 first derivative of 1/7*p**2 + 2/21*p**3 + g*p - 22. Factor h(v).
2*v*(v + 1)/7
Suppose 5*r - 4*u = 24, 15*r - u = 20*r - 19. Let y(o) be the first derivative of 1/20*o**5 + 1/4*o**2 + 2 - 1/12*o**3 - 1/8*o**r + 0*o. Factor y(p).
p*(p - 2)*(p - 1)*(p + 1)/4
Let j = 4597 - 4595. Suppose a + 52 = 3*x + x, 3*x = 2*a + 44. Let -2*d**2 - 10 + d**j - 2*d**2 - x*d - 2 = 0. What is d?
-2
Let h(k) = 4*k**3 - 7*k**2 - 5*k - 3. Let q = 289 + -292. Let m(c) = 3*c**3 - 6*c**2 - 5*c - 2. Let a = -2 - -4. Let x(w) = a*h(w) + q*m(w). Factor x(j).
-j*(j - 5)*(j + 1)
Let r(k) be the second derivative of k**4/6 - 86*k**3 + 40*k - 7. Let r(t) = 0. What is t?
0, 258
Solve -29/6*a**2 - 13*a - 1/6*a**3 + 0 = 0 for a.
-26, -3, 0
Let b = -126 - -129. Solve 16*m - 10*m - 3*m**b + 9*m**4 - 3*m**3 + 5*m**2 - 14*m**2 = 0.
-1, 0, 2/3, 1
Let q(h) be the first derivative of h**7/168 - h**6/36 - 91*h**3/3 - 30. Let m(j) be the third derivative of q(j). What is f in m(f) = 0?
0, 2
Factor -6*t - 32/13*t**2 + 0 - 2/13*t**3.
-2*t*(t + 3)*(t + 13)/13
Let u(c) be the second derivative of -c**7/273 - 11*c**6/195 - 21*c**5/65 - 32*c**4/39 - 32*c**3/39 + 14*c - 144. Suppose u(l) = 0. Calculate l.
-4, -2, -1, 0
Let i = 437079031/255 - 1714033. Let k = i + -7/85. Solve 0 - 5*m**3 - 1/3*m**5 + 0*m - k*m**4 - 3*m**2 = 0 for m.
-3, -1, 0
Suppose 1292*o + 288 - 846 = 2026. Factor 2/5*u**3 - 2/5*u - 6/5*u**o + 4/5 + 2/5*u**4.
2*(u - 1)**2*(u + 1)*(u + 2)/5
Suppose 15 = 5*n, -n - 7 = -3*r - 1. Suppose 0 = -r*v - 3*v + 1404. Factor w**3 + v*w - 4*w**3 - 3*w**4 - 231*w + 3*w**2.
-3*w*(w - 1)*(w + 1)**2
Let j(u) be the third derivative of u**9/604800 + u**8/6720 + u**7/224 + 13*u**5/15 - 75*u**2. Let l(h) be the third derivative of j(h). Factor l(t).
t*(t + 15)**2/10
Let x(d) be the third derivative of -27*d**6/140 + 69*d**5/14 + 650*d**4/21 + 500*d**3/7 - 2066*d**2. What is c in x(c) = 0?
-10/9, 15
Let q be (60/8*-3)/(30/(-10)). Let w(y) be the first derivative of -y**5 + 10*y**2 - 15*y**3 + 0*y + q*y**4 + 22. Factor w(r).
-5*r*(r - 4)*(r - 1)**2
Determine d so that 27*d**3 + 534589*d**4 + 492*d**2 + 22*d**3 + 2368 + 1840*d - 534588*d**4 = 0.
-37, -4
Factor -16 + 25/4*m**5 + 5/4*m**4 + 23/4*m**2 + 28*m - 101/4*m**3.
(m - 1)**3*(5*m + 8)**2/4
Let c = 6095 - 6089. Let v(u) be the third derivative of 0 - 1/42*u**7 + 5/2*u**3 + 0*u - 5/3*u**4 + 40*u**2 + 0*u**c + 1/2*u**5. Determine a so that v(a) = 0.
-3, 1
Let c = 151 + -147. Factor c*f**3 + 12*f**4 - 4*f**2 - 8*f**2 - 14*f**3 + 51*f - 41*f.
2*f*(f - 1)*(f + 1)*(6*f - 5)
Let g(w) be the second derivative of -1/140*w**5 - 2/7*w**2 - 16*w - 4/21*w**3 + 0 - 5/84*w**4. Let g(d) = 0. What is d?
-2, -1
Let s(p) be the second derivative of p**6/45 + 11*p**5/5 + 1153*p**4/18 + 704*p**3/3 + 1024*p**2/3 + 2*p + 713. Solve s(y) = 0 for y.
-32, -1
Let l = 3248 + -2092. Factor -2*m**3 + 280*m + 72*m**2 - 511*m + l - 483*m.
-2*(m - 17)**2*(m - 2)
Let b(x) be the second derivative of -104*x + 9*x**2 + 0 - 7/8*x**4 - x**3 - 3/40*x**5. Factor b(c).
-3*(c - 1)*(c + 2)*(c + 6)/2
Let p(v) be the third derivative of v**8/16 + 13*v**7/210 - 4*v**6/5 - 14*v**5/15 + 2*v**4 + 8*v**3/3 + 8*v**2 - 44. Solve p(q) = 0.
-2, -1, -2/7, 2/3, 2
Let w(b) = 8*b**3 + 48*b**2 - 13*b - 48. Let r(t) = -44*t**3 - 264*t**2 + 72*t + 264. Suppose -7*p + 14 - 49 = 0. Let m(a) = p*r(a) - 28*w(a). Factor m(j).
-4*(j - 1)*(j + 1)*(j + 6)
Suppose p = 4*p + 3*t - 210, 3*t = 2*p - 130. Suppose -2*v**4 - 100*v - 17*v**3 - 2286 + 2238 - p*v**2 + v**4 = 0. Calculate v.
-12, -2, -1
Let l(u) = u**3 - 38*u**2 - 77*u - 118. Let x be l(40). Let r be (6 + -3)*(-4)/(-4). Factor -f + 1/4*f**x + 1/4*f**r - 1.
(f - 2)*(f + 1)*(f + 2)/4
Let o(s) be the second derivative of 84*s - s**3 - 1/30*s**5 + 1/3*s**4 + 0*s**2 + 0. Factor o(p).
-2*p*(p - 3)**2/3
Let j(x) be the first derivative of 5*x**6/6 + 27*x**5 + 675*x**4/4 - 3355*x**3/3 + 300*x**2 + 4500*x - 850. Solve j(q) = 0 for q.
-15, -1, 2
Let h(d) be the first derivative of 25/4*d**4 + 27/4*d**2 - d + 104 - 25/2*d**3. Solve h(i) = 0.
1/10, 2/5, 1
Let v(r) be the first derivative of 2/7*r + 3/14*r**2 - 17/21*r**3 + 58 - 7/4*r**4 - 9/7*r**5 - 1/3*r**6. Determine d, given that v(d) = 0.
-1, -1/2, 2/7
Let q(u) = u**3 + 12*u**2 + 4. Let l be q(-12). Factor 36*r**2 + 72 - 3*r**l + 70 - 3*r**3 - 94 + 84*r.
-3*(r - 4)*(r + 1)*(r + 2)**2
Let j(d) be the third derivative of -d**5/60 - 3*d**4/2 - 33*d**3/2 - 10*d**2 + 61. Determine l so that j(l) = 0.
-33, -3
Suppose -5*a + 5*c + 60 = 0, 4*a + 2*c + 23 = 11. Factor 0 + 2/5*p**4 + 4/5*p**3 + 0*p + 2/5*p**a.
2*p**2*(p + 1)**2/5
Factor -1165*q + 80*q**3 + 4165*q - 5000 - 20*q**3 - 650*q**2 - 2*q**4.
-2*(q - 10)**2*(q - 5)**2
Let c(u) = -10*u**2 + 11922*u - 12. Let h(z) = 21*z**2 - 23843*z + 26. Let k(t) = 13*c(t) + 6*h(t). What is i in k(i) = 0?
0, 2982
Factor -3*a**5 + 196*a**3 - 576*a**2 + 140*a**3 - a**5 + 7*a**5 - 57*a**4.
3*a**2*(a - 8)**2*(a - 3)
Factor 8 + 44337*x + 2*x**5 - 2*x**2 - 44349*x + 7*x**3 - 3*x**5.
-(x - 2)*(x - 1)**2*(x + 2)**2
Let -1868*q - 372*q + 4*q**2 + 861343 - 859107 = 0. What is q?
1, 559
Factor 179572/5*t**2 + 2072/15*t**3 + 534578/15 + 2/15*t**4 + 1071224/15*t.
2*(t + 1)**2*(t + 517)**2/15
Let o(d) be the third derivative of -d**7/21 - 6*d**6/5 - 253*d**5/30 - 15*d**4/2 - 76*d**2 + 4*d. Let o(n) = 0. Calculate n.
-9, -5, -2/5, 0
Let f(m) be the first derivative of -5*m**6/6 - 51*m**5 - 1120*m**4 - 25480*m**3/3 + 41160*m**2 + 960400*m + 2167. Factor f(t).
-5*(t - 5)*(t + 14)**4
Let o(s) be the first derivative of 1/140*s**5 - 1/28*s**4 + 12 + 3*s - 2/21*s**3 + 0*s**2. Let m(x) be the first derivative of o(x). Factor m(z).
z*(z - 4)*(z + 1)/7
Let a(l) = 29*l**4 - 704*l**3 - 17*l**2 + 2044*l - 1380. Let v(y) = 6*y**4 - 141*y**3 - 3*y**2 + 408*y - 276. Let g(h) = -3*a(h) + 14*v(h). Factor g(f).
-3*(f - 46)*(f - 1)**2*(f + 2)
Let p(g) be the first derivative of -g**3/6 + 523*g**2/2 - 273529*g/2 - 2590. Factor p(t).
-(t - 523)**2/2
Suppose -h = 2*a - 12, 0 = -a - 2*a - 5*h + 25. Suppose 19894 - 8*z**3 - 10*z**4 - 19894 - 2*z**a = 0. Calculate z.
-4, -1, 0
Let r = 1771/502 - 29103/8534. What is v in -r*v**3 + 0 + 72/17*v**2 - 648/17*v = 0?
0, 18
Suppose 3/2*h**2 + 2782107/2 - 2889*h = 0. What is h?
963
Solve -46/3*i**3 + 2/3*i**4 - 8/3*i + 208/3 - 52*i**2 = 0.
-2, 1, 26
Let j be 36/(-66) - 671/(-121). Suppose -3*p + j = 2*l - 4, 4*p = 2*l - 44. Factor -68/5*w + l*w**2 + 8/5.
4*(w - 1)*(15*w - 2)/5
Suppose -2*n = 7*n. Suppose n = l - 87 + 82. Determine q so that 8*q + 18*q**l + 24*q**3 - 40*q**2 - 24*q**3 + 43*q**3 + 31*q**3 - 60*q**4 = 0.
0, 2/3, 1
Let q be (-4)/(144/105)*18/(-378). Let x = q - -119/180. Factor -2/5*s**3 + 0 + x*s + 2/5*s**2.
-2*s*(s - 2)*(s + 1)/5
Let c(x) be the first derivative of 0*x**2 - 19/3*x**3 - 13/24*x**5 - 5/4*x**4 + 0*x - 5/72*x**6 + 30. Let u(m) be the third derivative of c(m). Factor u(d).
-5*(d + 2)*(5*d + 3)
Factor -602*m - 13*m**2 - 705 + 3*m**2 + 7*m**2 - 106*m.
-3*(m + 1)*(m + 235)
Let a be ((-5)/15)/((-1)/267). Let s = -125 + a. Let b(l) = -10*l**2 + 7*l - 10. Let p(q) = q**2 - q + 1. Let i(u) = s*p(u) - 4*b(u). Factor i(x).
4*(x + 1)**2
Let s(b) be the first derivative of -1/12*b**3 + 7/4*b - 12 + 3/4*b**2. Factor s(d).
-(d - 7)*(d + 1)/4
Suppose 0 = -0*q + 7*q - 399. Let d be ((-2)/(-2 - 0))/(3/q). Factor -7*j**2 - 6*j**2 - 28*j + 4 - d*j**2.
-4*(j + 1)*(8*j - 1)
Factor 9*h**3 + 63/2*h + 12 + 3/4*h**4 + 111/4*h**2.
3*(h + 1)**2*(h + 2)*(h + 8)/4
Let w(d) be the first derivative of -56*d**5/5 + 2225*d**4/2 + 2396*d**3/3 + 160*d**2 - 2401. Suppose w(v) = 0. What is v?
-2/7, -1/4, 0, 80
Factor 3991*z - 1068 - 674*z - 768 - 8*z**2 + 359*z.
-4*(z - 459)*(2*z - 1)
Let a = -14/3937 + 8056/51181. Factor 18/13*z**2 - 20/13*z + 0 + a*z**3.
2*z*(z - 1)*(z + 10)/13
Let n(u) = 8*u**3 - 162*u**2 + 2712*u + 2882. Let w(j) = 15*j**3 - 322*j**2 + 5428*j + 5765. Let s(l) = -11*n(l) + 6*w(l). Factor s(v).
2*(v - 38)**2*(v + 1)
Find d such that -2/3*d - 1/3*d**2 + 143/3 = 0.
-13, 11
Suppose -118/3*j**2 - 356/9*j - 2/9 = 0. What is j?
-1, -1/177
Let i(m) be the third derivative of -5*m**8/336 + 11*m**7/21 - 19*m**6/4 - 40*m**5/3 + 4895*m**4/24 - 605*m**3 + 79*m**2 - 4*m - 1. Find k, given that i(k) = 0.
-3, 1, 2, 11
Suppose 25 = -5*f, t - 2*f - 12 = -0. Factor -3*j**3 - 4 + 6