 Factor 9 - 15 + 5*z - 2*z**x + 2 + z**w.
-(z - 4)*(z - 1)
Let y(g) be the first derivative of -g**6/1080 + g**4/72 - 2*g**3/3 + 53*g + 48. Let x(i) be the third derivative of y(i). Factor x(r).
-(r - 1)*(r + 1)/3
Let o(p) = -p**2 - 363*p + 16124. Let q be o(40). Find f such that 4/5*f + 6/5*f**2 - 2/5*f**3 - 6/5*f**q + 0 - 2/5*f**5 = 0.
-2, -1, 0, 1
Let j(z) be the second derivative of 42*z + 1/24*z**4 + 1/6*z**3 + 0 + 0*z**2. Determine l so that j(l) = 0.
-2, 0
Let o be 2396/(-420) + -5*1/25. Let j = 131/21 + o. Factor 1/3*b - j*b**2 + 0.
-b*(b - 1)/3
Suppose 75 = -10*c + 175. Let b be 62/c - (16 - 10). Factor -7/5*v + v**2 - b*v**3 + 3/5.
-(v - 3)*(v - 1)**2/5
Let i(m) = 2*m**5 + 113*m**4 - 3361*m**3 - 350*m**2 + 10330*m - 6734. Let o(n) = n**5 - n**4 + 2*n - 2. Let t(f) = -i(f) + 3*o(f). Factor t(d).
(d - 58)**2*(d - 1)**2*(d + 2)
Let d(s) be the third derivative of -s**6/90 - 19*s**5/30 + 10*s**4/3 + 25*s**3/2 - 4*s**2 + s. Let g(m) be the first derivative of d(m). Factor g(x).
-4*(x - 1)*(x + 20)
Let w(v) = v**2 - v - 506. Let r be w(-22). Let a(o) be the first derivative of -2/19*o**3 + 25 + r*o**2 - 1/38*o**4 + 0*o. Factor a(h).
-2*h**2*(h + 3)/19
Let u(i) = -4 + 2 + 5*i**2 + 0 + 3 + 2*i. Let l be u(-1). Factor -12*r**2 + l*r + 4*r**4 + 12 + 2 - 4*r**3 - 6.
4*(r - 2)*(r - 1)*(r + 1)**2
Let w = 211749 - 211713. Factor 9/2*a - 97/4*a**2 + w*a**3 - 16*a**4 - 1/4.
-(a - 1)**2*(8*a - 1)**2/4
Factor 3194*l + 982 + 12*l**2 - 1690*l - 5435*l - 4545*l + 1842.
4*(l - 706)*(3*l - 1)
Suppose 0 = 4*z - 37 + 25. Factor -192 + 6*r**3 + 36*r**2 - 96*r - 6*r**3 + 24*r**3 + z*r**4.
3*(r - 2)*(r + 2)*(r + 4)**2
Factor 7*b - 5*b**4 - 120*b**2 + 125 - 30*b**3 + 48*b - 20*b**3 - 4*b - b.
-5*(b - 1)*(b + 1)*(b + 5)**2
Let t(p) be the first derivative of -p**6/18 - 281*p**5/15 - 4970*p**4/3 - 19600*p**3/9 + 2928. Factor t(b).
-b**2*(b + 1)*(b + 140)**2/3
Let r(b) = -b**3 + 10*b**2 - 9*b - 16. Let n be r(9). Let h be 8/6*(92/n - -6). Suppose -h*c**3 - 4*c**2 - 12*c + 0 = 0. What is c?
-6, 0
Let y(t) be the third derivative of -t**6/320 + t**5/80 + 35*t**4/64 + 10*t**2 + 28*t. Factor y(d).
-3*d*(d - 7)*(d + 5)/8
Let l(w) be the third derivative of -w**5/420 - 52*w**4/21 + 223*w**2. Factor l(h).
-h*(h + 416)/7
Let t(i) be the second derivative of -11*i**6/40 - i**5 + i**4/2 - 63*i**2/2 - 2*i + 2. Let n(y) be the first derivative of t(y). Suppose n(l) = 0. What is l?
-2, 0, 2/11
Let i be (7 - -1) + (-58 - -41) - (-98)/10. Find l, given that 8/5 - i*l - 4/5*l**2 = 0.
-2, 1
Let m(y) be the third derivative of -11*y**5/240 - 53*y**4/96 - 3*y**3/2 - 1074*y**2. Factor m(k).
-(k + 4)*(11*k + 9)/4
Solve -1326/5 + 1299/5*h + 6*h**2 - 3/5*h**3 = 0 for h.
-17, 1, 26
Let f = 28 - 16. Suppose 10*x + 10 = f*x. Determine w so that 5*w**4 + 0*w**2 - 6*w - w**x + 3*w**3 - 2*w**4 - 7*w**2 = 0.
-1, 0, 2, 3
Let n be (-12)/(-810)*-9*((-15)/(-35) + 345/(-70)). Factor -96/5 + n*v**2 - 42/5*v.
3*(v - 16)*(v + 2)/5
Let y(m) = -m**2 - 10*m + 24. Let s(r) = -r**3 - 4*r**2 + 18*r + 53. Let t be s(-5). Let o be y(t). Factor 0*l + 1/6*l**2 + o.
l**2/6
Suppose 0 = -2*y + n + 25 - 133, 6*n = -y - 67. Let x be ((-25)/15)/(y/22). Let 0 + x*d**2 - 10/3*d = 0. What is d?
0, 5
Solve -182250000/7 - 2700/7*z**2 + 2/7*z**3 + 1215000/7*z = 0 for z.
450
Factor 25/3*h + 65/6*h**3 + 0 - 115/6*h**2.
5*h*(h - 1)*(13*h - 10)/6
Let s(p) be the third derivative of p**5/60 - 65*p**4/3 + 33800*p**3/3 + 3*p**2 - 305. Determine i so that s(i) = 0.
260
Suppose -5*f + 12*v - 8*v = -2924, -3*f + 1755 = -3*v. Let r = 584 - f. Let 1/4*p - 1/2*p**4 + 0*p**3 + r + 1/2*p**2 - 1/4*p**5 = 0. What is p?
-1, 0, 1
Let k = -13 + 14. Let v(x) = x**3 - x**2 - x - 5. Let g(h) = -12*h**3 + 48*h**2 + 45*h + 75. Let u(q) = k*g(q) + 15*v(q). What is t in u(t) = 0?
-10, -1, 0
Let a be 64/14 + 12/224*8. Let r be (a/(-33))/(80/(-192)). Suppose -6/11 - r*f + 2/11*f**2 = 0. Calculate f.
-1, 3
Let q(d) be the second derivative of 0*d**2 - 307*d - 53/66*d**4 - 5/22*d**5 - 9/11*d**3 + 0 + 1/165*d**6. Factor q(a).
2*a*(a - 27)*(a + 1)**2/11
Solve -1/5*t**2 - 1 - 6/5*t = 0.
-5, -1
Let q(t) = 308*t**2 - 143889*t + 258768189. Let s(a) = -855*a**2 + 395695*a - 711612520. Let g(i) = -25*q(i) - 9*s(i). Suppose g(f) = 0. What is f?
3597
Suppose -54 = -128*a + 95 + 235. Factor 5/2*x - 1 + 1/2*x**a - 2*x**2.
(x - 2)*(x - 1)**2/2
Factor 45*x**2 + 6*x + x - 576*x**3 - 70 + x + 7*x + 586*x**3.
5*(x - 1)*(x + 2)*(2*x + 7)
Let c(o) = o**2 - 2*o + 1. Let n(g) = -2012*g + 4. Let b(z) = -4*c(z) + n(z). Factor b(a).
-4*a*(a + 501)
Factor -z**4 + 19*z - 9*z**2 - 7*z + 4*z + z**2 - 7*z**3 + 0*z**4.
-z*(z - 1)*(z + 4)**2
Let o(p) = 48*p - 45. Let w be o(-8). Let d be (-8)/52 - 1496/w. What is f in 2/3 + 8/3*f**2 + d*f = 0?
-1, -1/4
Let p be (-2)/(-9) - 184/18. Let s be 3*(p/(-24) - (-10)/40). Find u such that -113*u**2 + 42*u**3 - 8*u + 3*u**3 + 2*u + 110*u**s = 0.
-1/3, 0, 2/5
Let t(c) be the first derivative of -28*c + 1/2*c**4 - 32 - 8/3*c**3 - 19*c**2. Find g, given that t(g) = 0.
-2, -1, 7
Find z such that -30 - 11*z - 1/3*z**2 = 0.
-30, -3
Let b(o) be the second derivative of -5/4*o**4 + 1/2*o**6 + 0*o**3 + 0 + 1/14*o**7 - 3/20*o**5 - 229*o + 0*o**2. Factor b(a).
3*a**2*(a - 1)*(a + 1)*(a + 5)
Factor -206 + 70 - 6366*p - p**2 + 6436*p.
-(p - 68)*(p - 2)
Let k be (4 + (-4 - -2))*2. Suppose -4*p + 2*h = -16, k*h = 2*p + 3*p - 23. Factor 9/7*c**p + 3*c**2 + 15/7*c + 3/7.
3*(c + 1)**2*(3*c + 1)/7
Let i(l) be the third derivative of 13/120*l**6 - 73*l**2 + 47/40*l**5 + 1/420*l**7 + 49/3*l**3 + 0*l + 0 - 91/12*l**4. Factor i(t).
(t - 1)**2*(t + 14)**2/2
Let s(b) be the first derivative of -8/5*b + 26 - b**2 - 2/15*b**3. Determine v, given that s(v) = 0.
-4, -1
Let p(w) be the third derivative of -1/8*w**4 + 1/4*w**5 + 0 + 1/40*w**6 + 35*w**2 - 2*w - 5/2*w**3. Factor p(q).
3*(q - 1)*(q + 1)*(q + 5)
Factor -276*n**3 + 67*n**4 + 400*n**2 + 0 - 11/2*n**5 - 64*n.
-n*(n - 4)**3*(11*n - 2)/2
Suppose -45 = -7*z - 10. Suppose z*v - 6 = 9. Solve -8 - 104*x**v - 5*x**5 - 44*x - 192*x**2 + 96*x**2 - 56*x**4 - 7*x**5 = 0 for x.
-1, -2/3
Let f = 108629/6 - 18103. Factor -1/6*q**3 + 0*q - f*q**2 + 0.
-q**2*(q + 11)/6
Let x = 16 + -31. Let g be (0 - (-5 - 5))*(-2)/x. Solve -g*s**3 - 32/3*s + 8*s**2 + 0 = 0 for s.
0, 2, 4
Factor 194688 - 18451*q**2 + 18453*q**2 - 165*q + 1413*q.
2*(q + 312)**2
Let y(c) be the second derivative of 0 - 16/13*c**6 - 235/78*c**4 - 25/13*c**3 - 69/26*c**5 + 63*c - 64/273*c**7 - 9/13*c**2. Factor y(m).
-2*(m + 1)**3*(8*m + 3)**2/13
Let w(s) = 34*s + 361. Let p be w(-28). Let v = -5303/9 - p. Determine u so that -v*u - 14/9 - 2/9*u**2 = 0.
-7, -1
Let t = 430318 + -4733482/11. Factor -t*s - 2/11*s**2 - 30/11.
-2*(s + 3)*(s + 5)/11
Let b(q) = -8*q**3 + 1826*q**2 + 3718*q + 1856. Let y(w) = 4*w**3 - 914*w**2 - 1858*w - 928. Let u(n) = -3*b(n) - 7*y(n). Factor u(i).
-4*(i - 232)*(i + 1)**2
Suppose b = i + 9, -5*b - 3*i = 23 - 100. Let g be (-7 - (-92)/b)*(5 - -3). Factor g*o**2 - 2/13*o**3 + 4/13 - 10/13*o.
-2*(o - 2)*(o - 1)**2/13
Factor 25560/7*f - 27221400/7 - 6/7*f**2.
-6*(f - 2130)**2/7
Suppose 2 = 12*c - 11*c. Factor -n**2 - 3*n**c - 16*n - 4538 + 4522.
-4*(n + 2)**2
Let u(o) = 6*o**2 - 240*o + 7434. Let b(a) = -7*a**2 + 239*a - 7432. Let s = -400 - -395. Let h(t) = s*u(t) - 4*b(t). Suppose h(w) = 0. Calculate w.
61
Let x be ((-197)/(11032/(-2016)))/((-21)/(-2)). Factor -18/7 + x*z - 8/7*z**3 - 2/7*z**4 + 4/7*z**2.
-2*(z - 1)**2*(z + 3)**2/7
Let y(d) be the third derivative of 2*d**7/105 - 7*d**6/120 - 23*d**5/30 + 37*d**4/24 + 2*d**3 - 308*d**2 - 4. Suppose y(w) = 0. What is w?
-3, -1/4, 1, 4
Let y be (-6)/(-69) - (17 + (-5655)/299). What is n in -n + 4/5*n**y + 0 - 1/5*n**5 + 6/5*n**3 - 4/5*n**4 = 0?
-5, -1, 0, 1
Let f(b) = 24*b**3 - 52*b**2 - 4*b + 2. Let x(j) = j**4 + 49*j**3 - 102*j**2 - 10*j + 5. Let v(z) = -5*f(z) + 2*x(z). Let v(t) = 0. What is t?
0, 4, 7
Let a(t) be the third derivative of t**5/90 + 505*t**4/18 + 255025*t**3/9 + 172*t**2. Factor a(m).
2*(m + 505)**2/3
Let f = 123 + -122. Factor 1 + 4*v**4 - 356*v**3 - f - 12*v**2 - 72*v + 372*v**3.
4*v*(v - 2)*(v + 3)**2
Let f(r) be the first derivative of -28*r**3/3 + 948*r**2/5 - 736*r/5 + 1697. Let f(y) = 0. Calculate y.
2/5, 92/7
Let x = 4966/1491 - -4/1491. Let d = 1/35 - -131/315. F