) be the third derivative of j**5/15 - 96*j**3 + 3*j**2 - 697. Factor g(a).
4*(a - 12)*(a + 12)
Suppose 3*b - 10 = 2*q, -b = -5*b - 4*q. Suppose -b*i - 1 = -43. Factor i + 20*g**2 - 14 - 2*g - 6*g - 23 - 6*g**3.
-2*(g - 2)**2*(3*g + 2)
Let d be (30 + -4)/((-36)/(-13)). Let c = d + -80/9. Factor 1/2*r**2 + 0 + 0*r - c*r**3.
-r**2*(r - 1)/2
Factor -106/3*p - 7/3*p**2 + 112/3 + 1/3*p**3.
(p - 14)*(p - 1)*(p + 8)/3
Let m(y) be the second derivative of y**5/20 - 3*y**4/2 - 13*y**3/2 - 10*y**2 - 4*y - 157. Factor m(o).
(o - 20)*(o + 1)**2
Let g be 1 - (0 - 2) - (7 + -6). Factor 82*x**2 + 40 + 83*x**2 - 190*x - 48*x**2 + 68*x**g - 35*x**3.
-5*(x - 4)*(x - 1)*(7*x - 2)
Factor -2*s**2 - 218 + 434 + 34*s - 140 + 0*s**2.
-2*(s - 19)*(s + 2)
Let r(n) be the first derivative of -9/28*n**4 + 0*n**2 - 201 + 5/21*n**3 + 1/42*n**6 + 3/35*n**5 + 0*n. Let r(h) = 0. What is h?
-5, 0, 1
Let b(m) be the first derivative of m**6/1440 - m**5/5 + 24*m**4 + 107*m**3/3 - 146. Let j(i) be the third derivative of b(i). Let j(y) = 0. What is y?
48
Suppose -23*o + 102*o = 237. Let d(s) be the first derivative of 0*s**2 - 1/3*s**o - 5/8*s**4 + 0*s - 14. Factor d(x).
-x**2*(5*x + 2)/2
Suppose -54 = -5*u + 4*j, -u - 7*j + 5*j = -22. Factor 4*g**2 - 8*g**3 - u*g - 36 - 13*g + 99*g.
-4*(g - 3)*(g + 3)*(2*g - 1)
Factor 304*a + 4*a**2 + 823113 + 246043 - 4440*a.
4*(a - 517)**2
Let q(r) be the first derivative of -r**4/28 - 130*r**3/21 + 131*r**2/14 - 1734. Solve q(p) = 0.
-131, 0, 1
Let o = 264069/119 - 2219. Let v = 135/238 - o. Factor -1/2*y**3 - y**2 - v*y + 0.
-y*(y + 1)**2/2
Let o be (6 - 0) + 0 + -4 + 0. Let a = -2 - -4. Factor a*h**3 - 20*h**o - 7*h**3 + h**3 - 16*h.
-4*h*(h + 1)*(h + 4)
Let q = -542 - -560. Let l = 4 - 1. Let 12*r + 7*r - 35 - 5*r**2 + l*r + q*r = 0. Calculate r.
1, 7
Let o(x) be the second derivative of -2/3*x**3 + 7/80*x**5 + 0 - 1/120*x**6 - 1/6*x**4 + 122*x + 0*x**2. Factor o(y).
-y*(y - 4)**2*(y + 1)/4
Find w, given that 0 + 0*w + 455*w**2 - 225*w**3 - 5/4*w**4 = 0.
-182, 0, 2
Let i(n) be the first derivative of -n**3/6 - 49*n**2/2 + 204*n - 1150. Find o, given that i(o) = 0.
-102, 4
Suppose 181*v - 211*v + 120 = 0. Let b(j) be the third derivative of 0*j + 15*j**2 + 2/15*j**3 + 0 + 1/150*j**5 - 1/20*j**v. Determine t so that b(t) = 0.
1, 2
Let i(o) be the third derivative of 0*o - 1/3*o**6 + o**2 + 0*o**3 + 5/336*o**8 - 1/42*o**7 + o**5 + 0*o**4 + 3. Factor i(c).
5*c**2*(c - 2)**2*(c + 3)
Let d = -24904 + 597697/24. Let n(t) be the third derivative of 5/24*t**4 - 5/6*t**3 - d*t**6 + 0*t + 0 - 33*t**2 + 1/12*t**5. Factor n(y).
-5*(y - 1)**2*(y + 1)
Factor 152/11 + 30/11*h - 2/11*h**2.
-2*(h - 19)*(h + 4)/11
Solve 1/2 + 263/4*y + 261/4*y**2 = 0.
-1, -2/261
Suppose 0 = 37*d - 39*d + 24. Let o(u) = u**3 - 13*u**2 + 13*u - 12. Let l be o(d). What is t in 1/3*t**2 - 1/3*t**3 + l + 0*t = 0?
0, 1
Let h = -86 - -116. Let a be (-48)/h*5/(-2). Determine g, given that -4*g**2 + 3*g**2 - a*g**2 - 2*g**3 + 3*g**2 = 0.
-1, 0
Let z = 126424/537013 + -4/31589. Factor z*q**2 + 2/17*q**3 + 0*q - 2/17*q**4 + 0.
-2*q**2*(q - 2)*(q + 1)/17
Suppose 38 - 11 = 9*g. Let y be (-1 - (-5)/g)/(14/84). Factor y*b - 15*b**2 + 6*b + 20*b**2.
5*b*(b + 2)
Let c = -47 + 72. Suppose 26*j = c*j + 2. Solve -5*x + j*x**3 + 8*x - 12*x**2 + 0*x + 7*x = 0.
0, 1, 5
Factor 774*m**2 - 82*m**3 + 14588510*m - 2682*m**2 + 29*m**4 - m**5 - 14591750*m.
-m*(m - 18)**2*(m + 2)*(m + 5)
Factor 0*w**2 + 254043 + 11*w**2 - 3*w**2 + 885*w - 2631*w - 5*w**2.
3*(w - 291)**2
Let q(f) be the first derivative of -52 - 45*f + 125/4*f**4 + 195/2*f**2 - 275/3*f**3. Factor q(u).
5*(u - 1)*(5*u - 3)**2
Let f = -172874/5 - -1210123/35. What is o in -36/7*o + 324/7 + f*o**2 = 0?
18
Let o(w) = -2*w**2 - 4. Let j(f) = 6*f**2 - 840*f + 88208. Let v(q) = -2*j(q) - 4*o(q). Factor v(k).
-4*(k - 210)**2
Let u be 15/2*(-64)/(-96) - 5. Let s(l) be the first derivative of 1/30*l**4 + u*l**3 + 13 + 0*l**2 + 0*l. Factor s(h).
2*h**3/15
Let a(n) be the third derivative of 7*n**6/480 + 55*n**5/8 + 701*n**4/24 - 39*n**3 - 5*n**2 - n + 98. Factor a(i).
(i + 2)*(i + 234)*(7*i - 2)/4
Let a(i) be the second derivative of i**7/840 - 7*i**6/240 + i**5/4 + 17*i**4/12 - i - 1. Let f(b) be the third derivative of a(b). Suppose f(l) = 0. What is l?
2, 5
Let p be (-5)/(-8) - ((-508)/(-280))/(388/(-1455)). What is a in -2/7*a**2 + p*a - 338/7 = 0?
13
Let p be 2/7*(-120)/288*-42. Let q(k) be the first derivative of k - 7 + 3/2*k**2 - 3/4*k**4 + 1/3*k**3 - 2/5*k**p. What is l in q(l) = 0?
-1, -1/2, 1
Let i be 13 - (-2 - -2 - -2). Suppose -i*j + 55 = -330. Suppose -2*p + j - 11 - 4*p**2 + 2*p + 4*p = 0. What is p?
-2, 3
Let a(g) = g**2 + 2*g + 1. Let w(z) = 6*z**2 - 19*z + 209. Let x(m) = 5*a(m) - w(m). Solve x(i) = 0.
12, 17
Suppose -23 + 3 = 4*n, 3*n = f - 55. Suppose -s + f*s = 117. Factor -4*w + 4/3*w**4 + 4/3*w**2 + 4*w**s - 8/3.
4*(w - 1)*(w + 1)**2*(w + 2)/3
Let z(q) be the third derivative of 101*q**5/450 - 11*q**4/20 - 2*q**3/45 - 34*q**2 - 6*q. Factor z(h).
2*(h - 1)*(101*h + 2)/15
Let s(j) be the third derivative of -1/300*j**6 - 1/1050*j**7 + 1/60*j**4 + 0*j + 1/300*j**5 + 0 + 6*j**2 + 0*j**3. Suppose s(n) = 0. What is n?
-2, -1, 0, 1
Let w(r) be the first derivative of -r**6/12 + 281*r**5/10 + 567*r**4/4 + 853*r**3/3 + 1139*r**2/4 + 285*r/2 - 3232. Find v such that w(v) = 0.
-1, 285
Determine i so that -2/3*i**4 + 0*i + 4*i**2 - 1/3*i**5 + 0 + 11/3*i**3 = 0.
-4, -1, 0, 3
Let l(s) = -12*s**3 + s**2 + 2*s. Let v(t) = -5517*t**3 + 17016*t**2 - 469*t + 3. Let f(d) = -18*l(d) - 2*v(d). Suppose f(b) = 0. Calculate b.
1/75, 3
Let s be (-244)/(-84) + 30/70. Let c(t) be the second derivative of 6/5*t**5 + 0 - s*t**6 + 0*t**4 + 0*t**2 - 16*t + 0*t**3 - 6/7*t**7. Factor c(p).
-4*p**3*(p + 3)*(9*p - 2)
Let s(r) be the first derivative of 5/3*r**2 + 2/9*r**3 + 0*r - 77. Determine p so that s(p) = 0.
-5, 0
Suppose 0 = -8*v + 3824 + 4360. Let x = 1025 - v. Factor -204/7*z - 12/7 - 867/7*z**x.
-3*(17*z + 2)**2/7
Factor 15/2*d**2 - 48 - 11*d + 1/2*d**3.
(d - 3)*(d + 2)*(d + 16)/2
Let b be 0/(51/(-1428)*-28). Factor -2/5*x**4 + 3456/5*x - 864/5*x**2 + 72/5*x**3 + b.
-2*x*(x - 12)**3/5
Let s(y) be the second derivative of -y**7/6 - 5*y**6/8 - y**5/6 - 37*y**2 - 226*y. Let g(x) be the first derivative of s(x). Suppose g(w) = 0. Calculate w.
-2, -1/7, 0
Suppose 198*q = 195*q + 54. Factor q*i**2 - 2*i**3 - 3*i**4 - 39*i**2 + 2*i - 2*i**4 + 3*i**4 + 23*i**2.
-2*i*(i - 1)*(i + 1)**2
Let n(t) be the third derivative of 121*t**8/560 - 1287*t**7/350 - 133*t**6/5 - 1298*t**5/25 - 174*t**4/5 - 56*t**3/5 - 5*t**2 - 22*t. Solve n(v) = 0.
-2, -1, -2/11, 14
Let y(i) be the first derivative of -i**4/12 + 16*i**3/9 - 59*i**2/6 + 44*i/3 + 630. Determine p so that y(p) = 0.
1, 4, 11
Let 186/5*b**2 - 783/5*b + 3/5*b**3 + 594/5 = 0. What is b?
-66, 1, 3
Let c(u) be the third derivative of u**5/12 - 5*u**4/6 - 25*u**3/6 + 39*u**2 - 17. Factor c(l).
5*(l - 5)*(l + 1)
Let i = -178341/10 + 35669/2. Factor 0 - i*v**2 + 2/5*v**5 - 2/5*v**3 + 0*v + 2/5*v**4.
2*v**2*(v - 1)*(v + 1)**2/5
Factor 3/5*u**3 - 36/5*u**2 + 96/5*u + 0.
3*u*(u - 8)*(u - 4)/5
Determine c, given that -7*c**2 + 6*c**2 - 17*c**2 + 6269*c**3 - 6272*c**3 + 405*c - 1200 = 0.
-16, 5
Suppose -9 - 11 = -5*b. Solve 4*a**5 - 8*a**5 + 14*a + 6*a - 40*a**3 + 24 + 3*a + 21*a - 24*a**b = 0 for a.
-3, -2, -1, 1
Let k be 1128/(-47) - (-7040)/288. Suppose -k*a**4 + 14/9*a + 2/9*a**5 - 4/9*a**2 - 16/9*a**3 + 8/9 = 0. Calculate a.
-1, 1, 4
Let f(a) be the second derivative of -a**5/60 + 14*a**4/9 - 259*a**3/18 + 34*a**2 + 719*a. Factor f(p).
-(p - 51)*(p - 4)*(p - 1)/3
Suppose 23 = 3*w + f + 7, 3*w - 5*f = -8. Suppose w*g + 94 = 5*g. Factor -4*k + 8*k**3 - 10*k**2 + 6*k**4 - g + 94.
2*k*(k - 1)*(k + 2)*(3*k + 1)
Let p(j) be the second derivative of j**3 + j + 0*j**2 - 33/4*j**4 - 5. Factor p(d).
-3*d*(33*d - 2)
Let s = 511 - 961. Let v = s + 454. Find c such that -1/2*c**v + 1/2 + 1/4*c**5 - 7/4*c + 2*c**2 - 1/2*c**3 = 0.
-2, 1
Let p(j) be the second derivative of 0*j**4 + 0 - 56*j - 3/10*j**5 + 11/14*j**7 + 0*j**3 - 9/10*j**6 + 0*j**2. Factor p(h).
3*h**3*(h - 1)*(11*h + 2)
Let x = 2516252/2245 - 56/2245. Let t = 1121 - x. Suppose -2/5*i + 0 - t*i**4 - 4/5*i**3 - i**2 = 0. What is i?
-2, -1, 0
Let d be (-22*4/(-20))/(134 