 Factor -13*o**3 + 432 - 108*o + 30*o**3 + 183*o**3 - 48*o**4 + 4*o**f + 141*o**2 - 429*o**2.
4*(o - 4)*(o - 3)**3*(o + 1)
Let v(w) = -2*w**3 + 53*w**2 - 26*w + 24. Let a be v(26). Suppose -a*i + 260 = 41*i. Solve -10/3*k**3 - 1/3*k**5 + 10/3*k**2 + 5/3*k**i - 5/3*k + 1/3 = 0 for k.
1
Let w(t) = t**2 + 31*t + 242. Suppose 6*h + 1440 = 1344. Let k be w(h). Factor 2*b**k + 4/3 + 1/3*b**3 + 3*b.
(b + 1)**2*(b + 4)/3
Let v(o) = -9*o**3 - 57*o**2 - 213*o - 270. Let q(w) = -5*w**3 - 33*w**2 - 107*w - 135. Let g(s) = -15*q(s) + 8*v(s). Determine p so that g(p) = 0.
-15, -1, 3
Let o(j) be the third derivative of j**5/80 + 639*j**4/32 - 80*j**3 + 1634*j**2. Factor o(y).
3*(y - 1)*(y + 640)/4
Let n = 62653 - 313256/5. Factor 3*w**3 + 33/5*w + n + 39/5*w**2.
3*(w + 1)**2*(5*w + 3)/5
Factor 10/7*m**2 - 71/7*m + 17/7*m**3 + 44/7.
(m - 1)**2*(17*m + 44)/7
Let s(z) be the second derivative of -z**7/180 - 13*z**6/72 - 3*z**5/10 - 137*z**4/12 - 105*z. Let a(g) be the third derivative of s(g). Solve a(r) = 0 for r.
-9, -2/7
Let 90/7*v**2 + 52/7 - 138/7*v = 0. Calculate v.
2/3, 13/15
Let t(y) be the third derivative of y**5/60 - 23*y**4/2 - 277*y**3/6 + 4*y**2 + 399. Factor t(u).
(u - 277)*(u + 1)
Let p(y) = y**3 + 46*y**2 - 6*y - 52. Let v be p(-46). Let o = v - 670/3. Factor 2/3*h**3 + 2 - 10/3*h + o*h**2.
2*(h - 1)**2*(h + 3)/3
Suppose -8*h**3 - 101 + 151 - 239*h + 19*h + 82*h**2 = 0. Calculate h.
1/4, 5
Suppose -3*n - 2 = -4*n. Suppose -106*g = -54*g. Let 3/5*q**3 + 3/5*q**n + 0 + g*q = 0. What is q?
-1, 0
Let s(u) be the third derivative of -2/3*u**5 + 0*u + 63*u**2 + 0 + 2/3*u**3 + 3/2*u**4. Suppose s(q) = 0. Calculate q.
-1/10, 1
Let t(q) be the third derivative of -q**8/84 - 172*q**7/105 - 587*q**6/10 + 3784*q**5/15 - 968*q**4/3 + 7*q**2 - 7*q - 4. Suppose t(i) = 0. What is i?
-44, 0, 1
Let g = 10709/8580 - 113/660. Factor -g*l - 2/13*l**2 - 12/13.
-2*(l + 1)*(l + 6)/13
Factor -89*y + 5*y**3 + 153*y**2 + 164*y**2 - 466*y - 30*y + 295 - 32*y**2.
5*(y - 1)**2*(y + 59)
Let k(r) = 5*r**3 + r. Let d = 318 + -317. Let c be k(d). Solve c + 2*i**2 + 6*i + 2/9*i**3 = 0.
-3
Let h = -56478 - -169439/3. Determine x so that -h + 8/3*x - 1/3*x**2 - 2/3*x**3 = 0.
-5/2, 1
Factor 1241201 + 45*h**2 - 23400 + 47628*h - 56*h**2 + 767*h**2 + 4*h**3 - 217613.
4*(h + 63)**3
Determine a so that -21*a - 125/2*a**2 - 39/2*a**4 + 1/2*a**5 + 0 - 123/2*a**3 = 0.
-1, 0, 42
Let a(v) be the third derivative of -v**8/2016 - 53*v**7/630 - 21*v**6/4 - 4655*v**5/36 - 42875*v**4/144 - 87*v**2 - 15*v. Factor a(l).
-l*(l + 1)*(l + 35)**3/6
Let x be (0 - (0 - 6)) + -4. Let a(o) = 4*o**3 + 11*o**2 + 5*o - 17. Let k(y) = 2*y**3 + 12*y**2 + 4*y - 16. Let u(b) = x*a(b) - 3*k(b). Factor u(z).
2*(z - 7)*(z - 1)*(z + 1)
Factor -231*x + 0 + 1/4*x**4 + 191/4*x**2 + 9*x**3.
x*(x - 3)*(x + 11)*(x + 28)/4
Let n(h) be the second derivative of -h**4/48 - 9*h**3 - 107*h**2/2 + 2923*h. Let n(s) = 0. What is s?
-214, -2
Let u = 8238 - 8238. Find a, given that u*a + 99/4*a**4 - 3 + 93/4*a**2 + 159/4*a**3 + 21/4*a**5 = 0.
-2, -1, 2/7
Find n, given that -7/4*n**2 + 5/4*n**5 - 1/2*n + 7/4*n**4 - 3/4*n**3 + 0 = 0.
-1, -2/5, 0, 1
Let c = -2504273/7 + 357815. Factor 24/7*x**3 + 4/7*x**5 - 32/7*x**4 + 1296/7 + c*x**2 - 1404/7*x.
4*(x - 3)**4*(x + 4)/7
Let u(x) = -x**3 - 21*x**2 + 7*x + 6. Let p(i) = 3*i**3 + 83*i**2 - 31*i - 22. Let z(v) = -6*p(v) - 22*u(v). Factor z(s).
4*s*(s - 8)*(s - 1)
Let b(v) be the second derivative of v**6/30 + 107*v**5/80 - 85*v**4/16 + 173*v**3/24 - 29*v**2/8 + 9*v + 34. Find c, given that b(c) = 0.
-29, 1/4, 1
Suppose -3*s + n - 3*n + 14 = 0, 0 = -s - 4*n + 8. Suppose 3*i - 26 = k - s, 2*i - 2*k = 16. Factor 24*w + 0*w**2 + 23 + 32 - i + 3*w**2.
3*(w + 4)**2
Let d(g) be the first derivative of -8/3*g - 77 + 2/27*g**3 + 4/9*g**2. Factor d(j).
2*(j - 2)*(j + 6)/9
Let i be ((-2)/(-3))/(2 - 38/18). Let w(c) = -c**3 - 7*c**2 - 7*c + 2. Let d be w(i). Factor -7*r**3 + 14*r**4 + 3*r**2 + 15*r - d*r**3 - 8*r**2 - 9*r**4.
5*r*(r - 3)*(r - 1)*(r + 1)
Let l(z) be the first derivative of 16 - 1/4*z**5 - 5/2*z**2 + 23*z + 5/6*z**3 + 5/12*z**4. Let m(d) be the first derivative of l(d). Solve m(f) = 0.
-1, 1
Let t(h) be the first derivative of -25*h**4 - 149 - 6/5*h**5 - 62/3*h**3 + 0*h + 16*h**2. Solve t(n) = 0.
-16, -1, 0, 1/3
Factor 696/5 - 52/5*n**2 - 4516/5*n.
-4*(n + 87)*(13*n - 2)/5
Let h be 115/25 + (-6)/10. Factor 95*g**4 - 21*g**2 - 183*g**h + 95*g**4 - 5 + 1 - 2*g**3 + 20*g.
(g - 1)**2*(g + 2)*(7*g - 2)
Solve -2/11*r**2 + 20 - 218/11*r = 0.
-110, 1
Let 4 - 6361*p**2 - 5*p + 6360*p**2 - 4 = 0. Calculate p.
-5, 0
Suppose 0 = -7*f + 5*f + 4. Suppose 0*c = -f*c, -2*c - 310 = -5*u. Factor 120*w - 7*w**2 - 50 + 10*w**3 + 14*w**3 - 2*w**4 - u*w**2 - 23*w**2.
-2*(w - 5)**2*(w - 1)**2
Let w = 20844/19 - 41669/38. Factor -w*q**2 + 11 + 21/2*q.
-(q - 22)*(q + 1)/2
Suppose 6 = -4*q + 3*m + 15, 0 = 4*q + 2*m - 34. Factor -v**3 - 10*v**2 + 90 - 5*v + 50*v - 11*v**3 + q*v**3 + v**3.
-5*(v - 3)*(v + 2)*(v + 3)
Let o be (-20)/(-110) - (-439920)/412566 - ((-8)/(-38))/2. Determine x so that -4/7*x**3 + o*x**4 + 4/7*x**5 + 0 + 0*x - 8/7*x**2 = 0.
-2, -1, 0, 1
Suppose 2*w - 19*w - 70 = -52*w. Factor -15/7*x**3 + 3/7*x**4 - 3*x + 6/7 + 27/7*x**w.
3*(x - 2)*(x - 1)**3/7
Let v(a) be the first derivative of 2*a**5/5 + a**4 - 32*a**3 + 32*a**2 + 512*a - 1407. Let v(s) = 0. What is s?
-8, -2, 4
Let u(y) = -44*y + 12. Let q(w) = 2*w**2 + 179*w - 47. Let s(z) = 4*q(z) + 18*u(z). Let v(n) = n - 1. Let l(o) = 5*s(o) + 5*v(o). Factor l(t).
5*(t - 9)*(8*t - 3)
Let m = -1448634/7 - -206950. Find b, given that -8/7*b + 12/7*b**2 + 10/7*b**3 + 2/7*b**4 - m = 0.
-2, 1
Let m(w) be the first derivative of 19 - 5/3*w**3 - 95/2*w**2 + 0*w. Factor m(l).
-5*l*(l + 19)
Let c be (-22)/7 + (-35568)/(-10640). Factor c*p**3 + 0 + 180*p + 12*p**2.
p*(p + 30)**2/5
Let z(q) be the second derivative of 7*q - 2 - 5/2*q**3 - 18/7*q**2 + 3/28*q**4. Factor z(i).
3*(i - 12)*(3*i + 1)/7
Let z = 3106 - 12415/4. Let x(h) be the second derivative of 38*h + 1/16*h**4 + 0 + 1/8*h**3 - z*h**2. Let x(d) = 0. What is d?
-3, 2
Let n(d) be the second derivative of -d**5/20 - d**4/12 + d**3 - 639*d - 3. Factor n(l).
-l*(l - 2)*(l + 3)
Factor 1515908*x**2 + 404 + 296*x - 1515907*x**2 - 109.
(x + 1)*(x + 295)
Suppose 0 = -3*m - 2*m + 1 + 14. Let r(j) be the first derivative of -2/51*j**m - 5/17*j**2 - 8/17*j - 2. Solve r(x) = 0 for x.
-4, -1
Let s be 10 - (4 + 186/(-84)) - 8. Let g(x) be the first derivative of -1/7*x**3 + s*x**2 + 24 + 6/7*x. Factor g(v).
-3*(v - 2)*(v + 1)/7
Let k(i) be the first derivative of 0*i - 78 - 2/15*i**3 - 3/5*i**2. Factor k(j).
-2*j*(j + 3)/5
Suppose -1 = m, -16*r + 12*r + m + 13 = 0. Let x(g) be the second derivative of 1/15*g**6 + 2/3*g**r - 2*g - 1/6*g**4 - 1/5*g**5 + 0*g**2 + 0. Factor x(l).
2*l*(l - 2)*(l - 1)*(l + 1)
Let p(q) be the third derivative of -q**6/180 + 2*q**5/15 - q**4 + q**3/3 + 5*q**2 - 4. Let n(z) be the first derivative of p(z). Factor n(d).
-2*(d - 6)*(d - 2)
Let b(v) be the second derivative of v**6/105 - 4*v**5/35 + 2*v**4/7 + 32*v**3/21 - 64*v**2/7 + 2268*v. Determine p, given that b(p) = 0.
-2, 2, 4
Factor -42849 + 42*s**2 + 277*s - 691*s - 43*s**2.
-(s + 207)**2
Let h(z) be the third derivative of z**5/210 + 107*z**4/21 + 45796*z**3/21 + 17*z**2. Factor h(f).
2*(f + 214)**2/7
Suppose 25*a = -13*a + 76. Solve 148 + 5*x**a + 29*x - x - 68 + 57*x = 0 for x.
-16, -1
Let t(j) be the first derivative of j**6/180 + j**5/20 + 5*j**3/3 + 18. Let r(b) be the third derivative of t(b). Factor r(o).
2*o*(o + 3)
Let d(l) be the first derivative of 5*l**4/4 - 80*l**3/3 - 95*l**2/2 + 170*l - 1283. Let d(p) = 0. What is p?
-2, 1, 17
Let c = 123 - 120. Suppose -1053*l**2 + l**3 + 2097*l**2 - 1047*l**2 + 1 + c = 0. What is l?
-1, 2
Let k(n) be the third derivative of n**5/40 - 33*n**4/8 + 1089*n**3/4 - 172*n**2. Factor k(m).
3*(m - 33)**2/2
Let l(i) = 13*i**4 - 60*i**3 + 19*i**2 + 13*i + 5. Let g(b) = b**4 + 2*b**3 + b**2 - b - 1. Let s(m) = 10*g(m) + 2*l(m). Suppose s(t) = 0. Calculate t.
-2/9, 0, 1, 2
Suppose f + 10 - 19 = 0. Solve 10*b**3 - 15*b**2 + 4*b + 9*b - f - 39*b - 14*b + 5*b**4 - 11 = 0 for b.
-2, -1, 2
Let x = -2292 + 3555. Factor 164*b**4 + 320*b**4 - 981*b**3 - 80*b - 864*b**2 - x*b**3.
4*b*(b - 5)*(11*b 