375. What is b in -27*b**3 + q*b**4 + 3224*b**5 - 18*b**3 + 10*b**2 - 3249*b**5 = 0?
0, 2/5, 1
Suppose 6*b + 7*b + 110 = 110. Let m(i) be the second derivative of 0 + 1/15*i**6 + b*i**3 - 26*i - 1/3*i**4 + i**2 + 0*i**5. Solve m(h) = 0 for h.
-1, 1
Suppose -42*r - 1 = 3 - 4. Let o(k) be the third derivative of 4/3*k**3 - 1/30*k**5 + 0 + r*k - 1/4*k**4 - 7*k**2. Let o(z) = 0. Calculate z.
-4, 1
Let v(m) be the second derivative of 121*m**5/30 + 253*m**4/9 + 89*m**3/9 + 4*m**2/3 - 147*m - 13. Factor v(f).
2*(f + 4)*(11*f + 1)**2/3
Let u = -111380 - -111382. Determine l, given that 2/3 - 2/3*l**3 + 2/3*l - 2/3*l**u = 0.
-1, 1
Let k(w) be the second derivative of -w**5/40 - 3*w**4/2 + 40*w**3/3 + 883*w + 5. Let k(c) = 0. What is c?
-40, 0, 4
Let d(o) be the third derivative of 130321*o**5/15 - 361*o**4/6 + o**3/6 - 8*o**2 - o + 20. Factor d(z).
(722*z - 1)**2
Let s(f) be the second derivative of 63/4*f**4 + 12*f - 31/20*f**5 + 289*f**2 + 5 + 799/6*f**3 + 1/30*f**6. Factor s(m).
(m - 17)**2*(m + 1)*(m + 2)
Let l = -10873 + 10875. Let i(h) be the second derivative of 2/5*h**5 - 4*h - 2/3*h**3 - 2/21*h**7 + 0*h**4 + 0*h**6 + 0*h**l + 0. Factor i(f).
-4*f*(f - 1)**2*(f + 1)**2
Factor 0 - 4/3*n**2 + 856/3*n.
-4*n*(n - 214)/3
Find x, given that 4*x**4 + 516*x + 51*x**2 - 3560*x**3 + 4068*x**3 - 1079*x**2 = 0.
-129, 0, 1
Let h be 6/(-4) - (-2 + (-371)/14). Let v(n) = n**3 + 27*n**2 + 52*n + 2. Let r(m) = -12*m**3 - 351*m**2 - 675*m - 27. Let y(d) = h*v(d) + 2*r(d). Factor y(z).
3*z*(z + 3)*(z + 6)
Let f(x) be the second derivative of -3*x - 11/9*x**3 + 0*x**2 - 42 - 1/18*x**4. Let f(k) = 0. What is k?
-11, 0
Let z(v) be the first derivative of -1/9*v**3 + 7/6*v**2 - 101 + 8/3*v. Let z(r) = 0. What is r?
-1, 8
Let t(s) be the first derivative of -2*s**6/15 - s**5 + 13*s**4/3 - 14*s**3/3 + 329*s - 268. Let d(l) be the first derivative of t(l). Solve d(q) = 0.
-7, 0, 1
Let j be 4 - (-6 + 3)/(-3). Factor -29*x + j*x**2 - 162 - 19*x + 367 - 160.
3*(x - 15)*(x - 1)
Let a(w) = -w**5 - 2*w**4 - 17*w**3 - 8*w**2. Let q(y) = -8*y**3 + 7*y**2 - 4*y**2 - 4*y**2 + 6*y**3. Let h(k) = 5*a(k) - 40*q(k). Factor h(z).
-5*z**3*(z + 1)**2
Suppose 3*w = -39 + 93, n = -0*n - 2*w + 39. Determine a, given that -29/2*a**n + 195/2*a**2 + 0 + 1/2*a**4 + 225/2*a = 0.
-1, 0, 15
Solve 0 + 211/5*h**2 - 7*h - 6/5*h**3 = 0.
0, 1/6, 35
Let w be (20/60)/((1 + 0)/9). Factor -57*z**2 - 12*z - 39*z**w + 2402 + 142*z**2 - 2406.
-(z - 2)*(3*z - 1)*(13*z + 2)
Let y(r) be the first derivative of 0*r**3 - 95 - 3/4*r**4 + 0*r + 1/16*r**6 + 0*r**2 + 3/20*r**5. Factor y(h).
3*h**3*(h - 2)*(h + 4)/8
Let w(q) be the first derivative of -3*q**4/20 - 53*q**3/5 + 363*q**2/2 - 945*q + 1181. Factor w(l).
-3*(l - 5)**2*(l + 63)/5
Let y(m) = m**2 + 14*m - 178. Let o be y(10). Suppose -58 = s - o. Factor -3/2*c**3 - 1/2*c + 0 + 1/2*c**s + 3/2*c**2.
c*(c - 1)**3/2
Let h = -167 + 235. Let j = h - 29. Find l such that 66*l + 3*l**2 + 71 + 331 - j = 0.
-11
Let h(c) be the third derivative of -c**6/120 + 7*c**5/40 + 3*c**3 - 2*c**2 + 8*c. Let f(m) be the first derivative of h(m). Factor f(q).
-3*q*(q - 7)
Let b(q) be the second derivative of -q**4/3 + 1444*q**3/3 - 260642*q**2 - 23*q. Factor b(r).
-4*(r - 361)**2
Suppose -52011*m**2 + 2*m**3 - 600*m + 25841*m**2 + 25874*m**2 = 0. Calculate m.
-2, 0, 150
Let v be (2/((-48)/234))/(6/(-32)). Determine h so that 4*h**3 - 5*h**3 + 384*h - 673 + 3*h**3 - v*h**2 + 97 = 0.
2, 12
Let w(h) be the third derivative of 5*h**6/12 + 277*h**5/30 - 139*h**4/6 - 8*h**3 - 2970*h**2. Factor w(v).
2*(v - 1)*(v + 12)*(25*v + 2)
Find n such that 3/7*n**2 + 165/7*n + 162/7 = 0.
-54, -1
Let n(v) be the first derivative of v**5/45 - 19*v**4/36 - 89*v**3/27 - 23*v**2/6 + 46. Suppose n(u) = 0. Calculate u.
-3, -1, 0, 23
Suppose 2*h = -3*h + 5*t, h + t - 8 = 0. Let y be (h + 426/(-108))/(2/6). What is f in -1/6*f**3 + 1/3 + y*f - 1/3*f**2 = 0?
-2, -1, 1
Let w(k) = -k**4 - 12*k**3 - 14*k**2 - 16*k - 9. Let i(z) = 2*z**4 + 23*z**3 + 29*z**2 + 32*z + 17. Let r = -818 + 814. Let p(a) = r*i(a) - 7*w(a). Factor p(c).
-(c + 1)**3*(c + 5)
Suppose 4*p + m - 23 = 0, -5*p = 4*m + 167 - 215. What is w in -2/9*w**p - 20/3*w**2 + 88/9*w + 2*w**3 - 16/3 = 0?
2, 3
Let x(f) be the first derivative of 0*f + 1/4*f**5 - 7/8*f**4 + 3/2*f**3 - 13*f**2 + 1 - 1/40*f**6. Let g(s) be the second derivative of x(s). Solve g(o) = 0.
1, 3
Find a, given that -56/3*a + 32 - 32*a**2 + 58/3*a**3 + 0*a**4 - 2/3*a**5 = 0.
-6, -1, 1, 2, 4
Suppose 41*j - 15 = 67. Let 0*a**2 - 108 + 56 + 35*a - 5*a**j + 52 = 0. Calculate a.
0, 7
Suppose -4*l + 4*l + 44 = 11*l. Let q(w) be the first derivative of 90*w**2 + 360*w + 5/12*w**l + 10*w**3 + 17. Suppose q(j) = 0. What is j?
-6
Factor 0 - 190/3*a**3 - 1/3*a**4 - 188/3*a - 377/3*a**2.
-a*(a + 1)**2*(a + 188)/3
Let l(b) be the third derivative of -b - 1/12*b**5 - 33*b**2 + 5*b**3 + 0 - 25/24*b**4. Factor l(z).
-5*(z - 1)*(z + 6)
Let i(t) be the second derivative of t**7/63 + 7*t**6/45 - 53*t**5/15 - 56*t**4/9 - 382*t + 1. Solve i(u) = 0.
-14, -1, 0, 8
Let j(c) = c**2 - 21*c + 123. Let b be j(9). Let p be 320/288*18/b. Factor -2/3*x**5 + p*x**3 + 0*x**2 + 0*x**4 - 2/3*x + 0.
-2*x*(x - 1)**2*(x + 1)**2/3
Suppose 2*m - 4 = -x - 2, 5*m = -2*x + 7. Let t be 23500/2375 - (-4)/38. Factor 7*z**5 + 9*z**3 - 10*z**m + 4*z**4 - t*z**5.
-z**3*(z - 1)*(3*z - 1)
Let w(h) be the first derivative of -2/15*h**3 + 290 + 1/5*h**2 + 4/5*h. Solve w(t) = 0 for t.
-1, 2
Let c(u) be the first derivative of 89 - 5*u + 25/8*u**4 - 25/4*u**2 + 5/3*u**3. Determine s, given that c(s) = 0.
-1, -2/5, 1
Let t(a) = 141*a**2 - 50802*a - 26813943. Let d(z) = 17*z**2 - 6350*z - 3351743. Let g(n) = -33*d(n) + 4*t(n). Let g(p) = 0. What is p?
-1057
Let p(b) be the second derivative of 13*b - 3/70*b**5 - 6/7*b**2 + 1/105*b**6 - 1/14*b**4 + 11/21*b**3 + 2. Factor p(j).
2*(j - 3)*(j - 1)**2*(j + 2)/7
Let g = 474546/223 + -2128. Let k = g - -4004/1115. Solve 0*t - k*t**4 + 0 + 0*t**2 - 6/5*t**5 - 12/5*t**3 = 0 for t.
-2, -1, 0
Suppose 0 = l - 4*z - 101, -l + 3*z = -43 - 60. Determine b so that 218*b**2 - 392*b - 97*b**2 + 256 - l*b**2 = 0.
2/3, 32
Factor -1/10*d**3 + 49/10*d - 5/2 - 23/10*d**2.
-(d - 1)**2*(d + 25)/10
Factor 32*m**2 + 26*m**2 - 102*m**2 - 28*m**3 + 566*m + 14400 + 2794*m + m**4.
(m - 20)**2*(m + 6)**2
Let j = 177 - 173. Suppose -12 + 45*c**3 - 14*c - 31*c**3 + 2*c**4 + 10*c**2 + 0*c**j = 0. Calculate c.
-6, -1, 1
Let z = 938 + -933. Let r = 9 + -5. Let i(a) = 2*a**5 + 2*a**3 + 4*a. Let h(s) = -2*s**5 - 3*s**3 - 5*s. Let y(g) = r*h(g) + z*i(g). Find c such that y(c) = 0.
-1, 0, 1
Let a(c) be the third derivative of -c**7/210 - 31*c**6/120 + 17*c**5/4 - 413*c**4/24 + 95*c**3/3 - 45*c**2 + 8*c. Factor a(q).
-(q - 5)*(q - 1)**2*(q + 38)
Let j(v) be the third derivative of v**7/42 + v**6/12 + v**5/12 + 102*v**2 + v. Suppose j(f) = 0. What is f?
-1, 0
Factor -49/2*r**4 - 30*r - 71*r**2 - 9/2 - 70*r**3.
-(r + 1)**2*(7*r + 3)**2/2
Suppose -54 = -3*w + 4*s - 36, -4*w + 4*s + 20 = 0. Factor 1250*p + 65*p**4 - 225*p**3 - 67*p**w - 63*p**5 + 33*p**5 + 25*p**5 - 58*p**2.
-5*p*(p - 5)**3*(p + 2)
Let s(x) be the second derivative of -31/14*x**3 + 65*x + 9*x**2 + 0 - 1/140*x**5 + 5/21*x**4. Determine p, given that s(p) = 0.
3, 14
Let o(k) = 5*k + 59. Let t be o(-8). Find s, given that -4*s**3 - 2*s**4 + t*s**2 - 4*s**5 + 10*s**4 - 19*s**2 = 0.
0, 1
Suppose 0 = 11*h + 8 - 30. Suppose -16*z**2 - 27*z**2 - 19*z**h + 53*z**2 - 12*z = 0. What is z?
-4/3, 0
Let p(w) be the first derivative of -5*w**3/3 + 515*w**2/2 + 1050*w - 1318. Suppose p(k) = 0. What is k?
-2, 105
Let h(d) be the third derivative of d**7/350 + 7*d**6/100 - d**5/100 - 7*d**4/20 - 398*d**2 + 2*d. Determine p, given that h(p) = 0.
-14, -1, 0, 1
Let r(s) be the third derivative of -s**6/72 - 29*s**5/15 - 23*s**4/6 + 24*s**3 + 3*s**2 + 16*s. Let t(g) be the first derivative of r(g). Factor t(b).
-(b + 46)*(5*b + 2)
Let j(c) be the first derivative of -2*c**3/39 - 40*c**2/13 + 168*c/13 - 921. Let j(i) = 0. What is i?
-42, 2
Let n(g) be the first derivative of 3/20*g**5 - 27/4*g**3 + 57/4*g**2 - 12*g + 3/4*g**4 + 52. Factor n(r).
3*(r - 2)*(r - 1)**2*(r + 8)/4
Let a(u) = -24*u**2 + 2 + 23*u**2 - 29*u + 30*u. Let r(m) = -m**2 + 41*m + 42. Let p(y) = 4*a(y) + r(y). Fact