(z) = 0?
0, 1, 3
Let j = -1088059/55 + 19783. Let r(b) be the first derivative of -36/11*b**2 + 10 - 26/11*b**3 - 9/11*b**4 - 24/11*b - j*b**5. Factor r(g).
-6*(g + 1)**2*(g + 2)**2/11
Factor -110*q + 849*q**4 + 78*q**3 - 808*q**4 + 41*q**2 + 31*q - 39 - 43*q**2 + q**5.
(q - 1)*(q + 1)**3*(q + 39)
Let d(m) be the second derivative of -m**5/10 + 64*m**4/3 + m**3/3 - 128*m**2 - 418*m + 3. Determine s, given that d(s) = 0.
-1, 1, 128
Let t be (-56)/(-196)*35/660. Let z(w) be the second derivative of -6/11*w**2 - 20*w + 7/33*w**3 - t*w**4 + 0. Find d such that z(d) = 0.
1, 6
Let o(r) be the first derivative of r**4/16 - 3*r**3/2 + 65*r**2/8 + 21*r - 1730. Factor o(d).
(d - 12)*(d - 7)*(d + 1)/4
Let w = -4463 + 4463. Let s(g) be the second derivative of 0*g**3 + 1/6*g**4 + w*g**2 - 1/10*g**5 + 0 - 6*g. Factor s(m).
-2*m**2*(m - 1)
Let g(l) = -47*l**2 + 959*l - 1910. Let i(c) = 40*c**2 - 960*c + 1910. Let d(p) = 5*g(p) + 6*i(p). Factor d(s).
5*(s - 191)*(s - 2)
Factor -2/19*g**2 + 56/19 - 54/19*g.
-2*(g - 1)*(g + 28)/19
Let h(b) be the second derivative of -1/240*b**6 + 0*b**2 + 0*b**4 + 0 - 5/2*b**3 + 1/20*b**5 + 3*b. Let k(m) be the second derivative of h(m). Factor k(z).
-3*z*(z - 4)/2
Let o(q) be the first derivative of -1/5*q**5 + 2*q**3 - 102 + 0*q + 0*q**2 - 5/4*q**4. Find a such that o(a) = 0.
-6, 0, 1
Let i(y) be the third derivative of -y**8/40320 + y**7/1008 - 5*y**6/288 - y**5/20 - 2*y**2 - 8. Let q(v) be the third derivative of i(v). Factor q(o).
-(o - 5)**2/2
Let r(c) be the second derivative of 0 + 0*c**4 - 17*c - 1/450*c**5 - 17/3*c**3 - 1/2700*c**6 + 0*c**2. Let n(v) be the second derivative of r(v). Factor n(d).
-2*d*(d + 2)/15
Suppose 306 = -17*i, i - 6*i - 58 - 38 = -w. Solve 1/6*u + 35/6*u**3 + 2*u**2 - w*u**5 - 2*u**4 + 0 = 0 for u.
-1, -1/6, 0, 1
Let c be 2/8 + (-21)/(-12). Let j be (-3 + 1)/(62/(-527)). Factor 16 + 0*d**c + 9*d - j*d + d**2.
(d - 4)**2
Let s = 69 - 66. Solve -147*v**4 - 2*v + 73*v**4 + v**2 + 73*v**4 - v**5 + 3*v**s = 0.
-2, -1, 0, 1
Factor 7/5*x**3 - 123*x - 270 - 59/5*x**2 + 1/5*x**4.
(x - 9)*(x + 5)**2*(x + 6)/5
Let y(b) be the third derivative of b**8/25200 + b**7/42 + 25*b**6/4 + 13*b**5/60 - 5*b**3/6 - 184*b**2. Let m(h) be the third derivative of y(h). Factor m(z).
4*(z + 75)**2/5
Let s(q) be the second derivative of -49*q**6/300 + 21*q**5/25 - q**4 + 8*q**3/15 + 101*q**2/2 - 2*q - 5. Let l(x) be the first derivative of s(x). Factor l(a).
-2*(a - 2)*(7*a - 2)**2/5
Factor 0*f + 0 - 2/7*f**4 - 104/7*f**2 + 106/7*f**3.
-2*f**2*(f - 52)*(f - 1)/7
Factor -54450/7 - 248*i**3 - 14*i**4 + 40920/7*i - 3068/7*i**2.
-2*(i + 11)**2*(7*i - 15)**2/7
Let x = -893/8 + 13403/120. Let g(o) be the third derivative of -x*o**3 - o**2 + 0 - 2/15*o**5 + 0*o + 3/20*o**4. Factor g(v).
-2*(4*v - 1)*(5*v - 1)/5
Suppose 488*x = 492*x - 8. Let d(t) be the first derivative of -4/25*t**x + 0*t + 2/75*t**3 - 5. Solve d(j) = 0.
0, 4
Let a = -495 - -770. Let q be (-30)/(-9)*(-11)/(a/(-10)). Factor -4/3 + 8/3*m**2 - 4/3*m**4 - q*m**5 - 4/3*m + 8/3*m**3.
-4*(m - 1)**2*(m + 1)**3/3
Let t(w) = -22464*w - 24. Let c be t(-13). Find k, given that -414*k**2 - 14*k**3 + 26*k**3 - 20335*k - 15*k**3 + 1291*k - c = 0.
-46
Let t = 5 - 2. Let f be 4*1 - 0/454. Factor -16/7*j**t + 2/7*j**2 + 26/7*j**f + 0*j + 0 - 12/7*j**5.
-2*j**2*(j - 1)**2*(6*j - 1)/7
Suppose d + 19*b = 21*b - 124, d + 3*b + 124 = 0. Let i be d + 130 + (-52)/(-14). Let 48/7 - 2/7*y**5 + 6/7*y**3 + 104/7*y + i*y**2 - 8/7*y**4 = 0. What is y?
-2, -1, 3
Let g(d) be the third derivative of d**6/960 - d**5/80 - d**4/48 + d**3/2 + 7*d**2 - 39*d. Find p, given that g(p) = 0.
-2, 2, 6
Let q be 1 + 5/(-15)*-6. Suppose -q*w + t + 521 = 164, 0 = -3*w + 3*t + 363. Factor -2*b**2 - 4*b**2 + 121*b - w*b - 9*b**3.
-3*b*(b + 1)*(3*b - 1)
Let s(d) be the third derivative of -d**5/30 - d**4 - 11*d**3/6 - 5*d**2. Let o be s(-11). Find p, given that -4 + 5*p - 29*p**2 + 27*p**2 - o*p = 0.
-2, -1
Suppose -3*x + 8*o = 6*o + 4, 0 = -2*x - 4*o - 8. Let z(i) = -i**2 + 1. Let l(u) = -u**2 + 2*u + 3. Let n(a) = x*z(a) + l(a). Determine j, given that n(j) = 0.
-1
Let j(x) be the first derivative of 10/7*x + 90 + 1/7*x**2 - 10/21*x**3 - 1/14*x**4. Factor j(i).
-2*(i - 1)*(i + 