pose -5 = -6*u + 5*u - c, -15 = -u - 3*c. Let d(t) be the second derivative of -2*t**2 + 4*t + 5/6*t**4 - 7/3*t**3 + u + 2/5*t**5. Factor d(n).
2*(n - 1)*(n + 2)*(4*n + 1)
Let j(y) be the third derivative of -5/2*y**4 + 2*y - 1/24*y**6 + 0 - 1/2*y**5 - 20/3*y**3 + 3*y**2. Factor j(t).
-5*(t + 2)**3
Let h(x) be the first derivative of x**9/1512 + x**8/210 + x**7/140 - x**6/45 - x**5/15 + 3*x**3 - 20. Let i(s) be the third derivative of h(s). Factor i(j).
2*j*(j - 1)*(j + 1)*(j + 2)**2
Let a(v) = 6*v - 6. Let c be a(-9). Let w be (-12)/c + (-9)/(-5). Solve -9*b**3 + 28*b**2 - b**5 - 2*b - 35*b**2 - 7*b**4 + w*b**4 = 0.
-2, -1, 0
Let u(k) be the first derivative of 0*k + 3*k**4 + 2/3*k**6 + 0*k**2 - 12/5*k**5 - 4/3*k**3 - 18. Factor u(f).
4*f**2*(f - 1)**3
Suppose 30*o - 58 = 62. Let z be -4*((-21)/10 - -2). Factor 0 + 2/5*x**2 + 0*x + 2/5*x**3 - 2/5*x**5 - z*x**o.
-2*x**2*(x - 1)*(x + 1)**2/5
Let y = -326/19 - -1687/95. Factor 0 + 9/5*q**2 + y*q.
3*q*(3*q + 1)/5
Let f(m) be the first derivative of -3/2*m**2 - 2/21*m**3 + 5/84*m**4 + 0*m + 6 + 1/30*m**5. Let n(o) be the second derivative of f(o). Factor n(r).
2*(r + 1)*(7*r - 2)/7
Let q be (0 + 3/(-7))/(9/(-2169)). Let g = q + -103. Suppose 1/7 + 1/7*m**2 + g*m = 0. Calculate m.
-1
Let u(n) be the third derivative of n**6/240 + 7*n**5/40 - 15*n**4/16 + 23*n**3/12 + 553*n**2. Factor u(t).
(t - 1)**2*(t + 23)/2
Suppose 16*k - 22 = 10. Let u(r) be the second derivative of 1/240*r**6 + 0*r**k + 0*r**3 + 0 + 4*r + 0*r**4 - 3/160*r**5. Factor u(m).
m**3*(m - 3)/8
Let h be (-10)/85 + 5 + 179178/(-36720). Let l(y) be the third derivative of 1/12*y**3 + h*y**5 + 3*y**2 + 1/36*y**4 + 0 + 0*y. Determine f so that l(f) = 0.
-3, -1
Let u(r) be the third derivative of -5*r**8/112 - 27*r**7/70 - r**6/4 - 168*r**2 - 2. Factor u(v).
-3*v**3*(v + 5)*(5*v + 2)
Let b(a) be the first derivative of 7 - 3/11*a - 4/11*a**3 - 3/22*a**4 - 1/55*a**5 - 5/11*a**2. Determine w so that b(w) = 0.
-3, -1
Let o(v) be the second derivative of -1/150*v**6 - 11/30*v**3 - 1/100*v**5 + 3/20*v**4 + 0 + 3*v + 2/5*v**2. Factor o(y).
-(y - 1)**3*(y + 4)/5
Let h(v) = -4*v**2 - 32*v + 4. Let y be h(-8). Let w(r) be the first derivative of -2*r + 0*r**3 + 2/5*r**5 + r**y - 3 - 2*r**2. Solve w(a) = 0 for a.
-1, 1
Let c(g) be the third derivative of 0 + 0*g**4 + 0*g - 7*g**2 + 1/70*g**7 + 0*g**3 - 1/20*g**5 + 0*g**6. Factor c(o).
3*o**2*(o - 1)*(o + 1)
Let m(o) be the first derivative of o**3/3 - 9*o**2 + 65*o - 221. Factor m(z).
(z - 13)*(z - 5)
Let i be (5 - 1056/225)*-21. Let o = 2371/275 + i. Factor 2/11*k**3 - 16/11 - 12/11*k**2 + o*k.
2*(k - 2)**3/11
Let p(i) be the third derivative of -i**8/112 - i**7/6 - 5*i**6/4 - 9*i**5/2 - 45*i**4/8 + 27*i**3/2 + 33*i**2. What is c in p(c) = 0?
-3, 1/3
Let a(r) = -r**2 - 2*r. Let t be a(0). Let p(x) = x + 7. Let f be p(-5). Determine o, given that -14/9*o**4 + 2/3*o**5 + 2/3*o**f + t + 2/3*o**3 - 4/9*o = 0.
-2/3, 0, 1
Let n(l) = 3*l**2 + 417*l + 5837. Let o(y) = -4*y**2 - 624*y - 8756. Let w(d) = 8*n(d) + 5*o(d). Factor w(u).
4*(u + 27)**2
Determine x so that -33/4*x - 1/4*x**2 - 8 = 0.
-32, -1
Let c = -2 + 3. Let s(j) = -j**5 - 17*j**4 + 13*j**3 + 5. Let m(u) = -u**5 - u**4 + u**3 + 1. Let p(w) = c*s(w) - 5*m(w). What is g in p(g) = 0?
0, 1, 2
Let t(y) be the third derivative of y**8/84 - 10*y**7/21 + 53*y**6/15 - 116*y**5/15 - 44*y**4/3 + 320*y**3/3 - 38*y**2 + 2. Factor t(h).
4*(h - 20)*(h - 2)**3*(h + 1)
Let r(t) = 4*t**2 + 10*t + 2. Let x be r(-4). Suppose -38*n = -x*n. Find v such that n*v**2 - 1/8*v**4 + 1/8*v**3 + 0*v + 0 = 0.
0, 1
Let j(a) be the first derivative of a**4/26 - 22*a**3/39 + 35*a**2/13 - 50*a/13 + 134. Factor j(h).
2*(h - 5)**2*(h - 1)/13
Let k(b) be the third derivative of -b**7/42 + b**6/6 - 5*b**5/12 + 5*b**4/12 - 25*b**2. Factor k(t).
-5*t*(t - 2)*(t - 1)**2
Let g be 2*2/(8/6). Let b = 4 + 0. What is o in 0*o - 2 - 4*o + 2*o**g + o**4 + 2*o**3 + o**b = 0?
-1, 1
Let u(r) be the third derivative of r**7/105 + 7*r**6/30 - 31*r**5/30 + 4*r**4/3 - 329*r**2. Factor u(n).
2*n*(n - 1)**2*(n + 16)
Let x be -4*-4*(-8)/(-64)*2. Let i(j) be the second derivative of -1/45*j**5 + 1/18*j**x + 1/18*j**2 - 2/27*j**3 + 1/270*j**6 + 12*j + 0. Factor i(n).
(n - 1)**4/9
Let j(q) be the first derivative of -3*q + 0*q**2 + 1/6*q**4 + 6 - 2/3*q**3. Let k(s) be the first derivative of j(s). Factor k(d).
2*d*(d - 2)
Let v = -41/2 - -85/4. Let l(a) be the first derivative of -7/2*a**2 + 2*a + v*a**4 + 2/3*a**3 + 6. Factor l(q).
(q - 1)*(q + 2)*(3*q - 1)
Let p(c) = -14*c**2 - 50*c + 28. Let f(x) = -2*x**2 - 3*x - 1. Let n(y) = -4*f(y) + 2*p(y). What is a in n(a) = 0?
-5, 3/5
Let d(b) be the second derivative of 5*b**4/12 - 10*b**3/3 + 11*b. Let d(r) = 0. What is r?
0, 4
Suppose 0 = 51*f - 112 - 92. Let c(p) be the second derivative of 10*p + 17/4*p**3 + 0 - 7/4*p**f + 9/40*p**5 - 9/2*p**2. Factor c(j).
3*(j - 3)*(j - 1)*(3*j - 2)/2
Let l = 35 + -33. Factor -3*p**4 - 3*p**2 + 6*p**l - 6*p + 3*p**2 + 3*p**2.
-3*p*(p - 1)**2*(p + 2)
Solve -k**4 - 29/2*k**2 + 21/2*k + 15/2*k**3 - 5/2 = 0.
1/2, 1, 5
Suppose 7*m - 8437 = 8055. Solve -g**2 + g**3 + 2356 + g**4 - g - m = 0.
-1, 0, 1
Let q(u) be the first derivative of u**3/24 + u**2/16 - u/4 + 196. Factor q(f).
(f - 1)*(f + 2)/8
Let a(q) be the first derivative of -q**4/34 - 32*q**3/17 - 768*q**2/17 - 8192*q/17 - 26. Factor a(d).
-2*(d + 16)**3/17
Solve 0 + 1760/7*r**2 + 1600/7*r + 4/7*r**4 + 164/7*r**3 = 0 for r.
-20, -1, 0
Let o(g) be the third derivative of 2809*g**5/20 + 159*g**4/4 + 9*g**3/2 + 2*g**2 - 321*g. Find a such that o(a) = 0.
-3/53
Suppose -7 + 1 = -3*t. Let i = 50 + -48. Factor -t*c**i - 4/3*c + 2/3.
-2*(c + 1)*(3*c - 1)/3
Let g(p) be the second derivative of -8*p**6/15 + 4*p**5/5 + 5*p**4/8 + p**3/6 + 15*p**2 + 16*p. Let c(d) be the first derivative of g(d). Factor c(w).
-(w - 1)*(8*w + 1)**2
Let l(i) = -i**2 - 40*i - 6. Let d(c) = -41*c - 5. Let f(p) = 3*d(p) - 4*l(p). Factor f(q).
(q + 9)*(4*q + 1)
Let u(l) be the third derivative of -l**8/1512 - l**7/945 + 2*l**6/135 + 2*l**5/45 - 22*l**2. Find n such that u(n) = 0.
-2, 0, 3
Let t = -1773/14 - -1779/14. Solve 0 + 24/7*q - t*q**2 = 0.
0, 8
Let k(y) = y**3 - 3*y**2 - 5*y + 6. Let z be k(4). Suppose 9*f - 2*f - 14 = 0. Determine c, given that -7*c + 2*c + 0*c**f + c + 6 - 2*c**z = 0.
-3, 1
Let i(q) be the first derivative of 3/2*q**2 + 3/8*q**4 + 0*q - 16 - 3/2*q**3. Factor i(n).
3*n*(n - 2)*(n - 1)/2
Let o(u) be the second derivative of 49*u**7/12 - 637*u**6/60 + 189*u**5/20 - 23*u**4/6 + 2*u**3/3 + 2*u + 5. Find w such that o(w) = 0.
0, 2/7, 1
Let a = -81 - -83. Determine o, given that 0*o**2 + 262*o + 45 - 292*o + 3*o**2 + 2*o**a = 0.
3
Determine s so that 6/5*s**4 - 96/5 + 0*s**2 - 24/5*s**3 + 96/5*s = 0.
-2, 2
Let c(w) be the first derivative of 14*w**3/3 + 7*w**2 - 1. Suppose -5*j = -j - 44. Let u(b) = -5*b**2 - 5*b. Let v(a) = j*u(a) + 4*c(a). Solve v(m) = 0 for m.
-1, 0
Let y(b) = -4*b**5 + 7*b**3 - 9*b**2 - 3*b - 3. Let v(i) = 7*i**5 - 14*i**3 + 17*i**2 + 5*i + 5. Let s(r) = 3*v(r) + 5*y(r). Let s(k) = 0. Calculate k.
-3, 0, 1, 2
Suppose 10 = -729*j + 731*j. Let r(p) be the second derivative of 0*p**4 - 13*p + 1/4*p**j + 0*p**2 + 0*p**3 + 0. Factor r(q).
5*q**3
Let g be 214/8 + -5*27/(-45). Let y = g + -29. Factor 0 - 3/4*h + y*h**2.
3*h*(h - 1)/4
Suppose 5*i - 16 = i + t, 3*t = 4*i - 8. Suppose -3*p = 2*r + 6, 0 = -i*r - 4*p + 4 - 5. Factor 3 + 3*s**3 - 3 - 2*s**r.
s**3
Let j(i) be the second derivative of -i**4/12 + 8*i**2 - i - 5. Factor j(b).
-(b - 4)*(b + 4)
Let i(g) be the second derivative of g**7/14 + 7*g**6/10 + 9*g**5/20 - 23*g**4/4 - 16*g**3 - 18*g**2 + 72*g. Suppose i(d) = 0. Calculate d.
-6, -1, 2
Let v(k) be the second derivative of -k**5/4 - 25*k**4/4 - 125*k**3/2 - 625*k**2/2 - 480*k. Factor v(x).
-5*(x + 5)**3
Factor -6*v**2 + 3/2*v + 6*v**3 + 0.
3*v*(2*v - 1)**2/2
Let v(a) = -76*a - 527. Let z be v(-7). Let n(w) be the first derivative of -z + 2/5*w**5 + 4/3*w**3 + 1/18*w**6 + 2/3*w**2 + 13/12*w**4 + 0*w. Solve n(k) = 0.
-2, -1, 0
Let f(r) be the first derivative of -r**3/3 + 9*r**2 - 4. Factor f(d).
-d*(d - 18)
Let g(s) = 21*s**3 + 151*s**2 + 481*s + 576. Let q(r) = r**4 - r**3 - 3*r**2 - r. Let y(d) = 5*g(d) + 5*q(d). Let y(u) = 0. What is u?
-6, -4
Let s(l)