*4 + 28*p + 3*p**4 - 15*p**3 = 0.
-1, 0, 2
Let b(a) = -a**3 - 9*a**2 + 11*a + 44. Let r be b(-10). Let y be (r/340)/((-2)/(-288)). Factor 48/5 + 3/5*d**4 - 18/5*d**3 + 3/5*d**2 + y*d.
3*(d - 4)**2*(d + 1)**2/5
Let l(u) be the second derivative of 2*u**3 - u + 7/6*u**4 + 47 + 0*u**2 + 1/10*u**5. Factor l(p).
2*p*(p + 1)*(p + 6)
Let a(n) be the second derivative of n**8/1680 + n**7/525 - n**6/600 - n**5/150 + 45*n**2/2 - 21*n + 1. Let b(y) be the first derivative of a(y). Factor b(k).
k**2*(k - 1)*(k + 1)*(k + 2)/5
Let t(w) be the first derivative of -675*w**4/8 + 15*w**3/4 - w**2/16 - 188*w - 141. Let v(x) be the first derivative of t(x). Suppose v(o) = 0. Calculate o.
1/90
Suppose -7*s - 4 = -4*o - 8*s, 48 = -6*s. Factor -24/5 - 3/5*u**2 - 6*u + 3/5*u**o.
3*(u - 4)*(u + 1)*(u + 2)/5
Let p(w) be the first derivative of -w**5/30 - w**4/12 + 10*w**3 + 110*w**2 - 75. Let o(m) be the second derivative of p(m). Factor o(y).
-2*(y - 5)*(y + 6)
Factor 63/4*l + 405/2 - 3/4*l**2.
-3*(l - 30)*(l + 9)/4
Let a(i) be the third derivative of i**6/420 + 2042*i**5/35 + 4169764*i**4/7 + 68117264704*i**3/21 - 1270*i**2. Factor a(w).
2*(w + 4084)**3/7
Let g = -161 - -20. Let f = g + 146. Factor -1/4*h**3 + 1/2*h**4 + 3/4*h**f + 0*h + 0*h**2 + 0.
h**3*(h + 1)*(3*h - 1)/4
Let x be ((-1)/(-15))/((-14)/(-107226)). Let k = x - 505. Factor -28/5*o**3 + 32/5 + k*o - 36/5*o**2 + 4/5*o**4.
4*(o - 8)*(o - 1)*(o + 1)**2/5
Let x(v) be the third derivative of v**5/15 + 197*v**4/6 + 392*v**3/3 + 296*v**2 + v + 2. Solve x(p) = 0.
-196, -1
Let g(p) be the third derivative of -p**6/60 + p**5/10 + 11*p**4/6 - 8*p**3 - 3*p**2 + 462. Factor g(z).
-2*(z - 6)*(z - 1)*(z + 4)
Let v(u) be the first derivative of -2*u**2 + 0*u - 34/3*u**3 - 115 - 16*u**4 - 24/5*u**5. Suppose v(y) = 0. What is y?
-2, -1/2, -1/6, 0
Let x(y) be the third derivative of -4/3*y**3 + 54*y**2 + 1/150*y**7 - 19/50*y**5 - 43/30*y**4 + 0*y - 1/120*y**6 + 0. Factor x(a).
(a - 5)*(a + 2)**2*(7*a + 2)/5
Let r(l) be the first derivative of -l**6/216 - 31*l**5/36 - 4805*l**4/72 + 83*l**3/3 + 204. Let f(v) be the third derivative of r(v). Factor f(h).
-5*(h + 31)**2/3
Suppose 2*v + 0*v = -2, -o = 5*v + 3. Let n be (-5)/o*(-36)/45. Solve 4 + 7*c**2 - 3*c**n + 4*c**2 - 4*c**2 + 8*c = 0 for c.
-1
Let v = -703 - -663. Let m be 5*16/v*2/(-30). Suppose -m*d**2 + 0 - 2/15*d = 0. Calculate d.
-1, 0
Let b(r) be the first derivative of -2*r**5/15 - 13*r**4/9 + 122*r**3/27 - 32*r**2/9 - 3468. Factor b(z).
-2*z*(z - 1)**2*(3*z + 32)/9
Let v be (-20)/(-8) + 294/4. Let 73*m**2 + v*m**2 - 4*m**3 - 154*m**2 = 0. Calculate m.
-5/4, 0
Factor -3*s**3 - 1399 + 279*s**2 - 17*s + 1672 - 78*s - 454*s.
-3*(s - 91)*(s - 1)**2
Let z be (-6)/(-2)*(3514/21 + 2). Let c = z - 1522/3. Find x such that -c - x**5 + 8/3*x**3 - 5/3*x + 2*x**2 - 4/3*x**4 = 0.
-2, -1, -1/3, 1
Let s(u) = 2*u - 488. Let m be s(-41). Let z be 15/(-9)*76/m. Factor -8/3*a + z*a**2 + 8.
2*(a - 6)**2/9
Let r(c) be the third derivative of c**5/60 - 65*c**4/24 + 59*c**3 - 715*c**2. Find j such that r(j) = 0.
6, 59
Determine o, given that -25/7*o + 116/7 - 1/7*o**2 = 0.
-29, 4
Let v(b) = -b**4 + 2*b**2 - b + 1. Let h(m) = m**4 + 13*m**3 + 136*m**2 + 2*m - 2. Let k(t) = 3*h(t) + 6*v(t). Factor k(q).
-3*q**2*(q - 20)*(q + 7)
Suppose -40/11*s**2 + 2/11*s**4 + 0 - 2/11*s**3 + 0*s = 0. Calculate s.
-4, 0, 5
Let y(k) be the third derivative of 0*k**5 - k + 1/240*k**6 + 0 - 1/16*k**4 + 16*k**2 - 1/6*k**3. Factor y(b).
(b - 2)*(b + 1)**2/2
Solve 145*a**2 - 63*a**2 + 247*a + 231*a + 57121 - 81*a**2 = 0.
-239
Let k(d) = -d**2 + 67*d - 94. Let m(q) = -q**2 - 3*q + 1. Let g(n) = -k(n) - 4*m(n). Determine v, given that g(v) = 0.
2, 9
Let l(b) be the second derivative of 2*b**4 + 5*b**3/2 - 9*b**2/2 - 333*b - 3. Determine d so that l(d) = 0.
-1, 3/8
Let x(f) = f**3 - 24*f**2 - 52*f + 11. Let n be x(26). Let p(d) be the first derivative of -n*d**3 - 3/4*d**4 - 75*d - 23 - 105/2*d**2. Factor p(r).
-3*(r + 1)*(r + 5)**2
Let m = 92161/6 + -460793/30. Solve 0*w + 0 + m*w**4 + 2/5*w**2 - 4/5*w**3 = 0.
0, 1
Let y(w) be the third derivative of -w**5/540 - 5*w**4/18 - 1950*w**2. Find o, given that y(o) = 0.
-60, 0
Suppose -5/4*i**4 + 0 + 0*i + 9/4*i**2 + 1/4*i**5 + 3/4*i**3 = 0. What is i?
-1, 0, 3
Let m(o) be the first derivative of -o**5/120 + o**4/16 + o**3/3 - 33*o**2/2 - 2*o + 29. Let w(u) be the second derivative of m(u). Find i, given that w(i) = 0.
-1, 4
Suppose 3 = -3*r + 3*y, 0 = 41*r - 38*r - 2*y + 4. Let x be ((-24)/(-18))/(r + (-12)/(-4)). Solve -x*v + 3/2 - 1/6*v**2 = 0.
-9, 1
Let j(i) = -61212*i - 306060. Let h be j(-5). Factor 22/3*n**4 + 0*n + h - 2/3*n**5 - 26*n**3 + 30*n**2.
-2*n**2*(n - 5)*(n - 3)**2/3
Suppose 0 = -1533*k + 1580*k. Let s be 4/(-2) - (-1 + -1). Factor 0 + 2/5*p**3 + k*p - 2/5*p**5 + s*p**4 + 0*p**2.
-2*p**3*(p - 1)*(p + 1)/5
Let f(i) be the second derivative of -i**6/6 + 5*i**5 + 215*i**4/12 + 55*i**3/3 - 2*i - 1000. Factor f(r).
-5*r*(r - 22)*(r + 1)**2
Let j(l) be the second derivative of -l**8/672 - l**7/315 - l**6/450 + l**4/12 + 107*l**3/6 - l - 11. Let s(h) be the third derivative of j(h). Factor s(c).
-2*c*(5*c + 2)**2/5
Factor 96 + 154/5*n - 2/5*n**2.
-2*(n - 80)*(n + 3)/5
Let i(z) be the second derivative of -z**5/30 + 13*z**4/18 - 19*z**3/9 - 11*z**2 + 38*z + 3. Factor i(g).
-2*(g - 11)*(g - 3)*(g + 1)/3
Let y(u) be the second derivative of u**4/4 + 15*u**3 - 93*u**2/2 - 127*u - 3. Suppose y(x) = 0. What is x?
-31, 1
Let g = 97/6 - 47/3. Let f(p) be the first derivative of 4 + g*p - 3/8*p**2 - 1/12*p**3 + 3/16*p**4 - 1/20*p**5. Factor f(m).
-(m - 2)*(m - 1)**2*(m + 1)/4
Let z be (21/18 - 1) + 2104/48. Factor 14*b**3 + 13*b**2 + 28*b - 51*b + 24*b + z*b**2 - 12.
(b + 4)*(2*b + 1)*(7*b - 3)
Let o(i) be the second derivative of -29*i - 1/360*i**6 - 1/4*i**4 - 6*i**3 + 0*i**2 + 0 - 7/120*i**5. Let j(p) be the second derivative of o(p). Factor j(k).
-(k + 1)*(k + 6)
Let x = 29 - 19. Let o(k) = -7*k + 219. Let a be o(31). Factor x*q - q**a + 9*q - 24*q.
-q*(q + 5)
Factor 1/2*m**3 - 5/2*m**2 - 253/2*m + 2057/2.
(m - 11)**2*(m + 17)/2
Let t(j) = 62*j**3 - 12*j - 26. Let i be t(-2). Let s = i - -1502/3. Factor -4/3*c**5 + s*c**2 + 0*c + 16/3*c**4 - 20/3*c**3 + 0.
-4*c**2*(c - 2)*(c - 1)**2/3
Suppose 0*b + 2*b = 2*z - 102, -4*z = 2*b - 234. Let k be 52/14 - (-16)/z. Solve 3*a**4 + 4*a**5 - 2*a**k - 12*a**2 - 20*a**3 - 5*a**4 = 0 for a.
-1, 0, 3
Let t(h) = 2*h**2 - h - 5. Let w be t(-2). Suppose 4*a - 33 = -w*f, -a - f = a - 9. Factor 1/4*z**3 - 3/4*z + 9/2 - z**a.
(z - 3)**2*(z + 2)/4
Let g(t) be the first derivative of -t**5 + 165 + 0*t - 5/4*t**4 + 40/3*t**3 + 30*t**2. Factor g(d).
-5*d*(d - 3)*(d + 2)**2
Let r(y) = y**3 - y + 7. Let c be r(0). Suppose c - 16 = -p. Factor 15 + 3*b**2 + p*b - 2 - 7.
3*(b + 1)*(b + 2)
Let t = 13306 + -13306. Let q(g) be the first derivative of t*g**2 - 1/9*g**3 - 24 + 0*g - 1/12*g**4. Factor q(i).
-i**2*(i + 1)/3
Let l(w) be the first derivative of -34*w**6/3 + 84*w**5 - 239*w**4 + 324*w**3 - 208*w**2 + 48*w - 13035. What is r in l(r) = 0?
3/17, 1, 2
Let a(t) be the second derivative of -1/4*t**5 - 21*t + 0 + 15*t**2 - 5/6*t**3 - 5/3*t**4. Factor a(n).
-5*(n - 1)*(n + 2)*(n + 3)
Factor 180/7*b + 0 - 178/7*b**2 - 2/7*b**3.
-2*b*(b - 1)*(b + 90)/7
Let h be 2 - -16 - 11993/670. Let r(x) be the first derivative of h*x**2 + 25 - 1/30*x**6 + 2/15*x**3 - 2/25*x**5 + 0*x**4 + 0*x. Solve r(u) = 0.
-1, 0, 1
Let h(g) be the second derivative of g**6/6 - 9*g**5/2 - 5*g**4/3 + 60*g**3 - 2*g + 227. Suppose h(b) = 0. Calculate b.
-2, 0, 2, 18
Find a, given that 113/7*a - 1/7*a**3 - 16*a**2 + 0 = 0.
-113, 0, 1
Let c(v) be the third derivative of -19/42*v**7 + 640/3*v**3 + 121*v**2 - 5/336*v**8 + 40/3*v**4 + 0 - 47/3*v**5 + 0*v - 14/3*v**6. Find g such that c(g) = 0.
-8, -2, 1
Let k(y) be the third derivative of 1/6*y**6 + 0*y - 3*y**2 + 10*y**5 + 1000/3*y**4 + 20000/3*y**3 + 1/840*y**7 + 8. Find i such that k(i) = 0.
-20
Suppose -m - w + 55 = -3*w, -3*m = 3*w - 201. Let j = m + -125/2. Solve 1/4*b**2 - 1/4*b - j = 0.
-1, 2
Let x(u) = -573*u + 29801. Let g be x(52). Suppose 0 + 0*m**2 - 4/3*m**g - 4*m**4 - 8/3*m**3 + 0*m = 0. Calculate m.
-2, -1, 0
Suppose 1052*q**3 - 783*q**4 - 130*q + 348*q**2 - 230*q + 9*q**5 - 36*q**5 - 230*q**3 = 0. Calculate q