**3/3 + 180*c**2 + 10427. Factor o(n).
-4*n*(n - 1)*(n + 9)*(n + 10)
Suppose -4*w + 12 = -2*g - 8*w, -3*g = -w - 10. Factor -8 - 166*f**2 - 162*f**2 + 329*f**g + 2*f.
(f - 2)*(f + 4)
Let y(j) = 29*j**3 - 67*j**2 - 1386*j + 7329. Let u(r) = -9*r**3 + 22*r**2 + 461*r - 2444. Let n(p) = 7*u(p) + 2*y(p). Factor n(t).
-5*(t - 7)**2*(t + 10)
Factor 1800 - 23621*o + 196*o**3 + 8394*o + 619*o**2 + 10287*o + 2629*o**2.
4*(o + 18)*(7*o - 5)**2
Let f(r) = -72*r + 1514. Let w be f(21). Let p(s) be the second derivative of -1/9*s**3 + 1/6*s**w + 1/36*s**4 + 0 + 5*s. Determine q, given that p(q) = 0.
1
Let r be 2 - (7 + 1932/(-6)). Let a = r + -317. Factor 0*o**2 + 2/3*o**5 + 2/3*o**4 - 4/3*o**3 + 0*o + a.
2*o**3*(o - 1)*(o + 2)/3
Let j(r) be the third derivative of r**7/70 - 33*r**6/4 + 27553*r**5/20 - 6765*r**4 + 13448*r**3 - r**2 + 139*r. Factor j(a).
3*(a - 164)**2*(a - 1)**2
Let u(s) be the first derivative of s**3/12 + 143*s**2/4 + 20449*s/4 + 3022. Let u(q) = 0. Calculate q.
-143
Let k be (-78)/(-5) - ((-86)/(-4515) - 2954/735). Suppose -168/5*z**2 + 32/5*z**5 - 94/5*z + 144/5*z**4 - 12/5 + k*z**3 = 0. What is z?
-3, -2, -1/4, 1
Let g(i) be the second derivative of 1/18*i**3 - 5/2*i**2 + 0 + 1/24*i**4 + 1/90*i**5 + 47*i. Let v(t) be the first derivative of g(t). Factor v(p).
(p + 1)*(2*p + 1)/3
Let g(v) be the second derivative of 0*v**2 + 5*v**3 - 25/12*v**4 + 1/4*v**5 - 13*v + 0. Factor g(b).
5*b*(b - 3)*(b - 2)
Suppose 5*u - 20 = -v, -3*u + 4*v - v = -30. Find y such that 695*y**4 - 40 - 99*y + 75*y**5 - 2*y + y + 470*y**2 - 77*y**5 + 1085*y**3 + 142*y**u = 0.
-2, -1, -1/4, 2/7
Let h be -18 + 1 - (-1131455)/1690. Factor 975/4*d**4 - 125/4*d**5 + 243/4 - 1377/4*d - h*d**3 + 1431/2*d**2.
-(d - 3)**2*(5*d - 3)**3/4
Let q(j) be the third derivative of 0*j**3 + 0 - 33/200*j**6 - 7*j**2 + 3/10*j**4 + 4/25*j**5 + 0*j + 1/70*j**7. What is c in q(c) = 0?
-2/5, 0, 1, 6
Let r(v) be the third derivative of -2/3*v**4 + 14/5*v**3 + 0 - 29*v - 1/75*v**5 - 3*v**2. Factor r(w).
-4*(w - 1)*(w + 21)/5
Let m be ((-2)/12)/((-1)/(-6)). Let b(s) = 3*s**3 - s**2 + s - 1. Let k(q) = -18*q**4 - 8*q**3 + 290*q**2 - 422*q + 78. Let o(c) = m*k(c) + 2*b(c). Factor o(h).
2*(h - 2)**2*(h + 5)*(9*h - 2)
Let t(y) be the first derivative of 15/13*y**2 - 2/65*y**5 + 0*y - 92 - 46/39*y**3 + 9/26*y**4. Find p, given that t(p) = 0.
0, 1, 3, 5
Factor -4*f**3 - 32*f**3 + 45*f + 18*f**2 + 38*f**3 - 9*f.
2*f*(f + 3)*(f + 6)
Suppose 3*s + 42 = 4*i, -22*s = i - 21*s - 7. Let -12*q**4 - i*q**3 - 128*q + 92*q + 3*q**5 + 60*q**2 - 6*q**4 = 0. Calculate q.
-2, 0, 1, 6
Let w(k) be the third derivative of 7*k**5/240 - 611*k**4/16 - 131*k**3/3 + 14*k**2 + 6*k - 2. Factor w(d).
(d - 524)*(7*d + 2)/4
Let d(z) be the third derivative of 0*z - 14*z**2 + 4 - 1/168*z**8 + 0*z**3 + 1/20*z**6 + 1/6*z**5 + 1/6*z**4 - 1/105*z**7. Solve d(x) = 0 for x.
-1, 0, 2
Let l(d) = 5*d**2 + 20*d - 5. Let q(b) = b**3 - 12*b**2 + 9*b + 18. Let o be q(11). Let j(z) = -5*z**2 - 19*z + 4. Let n(c) = o*l(c) - 5*j(c). Factor n(k).
5*k*(k + 3)
Let w(f) be the first derivative of f**6/900 + f**5/60 + f**4/15 + 2*f**3/3 + 10*f**2 + 60. Let b(t) be the third derivative of w(t). Factor b(a).
2*(a + 1)*(a + 4)/5
Let w(p) be the first derivative of 2*p**5/25 + 7*p**4/10 - 18*p**3/5 + 29*p**2/5 - 4*p + 484. Suppose w(i) = 0. What is i?
-10, 1
Let v(m) be the second derivative of m**6/15 - 141*m**5/10 + 344*m**4/3 - 364*m**3 + 544*m**2 + 115*m + 2. Solve v(o) = 0 for o.
1, 2, 136
Suppose 12*b - 21 = 11*b. Suppose 5*o + 5*a = 3*o + b, 0 = 2*o - 3*a - 29. Let 76*z**4 - o*z**3 + 3*z**3 - 4*z**2 - 84*z**4 - 2*z**5 = 0. Calculate z.
-2, -1, 0
Suppose -480/11 + 466/11*a**2 + 14/11*a**4 - 208/11*a - 2/11*a**5 + 210/11*a**3 = 0. Calculate a.
-4, -1, 1, 15
Find c such that -72*c**3 - 124*c**2 + 74*c**3 - 126*c**2 = 0.
0, 125
Let m = 875222/3 + -291708. Let 28*r - m - 6*r**2 = 0. Calculate r.
7/3
Let s(f) be the third derivative of -f**5/240 + 19*f**4/96 - 17*f**3/12 + 1128*f**2. Determine k so that s(k) = 0.
2, 17
Factor 769/3*t + 1/3*t**2 - 770/3.
(t - 1)*(t + 770)/3
Let f(d) be the first derivative of -d**4/4 + 4*d**3/3 + 9*d**2/2 - 36*d - 1204. Factor f(a).
-(a - 4)*(a - 3)*(a + 3)
Let s = 3/28009 - -112015/196063. Let -16/7*o - 8/7 - 6/7*o**2 + s*o**3 + 2/7*o**4 = 0. What is o?
-2, -1, 2
Let q = -672575/96 + 7006. Let u(z) be the third derivative of 0*z - 1/120*z**5 + 0 - 14*z**2 + 0*z**3 + q*z**4. Determine f so that u(f) = 0.
0, 1/2
Let l(j) = 2*j**2 + 140*j - 361 - 108*j - 3*j**2. Let m(c) = -3*c**2 + 97*c - 1083. Let v(w) = 17*l(w) - 6*m(w). Factor v(f).
(f - 19)**2
Let v be 8*(2 - 25/20). Let x be (v/(-15))/(3 + (-95)/25). Factor -x*t + 0 + 1/2*t**3 + 0*t**2.
t*(t - 1)*(t + 1)/2
Let n(h) = 4*h**2 - 237*h - 2074. Let s be n(67). Suppose 2/11 - 2/11*v + 2/11*v**s - 2/11*v**2 = 0. Calculate v.
-1, 1
Suppose 20*s - 47*s - 709 + 1303 = 0. Let i(k) be the second derivative of -1/8*k**4 - 9/4*k**2 - k**3 + 0 - s*k. Suppose i(q) = 0. Calculate q.
-3, -1
Let g(s) = 94*s - 185. Let w be g(2). Suppose 0*h**2 + 0 + 1/9*h**w - 4/9*h = 0. Calculate h.
-2, 0, 2
Let v(y) be the second derivative of 10/7*y**2 + 0 + 3/7*y**3 - 1/42*y**4 - 14*y. Factor v(t).
-2*(t - 10)*(t + 1)/7
Let u(j) = -j**3 - j**2 + 3*j. Let l be u(0). Suppose -2*o - m + 33 - 13 = l, -2*m - 20 = -o. Find w such that 28*w - o - 5*w**2 + 3*w**3 + w**3 - 15*w**2 = 0.
1, 3
Suppose -1619*h = -1086*h - 895*h + 1448. Let r = -43/2 - -22. What is p in -p**5 - 3/2*p**3 - 5/2*p**h + r*p + 1/2*p**2 + 0 = 0?
-1, 0, 1/2
Let r be 448/160 + (2/10)/1. Suppose 4*k + 7 = -r*w, w + 33 = 4*k - 4*w. Factor -3/7*q**k + 4/7*q**3 - 1/7*q**4 + 0 + 0*q.
-q**2*(q - 3)*(q - 1)/7
Let n(o) be the third derivative of -o**8/144 - 31*o**7/210 - o**6/72 + 53*o**5/36 - 3*o**4/2 - 26*o**3/9 - 2*o**2 + 1532*o - 1. Suppose n(r) = 0. What is r?
-13, -2, -2/7, 1
Let y = 18334 + -18332. Let f(i) be the second derivative of -7/48*i**3 + 10*i + 1/96*i**4 + 3/8*i**y + 0. Solve f(n) = 0.
1, 6
Let w(q) be the second derivative of -3*q**5/140 - 47*q**4/14 - 93*q**3/14 + 143*q + 3. Factor w(b).
-3*b*(b + 1)*(b + 93)/7
Let a be (-1 - -2)*(-13 + 15). Suppose 5*q - 21 = 34. Find k such that 22*k**2 - q*k**2 + 4*k - 13*k**a = 0.
0, 2
Let f be 22/(-286)*195/(-10). Factor 1/3*w**3 + 0 - 11/6*w - f*w**2.
w*(w + 1)*(2*w - 11)/6
Suppose -4*q + 3490*b + 6513 = 3487*b, 8135 = 5*q - 5*b. Factor -q*v - 24*v**2 - 36992 - 2/17*v**3.
-2*(v + 68)**3/17
Let j(m) be the third derivative of 0*m**3 + 1/336*m**8 + 0*m**5 + 2*m**2 + 3/20*m**6 - m - 4/105*m**7 - 9/8*m**4 + 0. Factor j(q).
q*(q - 3)**3*(q + 1)
Let b(y) = -y**2 - 2*y - 1. Let r(k) = 9*k**2 - 17*k + 34. Suppose 6 = -i + 7*i. Let g(d) = i*r(d) + 4*b(d). Suppose g(j) = 0. What is j?
2, 3
Let k(t) be the second derivative of t**4/3 + 14*t**3 - 92*t**2 - t - 113. Let k(a) = 0. Calculate a.
-23, 2
Let d(y) be the third derivative of -1/45*y**5 + 28/3*y**3 + 9*y + 2*y**2 + 19/18*y**4 + 0. Determine u, given that d(u) = 0.
-2, 21
Let s be 2/6*(3 - 2). Let m be (-18)/1260*10 + -1 + 29/7. Determine t so that -4/3*t**2 + 0 - s*t**m - t = 0.
-3, -1, 0
Let p(w) = w**2 + 4*w + 4. Let a be 40/16*(-16)/20. Let n be p(a). Factor 3/7*c**2 + n - 3/7*c**3 + 6/7*c.
-3*c*(c - 2)*(c + 1)/7
Let c(y) be the first derivative of 2/5*y**5 - 51 + 28/3*y**3 - 15/2*y**4 + 0*y**2 + 0*y. What is h in c(h) = 0?
0, 1, 14
Let s(z) = z**4 + 2*z**3 - 33*z**2 + 42*z - 19. Let o(m) = -42*m - 43*m + m**3 + 84*m + 1. Let b(l) = 14*o(l) + 2*s(l). Suppose b(d) = 0. What is d?
-12, 1
Let d(l) be the second derivative of l**7/336 + 89*l**6/240 - 273*l**5/160 + 275*l**4/96 - 23*l**3/12 - l + 1729. Factor d(v).
v*(v - 1)**3*(v + 92)/8
Let f(g) = g**2 + 30*g + 179. Let a be f(-8). Solve -253*x**3 + x**4 - 17*x**2 + 517*x**a - 248*x**3 = 0.
-17, 0, 1
Let f be 80088/24534 + 6/87. Let d(h) be the third derivative of -35/24*h**4 + 0*h + 1/24*h**6 - 29*h**2 + 0 + f*h**3 + 1/6*h**5. Factor d(p).
5*(p - 1)**2*(p + 4)
Let m(f) be the second derivative of 0*f**2 + 2*f + 5/48*f**4 + 26 + 85/24*f**3. Factor m(q).
5*q*(q + 17)/4
Let o(q) be the third derivative of q**5/60 - 7*q**4/12 + q**3/2 - q**2. Let j be o(14). What is w in -3*w**3 + 3*w**j - 4*w**2 - 4*w**4 + 2*w**4 - 6*w**3 = 0?
-2, -1, 0
Suppose -91*t + 100 = -81*t. Let f(r) = r + 5.