n**3/69 - 248*n**2/23 - 14*n - 64. Factor i(v).
2*(v - 1)*(v + 248)/23
Let s(u) be the second derivative of -u**8/448 - u**7/126 + u**6/36 - 7*u**4/12 - 104*u. Let o(h) be the third derivative of s(h). Suppose o(x) = 0. What is x?
-2, 0, 2/3
Let o(p) be the first derivative of 0*p**2 - 3/5*p**5 + 2/15*p**6 + 16*p - 2/3*p**3 + p**4 + 4. Let n(c) be the first derivative of o(c). Factor n(z).
4*z*(z - 1)**3
Let b = 350 - 341. Let k be (2/b)/(5*4/30). Factor 2/3*v**2 + k + v.
(v + 1)*(2*v + 1)/3
Let j = 789/47 + -1531/94. What is c in -1/2*c**2 + 1/6*c + j*c**3 - 1/6*c**4 + 0 = 0?
0, 1
Suppose 0*p - 3*p + 41218 = -14*p + 41240. Factor 0 - 3/8*h**p - 5/4*h.
-h*(3*h + 10)/8
Let c = -82 + 84. Let h be (-5 - 136/(-24)) + c/(-6). Factor 1/9*t**2 - h*t - 4/9.
(t - 4)*(t + 1)/9
Let g(o) = 22*o**3 + 2*o**2 - 68*o - 48. Let k(s) = 8*s**3 + s**2 - 23*s - 16. Let r = 349 - 341. Let y(d) = r*k(d) - 3*g(d). What is b in y(b) = 0?
-2, -1, 4
Let f = 309/160 - -459/160. Solve 0 - 32*r**2 - f*r**3 - 4/5*r**5 - 20*r + 32/5*r**4 = 0.
-1, 0, 5
Solve 0 - 22/3*k + 8*k**2 - 2/3*k**3 = 0 for k.
0, 1, 11
Let a = 33494 + -33489. Let n(t) be the first derivative of 5/3*t**3 + a*t - 5*t**2 + 33. Factor n(y).
5*(y - 1)**2
Let v(j) be the third derivative of 3*j**3 + 22*j + 13/120*j**6 + 0 - 11/8*j**4 - j**2 + 1/70*j**7 - 1/60*j**5. Factor v(c).
(c - 1)*(c + 3)**2*(3*c - 2)
Let u(y) be the third derivative of 17/36*y**4 + 1/60*y**6 + 1/6*y**5 + 0 + 58*y - 1/315*y**7 + 2/3*y**3 - y**2. Find i such that u(i) = 0.
-1, 6
Suppose 8*c = -16*c + 1344. Factor c - 45*l - 31 - 50*l**2 - 5*l**3 - 25.
-5*l*(l + 1)*(l + 9)
Let z = 20 - 18. Suppose 21*u - 7*u + 19*u = -u. Factor 3/2*l**z + u - 3/4*l - 3/4*l**3.
-3*l*(l - 1)**2/4
Let f = 844/189 + -82/27. Factor 6/7*v**3 - 2/7 + f*v - 2*v**2.
2*(v - 1)**2*(3*v - 1)/7
Let h(r) be the third derivative of r**7/105 + 11*r**6/30 + 4*r**5/3 - 10*r**2 + 314*r. Solve h(g) = 0.
-20, -2, 0
Factor -724*d + 1447/2 + 1/2*d**2.
(d - 1447)*(d - 1)/2
Let i = 198 - 195. Factor -10 - 10*w - 22*w**4 + 45*w + 32*w**4 + 10*w**i - 5*w**5 - 40*w**2.
-5*(w - 1)**4*(w + 2)
Let a(v) = -v - 17. Suppose 51*m + 171 = 42*m. Let g be a(m). Suppose -14 + 38*u - 8*u - 9*u**2 - 9*u**2 + g*u**3 = 0. What is u?
1, 7
Factor -16/15 - 2/15*t**2 + 6/5*t.
-2*(t - 8)*(t - 1)/15
Let d(q) be the second derivative of 0*q**2 + 1/126*q**7 - 22 + 1/9*q**6 - 5/3*q**4 + 2*q**3 - 2*q + 13/60*q**5. Factor d(j).
j*(j - 1)**2*(j + 6)**2/3
Let x = 2735 - 2731. Let z(q) be the second derivative of -8*q - 2/27*q**3 + 0 - 1/3*q**2 + 1/54*q**x. Factor z(a).
2*(a - 3)*(a + 1)/9
Let z be 1170/(-420)*(-1)/6 + (-4)/(-14). Let k(t) be the first derivative of -z*t**4 + 3/2*t**2 - 16 - 3*t**3 + 9*t. Let k(b) = 0. What is b?
-3, -1, 1
Let m(h) be the second derivative of -h**8/10080 + h**7/560 - h**6/270 + h**3/3 + 22*h**2 - 72*h. Let p(l) be the second derivative of m(l). Factor p(t).
-t**2*(t - 8)*(t - 1)/6
Let l(x) = 15*x**2 + 2844*x - 2843. Let f be l(1). Let -15*y**2 - f*y - 25/6*y**3 - 16/3 = 0. Calculate y.
-2, -4/5
Let r(m) be the third derivative of m**8/168 - 44*m**7/35 + 259*m**6/60 + 22*m**5/5 - 65*m**4/3 - 677*m**2 - 3. Suppose r(p) = 0. Calculate p.
-1, 0, 1, 2, 130
Let o be (-9 + 368/40)/(707/2020). Factor 1/7*k**3 + 5/7*k + 2/7 + o*k**2.
(k + 1)**2*(k + 2)/7
Suppose 290 = 9*p + 1424. Let w = p + 128. Determine u so that 2/7*u**w - 2/7*u - 4/7 = 0.
-1, 2
Let o be (0 + -1)*0 + 2. Let b(u) = 121*u**2 - 1571*u - 24. Let p be b(13). Factor -5/2*y + 1/4*y**3 - p - 1/4*y**o.
(y - 4)*(y + 1)*(y + 2)/4
Find g such that -704*g + 13*g**2 + 799 - 380 - 311 = 0.
2/13, 54
Let i(x) be the first derivative of -3*x**4/4 - 8670*x**3 - 37584450*x**2 - 72412707000*x - 3854. Solve i(j) = 0 for j.
-2890
Let g be (0 - 10) + (-276)/(-18) + 2/(-3). Let y(b) be the second derivative of 0 - 49*b**2 - 1/6*b**4 + 22*b - g*b**3. Find m, given that y(m) = 0.
-7
Let v(r) = -r**2 - 9. Let j(l) = 2*l**2 - 48*l + 145. Let c(m) = -5*j(m) - 45*v(m). Factor c(u).
5*(u + 8)*(7*u - 8)
Suppose -23*m + 17598 = -2*m. Factor -842*g**3 + 5 + 19 + m*g**3 + 4*g - 24*g**2.
-4*(g - 1)*(g + 1)*(g + 6)
Factor -52/3*c - 1/3*c**3 - 16 - 16/3*c**2.
-(c + 2)**2*(c + 12)/3
Let c = -5399 + 5401. Factor 7/2*t**c + 6 + 22*t.
(t + 6)*(7*t + 2)/2
Let g(d) = -660 + 2*d + 28*d**2 + 646 + 24*d**3 + 6*d**3. Let b(j) = 31*j**3 + 28*j**2 + 3*j - 15. Let s(t) = -6*b(t) + 7*g(t). Factor s(l).
4*(l + 1)*(2*l - 1)*(3*l + 2)
Let v be (-10)/(-100)*(9 + (3 - 11)). Let d(i) be the third derivative of 13*i**2 - v*i**5 + 0*i**3 + 0*i + 0 - 1/8*i**4 - 1/40*i**6. Factor d(o).
-3*o*(o + 1)**2
Let l(a) be the second derivative of -1/4*a**5 + 1/6*a**3 - 32*a + 0*a**2 + 25/24*a**4 + 1/72*a**6 + 0. Let h(c) be the second derivative of l(c). Factor h(g).
5*(g - 5)*(g - 1)
Factor 12/7*i**2 + 5/7 + 2*i - 1/7*i**4 + 2/7*i**3.
-(i - 5)*(i + 1)**3/7
Factor 2829*v**2 - 1587*v**3 + 2685/4*v + 75/2.
-3*(v - 2)*(46*v + 5)**2/4
Suppose -2*f + 13*f = 33. Factor 41*m**3 - 26*m**3 + 8*m**2 - 27*m**f + 4*m**4.
4*m**2*(m - 2)*(m - 1)
Let p = 24808 - 173644/7. Let 0 + 0*o**3 + 8/7*o + p*o**2 - 4/7*o**4 = 0. What is o?
-1, 0, 2
Let j be (-4)/(-5)*(60014/(-592) + 102). Factor -w**3 + 0 + 1/2*w**5 + j*w + 0*w**2 + 0*w**4.
w*(w - 1)**2*(w + 1)**2/2
Suppose 9*w - 11 = 7. Determine b, given that -16*b**2 + 26*b**2 - 11*b**w + 9 = 0.
-3, 3
Let g(k) be the third derivative of -k**5/105 - 370*k**4/21 - 273800*k**3/21 + 2*k**2 - 2053. Factor g(p).
-4*(p + 370)**2/7
Let l(n) = -15*n**3 - 8*n**2 + 23*n + 11. Let v(d) = -2*d**2 + 6*d + 52 - 35 - 14 - 4*d**3. Let s(c) = -6*l(c) + 22*v(c). Factor s(g).
2*g*(g - 1)*(g + 3)
Let w(h) be the first derivative of h**6/1080 - h**4/72 + 26*h**3/3 - 175. Let t(b) be the third derivative of w(b). Factor t(j).
(j - 1)*(j + 1)/3
Let f be (-4 - -6 - 4/2) + 3. Find l, given that -8*l**4 + f*l + 2*l - 5*l**3 + l**4 - 3*l**2 + 4 + 0*l**2 + 6*l**4 = 0.
-4, -1, 1
Suppose 3*f + 10 = 5*t, -8*f = 3*t - 13*f - 22. Let v(i) = -5*i**2 - 25*i + 65. Let x(l) = l - 1. Let p(m) = t*v(m) - 5*x(m). Determine k, given that p(k) = 0.
-6, 2
Let u(i) be the third derivative of -1/6*i**6 + 0*i**3 + 0*i + 0*i**4 + 5/42*i**7 + i**2 + 0*i**5 - 5/336*i**8 - 9. Factor u(f).
-5*f**3*(f - 4)*(f - 1)
Let d(b) be the second derivative of -50/3*b**3 + 185/12*b**4 + 0 - 93*b + 3/2*b**6 - 15/2*b**5 + 10*b**2. Find t such that d(t) = 0.
2/3, 1
Factor -2*i**3 - 185 + 3184 + 249*i**2 - i**3 + 74*i - 5363*i + 2044.
-3*(i - 41)**2*(i - 1)
Suppose -3*w - 18 = 0, 4*w = 3*g - 29 - 1. Let k(z) be the first derivative of 1/4*z - 5/16*z**g + 8 - 1/40*z**5 + 1/32*z**4 + 1/8*z**3. Factor k(x).
-(x - 1)**3*(x + 2)/8
Let s(u) be the first derivative of -u**5/75 - 73*u**4/90 - 76*u**3/5 - 108*u**2/5 + 21*u - 19. Let h(q) be the first derivative of s(q). Factor h(c).
-2*(c + 18)**2*(2*c + 1)/15
Let q be (10 + -6)/((-4)/(-5)). Let p be 4/q + (-1072)/(-335). Determine k so that -9/2*k**2 + 7/3*k**p + 4/3*k + 2/3 - 17/6*k**3 = 0.
-1, -2/7, 1/2, 2
Let r = 63 + -67. Let b(k) = 14*k**2 + 83*k + 479. Let w(z) = -12*z**2 - 84*z - 480. Let j(h) = r*b(h) - 5*w(h). Determine n so that j(n) = 0.
-11
Let b(z) = -z**2 + 131*z - 1318. Let o be b(11). Factor 6*x**o - 2/3 - 16/3*x.
2*(x - 1)*(9*x + 1)/3
Let w(c) = -8*c**2 - 14*c + 28. Let i(l) = 6*l**2 + 15*l - 28. Let v(n) = 2*i(n) + 3*w(n). Let r(z) = 2*z**2 - z - 2. Let u(j) = 4*r(j) + v(j). Factor u(y).
-4*(y - 1)*(y + 5)
Suppose -4*f - 9*f = -4992. Let m = f + -384. Factor 2/17*a**2 + 2/17*a**3 - 2/17*a**5 + 0*a + m - 2/17*a**4.
-2*a**2*(a - 1)*(a + 1)**2/17
Let w(c) = -195*c - 15 - 192*c + 390*c + 6*c**2. Let s(n) = -7*n**2 - n + 16. Let d(j) = 3*s(j) + 4*w(j). Let d(q) = 0. Calculate q.
-4, 1
Let n(q) be the first derivative of -q**5 + 55/4*q**4 + 15/2*q**2 - 5/3*q**6 - 17 - 55/3*q**3 + 0*q. Suppose n(h) = 0. What is h?
-3, 0, 1/2, 1
Let g(m) be the third derivative of m**6/30 + 4*m**5/15 - 16*m**4 - 1922*m**2. Solve g(r) = 0 for r.
-12, 0, 8
Let h(x) be the second derivative of x**4/54 + 46*x**3/27 + 91*x**2/3 - x - 702. Factor h(m).
2*(m + 7)*(m + 39)/9
Let a(q) = 2*q**2 - 62*q + 263. Let p be a(5). Suppose -17 = -i - p*z, z = 7*i - 4*i - 1. Solve 2/23*b**i - 2/23*b + 0 = 0 for b.
0, 1
Let y = 21752/3 - 108733/15. Factor -y*c**2 + 3/5*c**3 - 39/5*c + 9.
3*(c - 5)*(c - 1)