+ 405*a**3 + 2045*a**2 - 840*a + 85. Let v(s) = -31*s**4 + 29*s**3 + 146*s**2 - 60*s + 6. Let o(k) = -6*h(k) + 85*v(k). Factor o(n).
-5*n*(n - 3)*(n + 2)*(5*n - 2)
Let n(u) be the second derivative of -34*u + 0 + 7/30*u**4 - 2/15*u**3 - 4/25*u**5 + 0*u**2 + 1/25*u**6. Factor n(c).
2*c*(c - 1)**2*(3*c - 2)/5
Let r(p) be the first derivative of -p**6/90 + p**5/30 - p**3 - 15. Let t(g) be the third derivative of r(g). What is d in t(d) = 0?
0, 1
Let r(w) = w**2 - 2*w - 36. Let u be r(6). Let t be (-4)/12*u/7. Determine c, given that -t*c + 2/7*c**3 + 0 + 2/7*c**2 = 0.
-2, 0, 1
Let u(g) be the second derivative of -g**4/20 - g**3/10 - g + 14. Factor u(v).
-3*v*(v + 1)/5
Let c be 5/65*(-14)/7 + 23/65. Solve 0*y**2 - 2/5*y**3 + 1/5*y**5 + 0 + 0*y + c*y**4 = 0 for y.
-2, 0, 1
Determine h so that -12/7*h**3 - 4/7*h**2 + 0 + 0*h - 4/7*h**5 - 12/7*h**4 = 0.
-1, 0
Let j(d) be the second derivative of d**6/80 + d**5/40 - 31*d**2/2 + 23*d. Let q(u) be the first derivative of j(u). Solve q(m) = 0.
-1, 0
Let h(c) = c**2 - 18*c + 10. Let z be h(12). Let v = -60 - z. Solve -6/5*o**v - 3/5 + 9/5*o - 3/5*o**5 - 6/5*o**3 + 9/5*o**4 = 0.
-1, 1
Let h(t) be the third derivative of 13*t**2 + 0*t + 1/60*t**4 - 1/300*t**6 - 1/10*t**3 - 1/1050*t**7 + 1/75*t**5 + 0. Find x, given that h(x) = 0.
-3, -1, 1
Let l(s) be the first derivative of -s**4/14 + 2*s**3/7 + 10*s**2/7 + 78. Find d, given that l(d) = 0.
-2, 0, 5
Let c = 15 + -11. Find p such that c*p**2 + 98 + 5*p - 2*p**3 - 102 - 3*p = 0.
-1, 1, 2
Let b(h) be the first derivative of h**6/480 + h**5/120 + h**4/96 + 9*h**2/2 - 17. Let j(k) be the second derivative of b(k). Suppose j(a) = 0. Calculate a.
-1, 0
Let b(k) be the third derivative of 3*k**2 + 0*k**3 + 1/12*k**5 + 0*k + 5/24*k**4 + 0. Factor b(h).
5*h*(h + 1)
Let u(d) be the third derivative of 0*d**4 + 0 + 15*d**2 + 1/14*d**3 + 0*d - 1/140*d**5. Find m, given that u(m) = 0.
-1, 1
Let x(p) = -p + 8. Let w be x(5). Suppose -5*z**4 - z**3 - 5 - 30*z**2 + 4*z**w + 20*z + 17*z**3 = 0. Calculate z.
1
Let k = 25 - 20. Factor 11*j + 4*j**4 + j**5 - 9*j**k - 11*j.
-4*j**4*(2*j - 1)
Let l(s) be the third derivative of s**7/1260 + 19*s**6/360 + 529*s**5/360 + 133*s**4/6 + 196*s**3 + 106*s**2 - 3. Factor l(h).
(h + 7)**2*(h + 12)**2/6
Suppose -4 = -f - 0*f. Suppose -3*g = 2*a + 12, 2*a + 2*g = 5*a - 8. Factor a*x**f + 3*x**4 - 8*x**2 - 5*x**4 - 8*x**3.
-2*x**2*(x + 2)**2
Factor 222*a**2 + 911754 - 24642*a - 2/3*a**3.
-2*(a - 111)**3/3
Let i(c) = c**3 - 3*c**2 + 4. Let g be i(3). Determine r, given that g - 1 - 8 + 3*r**2 - 7 = 0.
-2, 2
Solve 0 + 0*m + 3/2*m**2 - 3*m**3 + 3/2*m**4 = 0 for m.
0, 1
Find t, given that 1/4*t**2 - 59/4 + 29/2*t = 0.
-59, 1
Suppose 4*z = -3 - 9. Let l be (z/4)/((-9)/24). Factor -5*r**3 + l*r**3 + 12*r**2 - 6*r**3 - 3*r**3 + 3*r**4.
3*r**2*(r - 2)**2
Let y(z) be the second derivative of -3*z**6/5 - 15*z**5/2 + 53*z**4/6 - 3*z**3 - 27*z + 4. Factor y(i).
-2*i*(i + 9)*(3*i - 1)**2
Let i(z) = z**3 - 3*z - 2. Let b be i(-2). Let g = -4 - b. Determine u so that -4 - u**4 + 14*u + g*u**4 - 4*u**3 - 18*u**2 + 14*u**3 - u**4 = 0.
1, 2
Let t(x) = -2*x**2 + 91*x + 49. Let k be t(46). Let q(d) be the second derivative of 4*d + 3/2*d**2 + 0 - 1/4*d**4 + 0*d**k. Let q(w) = 0. Calculate w.
-1, 1
Let s = -3 + 18. Let d be (-8)/10*s/(-6). Find p, given that -2*p**2 + 0 + 2*p + d + 2 = 0.
-1, 2
Let d(k) be the second derivative of -5*k**7/126 + k**6/6 + k**5/3 - 5*k**4/3 + 252*k + 1. Determine h so that d(h) = 0.
-2, 0, 2, 3
Let m(c) be the second derivative of 15*c + 0 - 1/6*c**6 - 5/3*c**3 - 5/21*c**7 + c**5 + 5/6*c**4 - 5/2*c**2. Suppose m(o) = 0. Calculate o.
-1, -1/2, 1
Let o be (-8)/((-4)/(-2)) + 6. Suppose 0 = o*t - 12. Factor -c**2 - t*c**4 + 40*c**5 + 7*c**2 - 3*c - 37*c**5.
3*c*(c - 1)**3*(c + 1)
Let n(g) be the first derivative of -g**8/84 - 2*g**7/35 - g**6/15 - 4*g**2 + 9. Let k(u) be the second derivative of n(u). Factor k(y).
-4*y**3*(y + 1)*(y + 2)
Let i(x) = -x**3 - 3*x**2 + 2*x - 6. Let u be i(-4). Factor -20*z**u - 25*z**2 + 43*z**2.
-2*z**2
Find k, given that 2/17*k + 0 - 2/17*k**3 + 2/17*k**4 - 2/17*k**2 = 0.
-1, 0, 1
Let s = -66 - -18. Let y be 3/((-18)/8*32/s). Find x such that -32/11*x**3 + 32/11*x + 14/11*x**4 - 8/11 - 6/11*x**y = 0.
-1, 2/7, 1, 2
Let u(g) be the first derivative of 1/2*g**4 + 15 + 0*g - 1/5*g**5 + 0*g**2 - 1/3*g**3. Suppose u(c) = 0. Calculate c.
0, 1
Let s(m) be the first derivative of m**3/4 - 309*m**2/4 + 31827*m/4 - 23. Solve s(u) = 0.
103
Suppose 3*l + 6 = 15. Suppose 14 = l*y - 34. Solve -20*d - 36 - 4*d**3 + 28 - y*d**2 + 0*d**2 = 0.
-2, -1
Let i = 357 + -1776/5. Let h(y) be the first derivative of 0*y - 6*y**4 + i*y**5 + 0*y**2 - 5 + 4*y**3. Suppose h(k) = 0. What is k?
0, 2/3, 2
Factor -5*a**2 + 60 + 18*a**2 + 20*a - 10*a**2 + 7*a.
3*(a + 4)*(a + 5)
Suppose -5 = 11*l + 28. Let q(c) = 9*c - 6. Let f(s) = s**2 - 18*s + 12. Let n(z) = l*f(z) - 5*q(z). Factor n(g).
-3*(g - 2)*(g - 1)
Let u be (-4)/24 + 8/12. Let h(r) = r**2 - 12*r - 11. Let m be h(13). Determine c so that 0*c**m + 0 + u*c**4 + 0*c + 1/2*c**3 = 0.
-1, 0
Let v(w) be the first derivative of 2*w**3/27 + 37*w**2/9 + 8*w + 18. Factor v(s).
2*(s + 1)*(s + 36)/9
Let n be (-21)/(-28) + 3 + 35/(-10). Let h(k) be the first derivative of -1/15*k**5 - n*k**4 - 2 + 1/18*k**6 + 0*k + 1/9*k**3 + 1/3*k**2. Factor h(r).
r*(r - 2)*(r - 1)*(r + 1)**2/3
Let r(f) = f**3 - 12*f**2 + f + 9. Let q be r(12). Let c = q + -14. Factor -4*z**2 - 7*z + 0*z**2 + 16 + c*z.
-4*(z - 2)*(z + 2)
Let m(b) be the third derivative of b**8/112 + 2*b**7/7 - 12*b**2 - 13*b. Solve m(j) = 0 for j.
-20, 0
Let o(k) = k**2 - k. Let y(n) = n**3 + 2*n**2 + 16*n + 5. Let i(q) = -15*o(q) - 3*y(q). Factor i(d).
-3*(d + 1)**2*(d + 5)
Let w(o) = -24*o**5 - 26*o**4 + 4*o**3 - 6*o**2 + 6. Let g(l) = 47*l**5 + 52*l**4 - 8*l**3 + 13*l**2 - 13. Let h(d) = 6*g(d) + 13*w(d). Solve h(i) = 0 for i.
-1, 0, 2/15
Let p be 1683/(-748) - 121/(-36). Let n = -125/6 + 379/18. Factor -20/9*c**3 - n - 10/9*c**4 - 2/9*c**5 - p*c - 20/9*c**2.
-2*(c + 1)**5/9
Let m(d) = -9*d**5 - 6*d**4 + 2*d**3 - 2*d**2 - 2. Let o(j) = -11*j - 68. Let z be o(-6). Let x(a) = -a**3 + a**2 + 1. Let n(f) = z*x(f) - m(f). Factor n(k).
3*k**4*(3*k + 2)
Let v(g) be the third derivative of g**7/735 - g**6/420 - g**5/70 + g**4/84 + 2*g**3/21 + 2*g**2 + 7*g. Factor v(q).
2*(q - 2)*(q - 1)*(q + 1)**2/7
Factor 1915*o**3 + 14*o**2 - 6*o**2 + 13*o**2 - 1948*o**3 - 3*o**2 + 15*o**4.
3*o**2*(o - 1)*(5*o - 6)
Factor 1072/3*o + 71824/3 + 4/3*o**2.
4*(o + 134)**2/3
Let o = 4457/180 + -99/4. Let y(q) be the second derivative of 0*q**3 + 0*q**4 + 1/60*q**5 + q + 0*q**2 + 0 + o*q**6. Let y(t) = 0. Calculate t.
-1, 0
Let n = -46 - -25. Let u = -19 - n. Factor -c**u + 46*c - 46*c - c**2 + c**3.
c**2*(c - 2)
Determine x so that 3/2*x**3 + 1/2*x**4 - 105/2*x**2 + 325/2*x + 0 = 0.
-13, 0, 5
Let b = -11922 + 83669/7. Let x = b - 29. Factor -8/7 + 4*c + x*c**3 - 32/7*c**2.
4*(c - 1)**2*(3*c - 2)/7
Let f = 113 - 27. Solve 44*s + 257*s**3 + 10*s**2 - 8 - 12*s**4 - f*s**2 - 205*s**3 = 0.
1/3, 1, 2
Factor -1/4*f**4 - 13/4*f**2 + 0 - 3/2*f - 2*f**3.
-f*(f + 1)**2*(f + 6)/4
Let l(p) be the second derivative of p**6/18 - 5*p**5/12 + 5*p**4/18 + 50*p**3/9 - 20*p**2 - 57*p + 1. Factor l(v).
5*(v - 3)*(v - 2)**2*(v + 2)/3
Suppose -2/3*n**2 - 10/3*n + 16 = 0. Calculate n.
-8, 3
Let s(k) = 8*k**3 - 52*k**2 + 92*k - 36. Let c = 33 - 36. Let y(u) = -8*u**3 + 52*u**2 - 93*u + 36. Let m(n) = c*s(n) - 4*y(n). What is l in m(l) = 0?
1/2, 3
Let p(s) = -5*s**2 - 6*s - 4. Let f(u) = -2*u**2 - 2*u - 1. Let j(q) = -3*f(q) + p(q). Factor j(b).
(b - 1)*(b + 1)
Suppose 0 = 2*n + 2*q - 16, 5*n - 4*q - 22 = 18. Suppose -n*s = -3*s - 15. Factor -5*a**4 + 10*a**4 - 5 - 15*a + 5*a + 10*a**s.
5*(a - 1)*(a + 1)**3
Let a = -6353 - -6356. Solve 5/11*p + 1/11*p**a + 4/11*p**2 + 2/11 = 0.
-2, -1
Let o(x) be the second derivative of 1/600*x**6 + 1/100*x**5 + 0*x**4 - 5/6*x**3 + 3*x + 0*x**2 + 0. Let r(m) be the second derivative of o(m). Factor r(s).
3*s*(s + 2)/5
Suppose 28 = 4*m - 2*d - 2*d, 5*m + 3*d = -5. Solve 1/3*o**4 - 2/3*o**m + 0 - 1/3*o**3 + 0*o = 0 for o.
-1, 0, 2
Let f(m) = -m**3 + 2*m + 1. Let x(a) = a**4 + 28*a**3 + 277*a**2 + 784*a + 678. Let w(h) = -2*f(h) + x(h). What is t in w(t) = 