86*d + 2*n + 8 = -84*d, 20 = 5*d - 3*n. Let g(f) be the second derivative of 1/21*f**d + 0*f**2 + 43*f + 0 - 2/7*f**3. Suppose g(o) = 0. Calculate o.
0, 3
Let f(b) = -33*b**2 + 2*b - 1. Let p(v) = -133*v**2 + 6774*v - 11444693. Let g(a) = -20*f(a) + 5*p(a). Factor g(q).
-5*(q - 3383)**2
Let q(r) = -r**3 + 6*r**2 - 4*r - 7. Let d be q(5). Let g be d*3/(-12) - (-7)/2. Solve -15*m + 3*m**3 - 3*m**4 + 6*m**2 + 19*m - g*m = 0 for m.
-1, 0, 2
Let n = 76691 - 153379/2. Suppose -3/2*p + 1/2 - 1/2*p**3 + n*p**2 = 0. Calculate p.
1
Suppose 0 = 100*g + 307 - 307. Let x(d) be the first derivative of 3/4*d - 3/20*d**5 + 3/4*d**2 + g*d**3 - 26 - 3/8*d**4. Solve x(i) = 0.
-1, 1
Suppose 0 = 2*a - 4*u - 20, -a + 0*u + 6 = -u. Solve 4 + a - 178*o**5 + 175*o**5 - 6*o**2 - 9*o + 12*o**3 = 0 for o.
-2, -1, 1
Suppose -7*u + 54 = 20*u. Let -58*a**3 - 6*a**u + 26*a + 55*a**3 - 72 + 34*a = 0. What is a?
-6, 2
Suppose -4*r + 14 = 110. Let n(b) = 7*b**3 - 27*b**2 - 5*b - 5. Let g(z) = -33*z**3 + 135*z**2 + 24*z + 24. Let s(d) = r*n(d) - 5*g(d). Solve s(a) = 0 for a.
-9, 0
Let v(g) be the second derivative of 0 + 162/5*g**2 + 19/15*g**4 + 66/5*g**3 + 1/25*g**5 - 10*g. Factor v(j).
4*(j + 1)*(j + 9)**2/5
Find m such that 33/2*m**2 + 17*m - 1/2*m**3 + 0 = 0.
-1, 0, 34
Let w(k) be the second derivative of -k**8/1176 - k**7/210 + k**6/420 + 185*k**3/6 - 251*k. Let p(b) be the second derivative of w(b). Factor p(i).
-2*i**2*(i + 3)*(5*i - 1)/7
Suppose 0 = -12*x + 14212 + 14096. Solve -2*f**2 - x + 1924 - 252*f - 4133 - 3370 = 0.
-63
Let n(s) be the first derivative of -4*s**5/5 - 5*s**4 + 28*s**3/3 + 82*s**2 + 120*s - 2162. What is i in n(i) = 0?
-5, -2, -1, 3
Let s(d) be the third derivative of d**6/40 + 14*d**5/5 - 57*d**4/8 + 1595*d**2. Suppose s(b) = 0. What is b?
-57, 0, 1
Let h = -1433 + 1379. Let m be 11/(-99) + (-6)/h. Factor m*c + 0 + 3/5*c**2 - 3/5*c**3.
-3*c**2*(c - 1)/5
Let g(m) be the second derivative of 6*m**5/35 - 23*m**4/28 - 5*m**3/2 - 6*m**2/7 - 975*m. Solve g(n) = 0 for n.
-1, -1/8, 4
Let f(b) be the third derivative of 1/60*b**5 + 0*b - 1/24*b**4 + 0*b**3 + 0 - 100*b**2. Factor f(h).
h*(h - 1)
Let w(h) = -20*h**3 + 24*h**2 + 4*h - 4. Let j(u) = -22*u**3 + 23*u**2 + 5*u - 3. Let z be (3/6)/(17/102). Let k(i) = z*w(i) - 4*j(i). Solve k(p) = 0 for p.
-2/7, 0, 1
Let d = 317 - 317. Find g, given that -14*g**4 - 6*g**5 + 29*g**4 + d*g**2 + 3*g**5 + 9*g**2 - 21*g**3 = 0.
0, 1, 3
Let w be (-50)/(-6) - (-1)/(-3). What is n in 3*n**5 + 18*n + 5*n**4 - w*n**4 + 3*n**2 + 0*n**5 - 21*n**3 = 0?
-2, -1, 0, 1, 3
Let j = 190361 + -380721/2. Factor j*t**2 + 81*t + 6561/2.
(t + 81)**2/2
Let o(m) be the second derivative of -6*m + 1/2*m**3 - 1/40*m**5 - 5/24*m**4 + 0*m**2 + 4. Determine g, given that o(g) = 0.
-6, 0, 1
Let i(q) = q**2 - 693*q + 13462. Let h be i(20). Factor 0 - 8/5*p**3 + p**h + 1/5*p**4 + 10*p.
p*(p - 5)**2*(p + 2)/5
Let k(s) be the first derivative of 174 - 2/7*s**2 + 22/7*s**3 + 0*s. What is c in k(c) = 0?
0, 2/33
Factor 2/5*z**3 + 278/5*z**2 - 56*z + 0.
2*z*(z - 1)*(z + 140)/5
Let b(r) = 9*r**5 - 17*r**4 - 4*r**3 + 7*r**2 - 5*r - 20. Let k(s) = -8*s**5 + 13*s**4 + 5*s**3 - 6*s**2 + 4*s + 16. Let o(i) = -4*b(i) - 5*k(i). Factor o(d).
d**2*(d - 1)*(d + 2)*(4*d - 1)
Let v(w) be the third derivative of w**7/1470 + 11*w**6/840 - w**5/21 - w**4/2 + 24*w**3/7 - 3031*w**2. Factor v(k).
(k - 2)**2*(k + 3)*(k + 12)/7
Let k(w) be the second derivative of -2*w**6/45 + 53*w**5/15 - 17*w**4/3 - 106*w**3/9 + 104*w**2/3 + 9979*w. Let k(m) = 0. What is m?
-1, 1, 52
Factor 26365*q**2 - 26461*q**2 - 216 - 138*q + 4*q**3 - 178*q.
4*(q - 27)*(q + 1)*(q + 2)
Let v(g) be the second derivative of g**5/15 + 47*g**4/9 + 256*g**3/9 - 352*g**2/3 - 935*g. What is s in v(s) = 0?
-44, -4, 1
Let r(t) = 15*t**2 + 10*t. Suppose -5*d = 2*d. Let u(n) = -1 + n**2 + d*n**2 - n**2 - 15*n**2 - 10*n. Let c(a) = 6*r(a) + 5*u(a). Factor c(x).
5*(x + 1)*(3*x - 1)
Let v(z) be the third derivative of 16*z**7/945 + 158*z**6/135 + 313*z**5/270 + 13*z**4/36 - 6*z**2 - 29. Factor v(d).
2*d*(d + 39)*(4*d + 1)**2/9
Let s(k) be the second derivative of k**6/90 - 13*k**5/15 + 169*k**4/6 - 23*k**3/6 - 78*k. Let n(u) be the second derivative of s(u). Factor n(h).
4*(h - 13)**2
Let f(n) be the first derivative of -2*n**3/27 + 1970*n**2/9 - 1940450*n/9 + 6368. Suppose f(l) = 0. Calculate l.
985
Let o(n) be the second derivative of -n**4/12 + n**3/6 + 6*n**2 + 106*n + 2. Suppose o(a) = 0. Calculate a.
-3, 4
Let s(z) be the second derivative of 0 - 2/21*z**7 + 2/15*z**6 + 0*z**2 - 1/3*z**4 + 163*z + 0*z**3 + 1/5*z**5. Determine t so that s(t) = 0.
-1, 0, 1
Let y(o) = 8*o + 4. Let g be y(5). Factor 19*x**2 - 53*x - 115*x + 100 + g - x**3 + 6*x**2.
-(x - 12)**2*(x - 1)
Let v(t) = -t**2 + 21*t - 96. Let a be (0 - -1) + 13*(-30)/(-65). Let i be v(a). Find p, given that 0 + 29/5*p**3 + 0*p + 2*p**5 - 39/5*p**4 - 6/5*p**i = 0.
0, 2/5, 1/2, 3
Let f = -219 + 310. Let j be (1 + f/(-35))/(-2). Determine r, given that -j*r**3 - 4/5*r**2 + 4/5 + 4/5*r = 0.
-1, 1
Factor -21 - 36*s - 66/7*s**2 - 3/7*s**4 + 36/7*s**3.
-3*(s - 7)**2*(s + 1)**2/7
Factor -889*j - 16641 - 128*j**2 - 1088*j - 3*j**3 - 139*j**2 - 2490*j - 1854*j.
-3*(j + 3)*(j + 43)**2
Let d(a) = 17*a**3 - 848*a**2 + 851*a + 1704. Let g(l) = -92*l**3 + 4240*l**2 - 4252*l - 8520. Let z(y) = -16*d(y) - 3*g(y). Factor z(q).
4*(q - 2)*(q + 1)*(q + 213)
Let a(u) be the third derivative of u**6/600 + u**5/75 - u**4/30 - 8*u**3/15 + 1096*u**2. What is m in a(m) = 0?
-4, -2, 2
Factor -588*i**2 + 90*i**2 + 990 - i**3 - 10*i**3 + 8*i**3 - 489*i.
-3*(i - 1)*(i + 2)*(i + 165)
Let n(h) = h**3 - 110*h**2 + 31*h + 8504. Let z be n(109). Suppose 0*p**z - 8/7*p**4 + 0*p - 2/7*p**5 - 8/7*p**3 + 0 = 0. What is p?
-2, 0
Suppose 3023 = 4*j - 433. Let i be 9*12/j*6. Factor 0 + 3/2*x**4 + 3/4*x - i*x**5 - 3/2*x**2 + 0*x**3.
-3*x*(x - 1)**3*(x + 1)/4
Let p(b) be the first derivative of b**5/30 - 5*b**4/6 + 16*b**3/3 + 20*b**2/3 - 200*b/3 + 1223. Factor p(z).
(z - 10)**2*(z - 2)*(z + 2)/6
Suppose i + 3*i = 44. Factor -18*v + 68*v + 4 - 68*v**4 - 112*v**2 - i + 78*v**3 + 59*v**4.
-(v - 7)*(v - 1)*(3*v - 1)**2
Suppose 1099*y**2 - 4239*y**2 - 10*y**3 + 3*y**3 + 3145*y - 12*y**3 + 14*y**3 = 0. Calculate y.
-629, 0, 1
Let l be (-2)/2*5*(-201)/335. Suppose 13*f = 15*f - 3*a + l, 0 = -2*f + 2*a - 2. Find x, given that -2/3*x**2 + 8/9 + 2/9*x**3 + f*x = 0.
-1, 2
Let o(w) = -w**3 + w + 92. Let j be o(0). Suppose -9*q + 48 = 3*q. Factor -43 - 47 + 2*b + 2*b**4 - q*b**2 - 4*b**3 + 2*b**5 + j.
2*(b - 1)**2*(b + 1)**3
Let c = 11 + 14. Suppose 8 = 3*o + 2*k, -3*o + 4*k = 5 - c. Solve -70 - o*s**2 - 120*s - 9*s**2 - 30 - 23*s**2 = 0 for s.
-5/3
Factor 1131*s**2 + 923*s**4 - 160*s - 3120*s**4 - 11*s**2 + 1072*s**4 - 1650*s**3.
-5*s*(s + 2)*(15*s - 4)**2
Let c(m) be the third derivative of m**6/24 + 3*m**5/4 - 10*m**4 - 1120*m**3/3 - m**2 + 5*m + 17. Determine t, given that c(t) = 0.
-8, 7
Determine h, given that 1245*h**3 - 1179*h**4 + 762*h + 1182*h**4 + 1527*h**2 - 477*h**3 = 0.
-254, -1, 0
Let z be ((-21)/(-35) - (-6)/(-60))/(64 - 62). Solve -19/4 + 1/4*o**3 - z*o + 19/4*o**2 = 0 for o.
-19, -1, 1
Let l(m) be the third derivative of m**7/42 + 31*m**6/24 + 56*m**5/3 - 160*m**4/3 - 2*m**2 + 293. Find f such that l(f) = 0.
-16, 0, 1
Suppose -h - 3*l = -2, -6*h + 2*h + 2*l = -22. Suppose 6 = -h*c + 7*c. Suppose 3 - 12*t**2 - 14*t**5 - 3 + 18*t**3 + 17*t**5 + c*t - 12*t**4 = 0. Calculate t.
0, 1
Let k(i) = 21*i - 15. Let o be k(1). Let l(n) be the second derivative of 1/45*n**o + 1/2*n**5 + 25/6*n**4 + 0 + 125/9*n**3 + 0*n**2 + 15*n. Factor l(t).
2*t*(t + 5)**3/3
Let v(i) be the first derivative of -5*i**4/4 + 80*i**3 - 675*i**2/2 + 995. Solve v(q) = 0.
0, 3, 45
Factor -237*g**3 - 1020*g**5 - 60*g**2 + 3049*g**5 + 1450*g - 1011*g**5 - 35*g**2 - 1019*g**5 - 37*g**4.
-g*(g - 2)*(g + 5)**2*(g + 29)
Let d be 4/(-3) + (-1258)/(-111). Suppose -314*v - d = -319*v. What is m in 2*m**3 - 2/3*m**2 - 2/3*m**4 - v*m + 4/3 = 0?
-1, 1, 2
Let f = 508 + -506. Let y(m) be the first derivative of -2/3*m**3 - 5 + f*m + 1/2*m**2 - 1/4*m**4. Determine v so that y(v) = 0.
-2, -1, 1
Suppose -126 - 3*f**2 + 144*f - 809 - 793 = 0. Calculate f.
24
Let n(b) be the third derivative of -7/60*b**5 - 2*b**2 + 65/24*b**4 + 0*b - 3*b**3