et q(n) be the second derivative of -13/15*n**6 - 93*n - 1/7*n**7 + 29/10*n**5 - 2*n**3 + 0 - 7/6*n**4 + 0*n**2. Find g such that q(g) = 0.
-6, -1/3, 0, 1
Let z(y) be the first derivative of 8*y**3/21 - 261*y**2 - 914*y/7 - 5371. Factor z(i).
2*(i - 457)*(4*i + 1)/7
Factor 1/4*q**4 - 93/4*q**2 + 45/4*q**3 + 47/4*q + 0.
q*(q - 1)**2*(q + 47)/4
Let a(b) = -32*b**2 - 173*b - 210. Let n(s) = 30*s**2 + 158*s + 210. Let k(c) = -14*a(c) - 15*n(c). Suppose k(h) = 0. What is h?
5, 21
Let o(v) be the third derivative of -v**5/270 - 5*v**4/9 + 325*v**3/27 - 1335*v**2. Factor o(j).
-2*(j - 5)*(j + 65)/9
Let b = -4743 + 4745. Let u(g) be the first derivative of 16 + 7/6*g - 1/18*g**3 + 1/2*g**b. Find z such that u(z) = 0.
-1, 7
Suppose 5*i = 4*p - 36, -78 = p - 6*p - 2*i. Factor 19*b - 9 + 39 - 5*b**2 - p*b.
-5*(b - 3)*(b + 2)
Let t = 1506331/4 + -376582. Factor -15/2*w + t*w**2 + 12.
3*(w - 8)*(w - 2)/4
Factor -1258/9*k**2 - 40/9*k**3 + 2/9*k**4 + 0*k + 0.
2*k**2*(k - 37)*(k + 17)/9
Suppose -44*f + 43*f + 8 = 0. Let a(b) = b**3 - 6*b**2 - 17*b + 10. Let t be a(f). Factor 1/4*d**t - d + 1.
(d - 2)**2/4
Let b(t) be the second derivative of -961/6*t**4 + 0 - 124/3*t**3 - 19*t - 4*t**2. Suppose b(p) = 0. What is p?
-2/31
Let n(d) be the third derivative of d**8/840 + d**7/84 + d**6/60 - d**5/12 - d**4/3 - 5*d**3/2 - 92*d**2. Let k(j) be the first derivative of n(j). Factor k(r).
2*(r - 1)*(r + 1)**2*(r + 4)
Let k(i) be the first derivative of i**5/70 + 2*i**4/7 + 16*i**3/7 + 43*i**2/2 - 62. Let y(m) be the second derivative of k(m). Suppose y(z) = 0. Calculate z.
-4
Let j(k) = -6*k - 153. Let w be j(-23). Let o be (-1)/(4/(-12)) + w/9. Determine i, given that -o + i + 1/3*i**2 = 0.
-4, 1
Let p(a) be the first derivative of -1/25*a**5 - 56/5*a**3 + 0*a - 5/4*a**4 + 62 - 72/5*a**2. Solve p(j) = 0.
-12, -1, 0
Let p(q) be the second derivative of 1/12*q**4 + 24*q - 9/2*q**3 - 29*q**2 - 1. Factor p(s).
(s - 29)*(s + 2)
Let c(a) be the first derivative of -a**3/6 + 328*a**2 + 1313*a/2 + 7510. Factor c(o).
-(o - 1313)*(o + 1)/2
Let v(p) be the second derivative of -8*p**2 - 36 - 8/3*p**3 + 1/3*p**4 + 1/5*p**5 + p. Solve v(u) = 0.
-2, -1, 2
Let u(j) = -j**2 + 2. Let o(s) = s**2 - 204*s + 204. Let q(f) = 2*o(f) - 2*u(f). Factor q(t).
4*(t - 101)*(t - 1)
Let g = 4883/12 - 813/2. Let s(d) be the second derivative of 0 + g*d**4 + 45/2*d**2 - 7*d - 5*d**3. Find f such that s(f) = 0.
3
Let g(b) = 8*b**2 - 90*b - 366. Let y(h) = 7*h**2 - 91*h - 356. Let o(u) = -5*g(u) + 6*y(u). Solve o(v) = 0 for v.
-3, 51
Suppose 70 = 2*s + 2*v, 0 = -0*s + 4*s + 2*v - 144. Let l be s/3 - (5 - -4). Let l*f - 34/3*f**3 + 4*f**4 - 4/3 + 16/3*f**2 = 0. What is f?
-1/2, 1/3, 1, 2
Let h = -1/9336 + 12451/28008. Factor 38/9*d + h*d**2 + 16/3.
2*(d + 8)*(2*d + 3)/9
Let v = 3207 + -3207. Let k(r) be the third derivative of -1/24*r**4 + 7/120*r**5 + 15*r**2 + 0*r**3 + v*r + 0. Factor k(d).
d*(7*d - 2)/2
What is c in 114*c**2 + 75*c**3 - 40 - 23*c**3 - 999*c**4 + 489*c**4 - 112*c + 496*c**4 = 0?
-2, -2/7, 1, 5
Determine x so that 0*x + 0 + 6*x**3 - 9/2*x**4 + 0*x**2 = 0.
0, 4/3
Let h(f) be the third derivative of 0 - 164*f**2 + 1/10*f**5 - f**3 + 0*f + 1/40*f**6 - 1/8*f**4. Factor h(v).
3*(v - 1)*(v + 1)*(v + 2)
Let l(u) = 93*u**2 + 278*u - 2. Let i be l(-3). Let r(a) be the first derivative of 0*a + 7/8*a**4 - 5/6*a**3 + i - 1/2*a**2. Factor r(o).
o*(o - 1)*(7*o + 2)/2
Let w(a) = 6*a**2 - 55*a + 11. Let d be w(9). Factor 7 + d*v**2 - 11 + 32 - v**2 - 29*v.
(v - 28)*(v - 1)
Let p(b) = -62*b**2 - 2228*b - 2226. Let f(u) = -73*u**2 - 2230*u - 2227. Let z(o) = -6*f(o) + 7*p(o). Factor z(r).
4*(r - 555)*(r + 1)
Let q(k) = k**2 - 216*k - 655. Let w be q(-3). Let v(d) be the second derivative of 0 - 1/4*d**4 + 0*d**3 - 15*d + 3/2*d**w. Factor v(a).
-3*(a - 1)*(a + 1)
Let i = 32587/16 - 32547/16. Factor -5/2*o + 5*o**2 + i*o**3 - 5.
5*(o - 1)*(o + 1)*(o + 2)/2
Suppose -64 - 2/7*i**2 + 450/7*i = 0. What is i?
1, 224
Suppose 14*l = 92*l. Suppose 3*u - 4*n - 26 = l, -2*u - 26 = 5*n - 5. Solve 0 - 3/4*g + 1/4*g**u = 0 for g.
0, 3
Let p(b) = 8*b**3 + 3064*b**2 - 3088*b - 6162. Let s(h) = 15*h**3 + 6130*h**2 - 6175*h - 12320. Let d(o) = 5*p(o) - 3*s(o). Solve d(n) = 0.
-615, -1, 2
Suppose 0 = 1196*k - 1188*k - 56. Factor 2*d - 10*d**3 + 3 - 10*d + 56*d**2 + k*d**3 - 13*d**3 - 17*d.
-(d - 3)*(4*d - 1)**2
Solve -6*t**4 + 2/9*t**5 + 176/3*t**3 + 640/3*t - 2104/9*t**2 + 512 = 0 for t.
-1, 6, 8
Let q(x) = -39*x**3 - 137*x**2 + 39*x + 444. Let z(b) = 19*b**3 + 68*b**2 - 22*b - 224. Let g(w) = 6*q(w) + 13*z(w). Let g(a) = 0. What is a?
-62/13, -2, 2
Let r = -2 + 6. Suppose -3*x - 2 = q - 0, 2*x = -r. Factor 10*i**2 + 2*i**q - 5*i**4 - 5 - 3*i**4 + i**4.
-5*(i - 1)**2*(i + 1)**2
Let l(q) be the second derivative of 0*q**2 - 1/4*q**3 + 7/48*q**4 - 1/80*q**5 - 15*q - 5. What is w in l(w) = 0?
0, 1, 6
Suppose -f + x - 5 = 0, -f + 11 = -1720*x + 1721*x. Determine y so that 0 - 10/9*y**2 + 8/9*y**f + 4/9*y - 2/9*y**4 = 0.
0, 1, 2
Factor -2/7*i**3 - 244/7*i - 160/7 - 86/7*i**2.
-2*(i + 1)*(i + 2)*(i + 40)/7
Solve 8*j**3 - 159 + 586*j + 5*j**3 - 418*j**2 - 5*j**3 - 17*j**2 = 0.
3/8, 1, 53
Factor 1/6*z**3 + 293/6*z - 172/3 + 25/3*z**2.
(z - 1)*(z + 8)*(z + 43)/6
Let c(r) be the third derivative of 42*r**2 + 625/14*r**3 + 0*r + 25/28*r**4 - 1 + 1/140*r**5. Solve c(l) = 0.
-25
Let x = -478735/108 - -17428/27. Let p = x - -3806. Solve 60*v - p*v**2 + 80 + 5/4*v**3 = 0 for v.
-1, 8
Let d(c) be the third derivative of 0 + 0*c - 1/2*c**5 + 5/2*c**3 + 1/14*c**7 - 75*c**2 + 5/24*c**4 + 5/336*c**8 - 1/12*c**6. Suppose d(k) = 0. Calculate k.
-3, -1, 1
Suppose -p = -9*p + 32. Factor 55 + 4*k**3 + 25 + 12*k + p*k**2 - 76*k.
4*(k - 2)**2*(k + 5)
Suppose -4*h**2 - 88*h + 258*h - 90*h - 89*h + h**2 = 0. What is h?
-3, 0
Let q(u) be the second derivative of -u**4/8 + 97*u**3 - 28227*u**2 - 15*u - 89. Factor q(d).
-3*(d - 194)**2/2
Suppose -k + 52 = -2*i, 20*i - 23*i = 4*k - 252. Suppose -188*w + 198*w = k. What is s in -3 - w*s**2 - 3/2*s**3 - 15/2*s = 0?
-2, -1
Let v(p) be the second derivative of p**5/20 - 49*p**4/9 - 133*p**3/2 - 355*p**2/3 + 3246*p. Suppose v(f) = 0. What is f?
-5, -2/3, 71
Suppose -5*p = -4*k - 43, 3*p + 373*k = 372*k + 2. Let n(b) be the first derivative of 17 - 1/3*b**p + b - 1/8*b**4 + 1/4*b**2. Factor n(v).
-(v - 1)*(v + 1)*(v + 2)/2
Factor -8015415*j + 254094060 + 41863827 - 686091600 - 10965*j**2 - 5*j**3 - 144314199 - 1418641543.
-5*(j + 731)**3
Find d such that 153/4*d**3 + 1395*d + 1026 + 3/4*d**4 + 813/2*d**2 = 0.
-38, -6, -1
Factor -14*q**2 + 16888*q**3 - 33762*q**3 + 16886*q**3 + 2*q**4.
2*q**2*(q - 1)*(q + 7)
Let q(u) be the third derivative of u**5/30 - 95*u**4/18 + 7*u**3 + 3*u**2 + 56. Factor q(p).
2*(p - 63)*(3*p - 1)/3
Let v be 0 + (4/4 - -1). Suppose -7*g + 3*g + 8 = 0. Factor 249*z**g - 8 - 123*z**2 - 124*z**v.
2*(z - 2)*(z + 2)
Let p(j) be the first derivative of j**5/240 - 11*j**4/48 + 121*j**3/24 + j**2 + 146*j - 186. Let f(i) be the second derivative of p(i). Solve f(m) = 0.
11
Let i be ((-432)/(-27))/(2/10). Find u such that 640*u**3 + i*u - 3 - 10 - 400*u**2 + 2 + 6 = 0.
1/8, 1/4
Suppose 4*k - 5*y - 104 = 0, -4*k - 2*y + 30 = -102. Determine f so that 9*f**3 + 6*f**4 + 56*f + 8*f**2 - 11*f - 12 - k*f**2 - 25*f**2 = 0.
-4, 1/2, 1
Factor -8*l**3 - 16*l**2 + 8 + 4 + 2966878*l + 4*l**4 - 2966870*l.
4*(l - 3)*(l - 1)*(l + 1)**2
Suppose 14*g**4 - 38*g**2 - 475 - 720*g - 317 - 2*g**5 - 661019*g**3 + 661117*g**3 = 0. Calculate g.
-3, -2, 3, 11
Let s(u) = -2*u**3 + 31*u**2 - 1172*u + 15822. Let l be s(14). Solve -c**3 + 11/4*c + 1/8*c**4 + 2 - 3/8*c**l = 0 for c.
-1, 2, 8
Let i(h) be the first derivative of -h**4/2 - 4*h**3/3 + h**2 - 5*h - 68. Let m(o) = 5*o**3 + 10*o**2 - 5*o + 11. Let b(y) = 7*i(y) + 3*m(y). Factor b(u).
(u - 1)*(u + 1)*(u + 2)
Let t(k) be the first derivative of -k**5/25 + k**4/5 + 7*k**3/15 - 11*k**2/5 - 24*k/5 + 6381. Solve t(d) = 0.
-2, -1, 3, 4
Let v(y) be the third derivative of -y**7/1365 - 531*y**6/130 - 2540833*y**5/390 - 422676*y**4/13 - 2534464*y**3/39 - 1099*y**2 - 6. Let v(r) = 0. What is r?
-1592, -1
Let n(d) be the first derivative of 5*d**3/3 + 35*d**2 + 541. Factor n(h).
5*h*(h + 14)
Suppose -5*q + 6 = -3*q. Let k be 6/7 + ((-7385)/(-245) - 31). Factor -1/5*u - 4/5