t x(p) = -39*p**4 + 117*p**3 - 228*p**2 - 2160*p - 2580. Let i(c) = 12*s(c) - x(c). Factor i(b).
3*(b - 27)*(b - 8)*(b + 2)**2
Let r(g) = -461*g - 6901. Let f be r(-15). Let a(o) be the first derivative of -10/3*o**3 + 26 - 13*o**2 - f*o + 1/2*o**4. Factor a(s).
2*(s - 7)*(s + 1)**2
Let d be (-399)/189 - 2/(-18). Let t be (-5)/d + (-798)/(-2964). Factor 0*w + 24/13*w**3 + 10/13*w**5 - t*w**4 + 0 + 16/13*w**2.
2*w**2*(w - 2)**2*(5*w + 2)/13
Let v(b) be the third derivative of b**5/66 - 16*b**4/33 - 125*b**2 - 1. Find g such that v(g) = 0.
0, 64/5
Let y(h) = -2*h**2 - 6*h - 6. Let i(p) = p**2 - 2*p - 1. Let x be (-1813)/(-148) - (0 + 1/4). Let w(z) = x*i(z) - 2*y(z). Find t, given that w(t) = 0.
0, 3/4
Let d = -42834 + 299840/7. Factor -d*r**2 + 20/7 + 18/7*r.
-2*(r - 10)*(r + 1)/7
Find s, given that -660 + 290*s - 240*s**2 - 3846*s**3 + 3841*s**3 - 1185*s = 0.
-44, -3, -1
Let t = 5377 - 5374. Let p(a) be the second derivative of 0*a**2 + 0 + t*a - 1/6*a**4 + 1/20*a**5 + 0*a**3. Suppose p(r) = 0. Calculate r.
0, 2
Let g be ((-5)/20)/(562/32). Let q = 269/843 - g. Factor q*i**3 + i + 0 - 4/3*i**2.
i*(i - 3)*(i - 1)/3
Let x(v) be the first derivative of v**3/3 + 131*v**2/2 + 258*v + 8352. Solve x(z) = 0.
-129, -2
Solve 104 - 6*v**2 + 59*v + 2*v**2 + v**2 + 127*v - 287 = 0 for v.
1, 61
Let d(x) be the first derivative of 0*x + 0*x**2 + 1/3*x**6 + 1/3*x**3 - 1/2*x**5 - 7/8*x**4 + 29. Let d(n) = 0. What is n?
-1, 0, 1/4, 2
Let m(l) = l**2 - l - 40. Let d(v) = 6*v**2 - 28*v + 10. Let u be d(4). Let j be m(u). Factor -1/5*k**5 + 0 + 0*k + 8/5*k**j - 2/5*k**4 + 4/5*k**3.
-k**2*(k - 2)*(k + 2)**2/5
Let u(v) = -13*v**3 - 27*v**2 - 80*v - 84. Let m(n) = 12*n**3 + 28*n**2 + 80*n + 81. Let h(j) = 8*m(j) + 7*u(j). Solve h(k) = 0.
-3, -2
Let c(j) be the second derivative of -1/30*j**5 - j - 23 + 0*j**2 + 1/12*j**4 + 0*j**3. Determine a so that c(a) = 0.
0, 3/2
Let p(d) be the second derivative of 450*d**2 + 1/3*d**4 - 20*d**3 + 11 - d. Factor p(h).
4*(h - 15)**2
Factor 3/4*g + 1/8*g**2 - 55/8.
(g - 5)*(g + 11)/8
Let j(p) = 41*p**2 - p + 2. Let o(a) = -79*a**2 + 2*a - 5. Let u = -166 + 164. Let d(m) = u*o(m) - 5*j(m). Let d(v) = 0. What is v?
0, 1/47
Let v(z) = -2*z**3 + z**2 - 3. Let d(s) = -28*s**3 + 5302*s**2 - 5284*s + 1302. Let q(c) = -d(c) + 6*v(c). Determine y, given that q(y) = 0.
1/2, 330
Suppose 400*y = 379*y + 378. Suppose 0 = 3*r - 4*b - 5, 5*r - 3*b - 14 = -2*b. Factor 12*p**2 - y*p**2 - 6*p**3 + 4*p + 8*p**r.
2*p*(p - 2)*(p - 1)
Factor -1/4*u**3 - 142884*u + 0 + 378*u**2.
-u*(u - 756)**2/4
Factor 2/7*m**4 - 66/7*m**3 - 30*m**2 - 214/7*m - 72/7.
2*(m - 36)*(m + 1)**3/7
Suppose -300/19 - 472/19*r**2 - 44/19*r**3 - 6/19*r**5 + 52/19*r**4 + 770/19*r = 0. What is r?
-3, 2/3, 1, 5
Let g be -10 + 5/1 - ((-14620)/(-40))/(-43). Find h such that 23/2*h**2 - 1/2*h**5 + 4*h - g*h**3 - 7/2*h**4 - 8 = 0.
-4, -1, 1
Let x be 6/3 + 6 + -6 + -1. Let w(y) be the first derivative of -x - 5/4*y**4 - 5/3*y**3 + 5*y**2 + 0*y. Factor w(b).
-5*b*(b - 1)*(b + 2)
Let b(q) be the first derivative of q**4/8 + 9*q**3/2 + 60*q**2 + 352*q - 605. Find w, given that b(w) = 0.
-11, -8
Let b(v) = 4*v**2 + 4*v + 134. Let l be b(18). Let x = l - 1502. Factor 0 - 154/9*i**4 - 8/9*i**2 + 98/9*i**5 + x*i + 64/9*i**3.
2*i**2*(i - 1)*(7*i - 2)**2/9
Let 11/5*l + 107/5*l**2 - 3/5*l**4 - 104/5 - 11/5*l**3 = 0. What is l?
-8, -1, 1, 13/3
Factor 238007/2*t + 1/2*t**4 + 80649/2*t**2 + 78961 + 565/2*t**3.
(t + 1)*(t + 2)*(t + 281)**2/2
Let q = 35244 + -35240. Let c(w) be the first derivative of 4/3*w**3 + 39 - 4*w**4 + 0*w + q*w**2 - 12/5*w**5. Solve c(p) = 0.
-1, 0, 2/3
Let a be 8/21 + 20/(-1470)*-21. Let f(r) be the first derivative of a*r**2 + 16/9*r**3 + 24 + 0*r. Factor f(v).
4*v*(4*v + 1)/3
Let j(i) = i**2 - 2*i + 12. Let y(k) = 3*k**2 - 8*k + 37. Let q(h) = -11*j(h) + 4*y(h). Factor q(u).
(u - 8)*(u - 2)
Suppose -w = -i - 5*w + 84, 4*i - 2*w = 354. Suppose 8*n + 88 = i. What is a in 0*a + 2/11*a**4 + n - 4/11*a**3 + 2/11*a**2 = 0?
0, 1
Let a be 6*(-2)/(-36)*-39. Let q = a - -35. Factor -4*x + q + 2/11*x**2.
2*(x - 11)**2/11
What is f in 7/2 - 5/4*f - 1/4*f**2 = 0?
-7, 2
Let g = -10918 + -1402. Let f be ((-4)/(-7))/((-16)/(g/33)). Determine c, given that f*c + 244/9*c**2 + 14/3*c**3 - 98/9*c**4 + 16/9 = 0.
-1, -2/7, 2
Let r(a) = 7*a**2 - 71*a - 1014. Let q be r(-8). Factor -27/8*i**3 - 3/8*i**4 + 0*i + 15/4*i**q + 0.
-3*i**2*(i - 1)*(i + 10)/8
Factor -518*m - 256*m**2 + 168 - 43*m**3 - 45*m**3 - 428 - 46*m**3 + 136*m**3.
2*(m - 130)*(m + 1)**2
Let -48*i + 135*i**4 + 0 - 747*i**3 + 1848/5*i**2 = 0. Calculate i.
0, 4/15, 5
Let u(v) = -v**2 + 3*v + 11. Let l be u(4). Suppose -3*q + 4*a = -64, -63 = 4*q - l*q + 3*a. Factor -5*j**2 - 860*j**3 + 6*j + 14*j + q + 855*j**3.
-5*(j - 2)*(j + 1)*(j + 2)
Let n(r) = 171*r**3 - 124*r**2 - 11*r. Let k(j) = -343*j**3 + 245*j**2 + 23*j. Let a(q) = -12*k(q) - 25*n(q). Factor a(w).
-w*(w - 1)*(159*w - 1)
Let u(g) be the first derivative of -4/3*g**2 - 1/18*g**3 - 32/3*g + 4. Factor u(m).
-(m + 8)**2/6
Suppose 20 = -4*p - 4*i, -5*i + 13 = 38. Suppose p = -7*d - 2*d - 13*d. Factor d*o - 4/7*o**2 + 2/7*o**5 + 0 - 6/7*o**3 + 0*o**4.
2*o**2*(o - 2)*(o + 1)**2/7
Let u(t) be the second derivative of 11*t**6/80 + 3*t**5/5 - 29*t**4/16 - 3*t**3/2 + 79*t**2/2 - 36*t. Let c(n) be the first derivative of u(n). Factor c(g).
3*(g - 1)*(g + 3)*(11*g + 2)/2
Let z(i) be the first derivative of i**4/3 - 808*i**3/9 + 20402*i**2/3 - 565. Factor z(t).
4*t*(t - 101)**2/3
Suppose 0 = 5*p - 3*r - 20, -4*p + 2*r = r - 16. What is a in 915*a**4 - 49*a**5 - 12*a**2 - 1034*a**p + 28*a**3 + 52*a**3 = 0?
-3, 0, 2/7
Let s(r) be the second derivative of -r**6/120 - 1039*r**5/80 + r**4/16 + 3115*r**3/24 - 1039*r**2/4 + 666*r - 2. Solve s(w) = 0.
-1039, -2, 1
Let x(p) be the first derivative of p**4/38 - 1730*p**3/19 + 2244675*p**2/19 - 1294429250*p/19 - 1528. Solve x(h) = 0.
865
Let o(t) be the second derivative of -t**4/3 + 1994*t**3 + 5984*t**2 - t - 5930. Factor o(q).
-4*(q - 2992)*(q + 1)
Suppose 0 = -17*r + 319 - 30. Suppose -r = -w + 13*a - 8*a, 5*a + 21 = 3*w. Factor 3*f**w + 0 + 9/5*f + 3/5*f**3 - 3/5*f**4.
-3*f*(f - 3)*(f + 1)**2/5
Let c(g) be the first derivative of 93/2*g**2 + 36*g - 27 + 3/2*g**4 + 15*g**3. Solve c(b) = 0.
-4, -3, -1/2
Let a(o) be the second derivative of -o**7/14 + 18*o**6/5 - 39*o**5/2 + 15*o**4 + 131*o**3/2 - 144*o**2 + 5*o. Let a(k) = 0. Calculate k.
-1, 1, 3, 32
Let o(q) = -13*q**3 + 8*q**2 + 12*q + 5. Let b be o(-1). Let w be (49/21)/(-7)*(-6)/b. Solve 8/7 + 6/7*l**2 + w*l**3 + 12/7*l = 0 for l.
-2
Let c(v) be the first derivative of v**6/18 - 7*v**5/5 - 11*v**4/6 - 1180. Factor c(m).
m**3*(m - 22)*(m + 1)/3
Let u(o) be the first derivative of 20164*o**5/35 - 5325*o**4/7 + 384*o**3/7 - 8*o**2/7 + 89. Solve u(t) = 0 for t.
0, 2/71, 1
Determine v, given that -31/8*v**3 + 99/8*v**2 - 1/8*v**4 - 101/8*v + 17/4 = 0.
-34, 1
What is c in -364/3*c**2 - 4*c**3 - 1120/3 + 1928/3*c = 0?
-35, 2/3, 4
Let h = 109 + -107. Suppose -b**3 + 6*b**2 + 19*b**h - 32*b**2 + 8*b = 0. What is b?
-8, 0, 1
Let r(t) be the third derivative of t**6/48 - t**5/24 - 5*t**4/24 + 524*t**2 - t. Factor r(n).
5*n*(n - 2)*(n + 1)/2
Let j(r) be the third derivative of 0 + 1/210*r**6 - 8/105*r**5 + 0*r**3 + 0*r + 0*r**4 + 50*r**2. Find g such that j(g) = 0.
0, 8
Let f(c) be the second derivative of 3*c**5/80 + 15*c**4/16 + 6*c**3 - 24*c**2 - 96*c - 6. Let f(a) = 0. Calculate a.
-8, 1
Let u(i) = 5*i**2 + 124*i + 228. Let o(s) = -35*s**2 - 870*s - 1600. Let n(c) = -2*o(c) - 15*u(c). Factor n(t).
-5*(t + 2)*(t + 22)
Suppose 108/7 + 3/7*i**2 + 39/7*i = 0. What is i?
-9, -4
Factor 724/5*h - 96 + 2/5*h**3 - 246/5*h**2.
2*(h - 120)*(h - 2)*(h - 1)/5
Let w(j) be the first derivative of j**4/30 + 13*j**3/15 + 6*j**2 - 47*j + 33. Let q(x) be the first derivative of w(x). Factor q(m).
2*(m + 3)*(m + 10)/5
Suppose -33*v + 13*v = 39*v. Solve 0*x - 1/8*x**5 + v - 1/2*x**2 + 3/8*x**4 + 0*x**3 = 0 for x.
-1, 0, 2
Suppose 0 = d + z + 241, 4*d + 1479 = 4*z + 499. Let v be (d/(-36) - 4) + -1*2. Solve 0 - 1/2*p + v*p**2 - 1/4*p**3 = 0 for p.
0, 1, 2
Let h(v) be the second derivative of -1/20*v**5 - 7/6*v**4 + 17/6*v**3 + 0 + 15*v**2 - 82*v. Factor h(q).
-(q - 2)*(q + 1)*(q + 15)
Let c(j) = -10*j + 122. Let x be