 v = 11649/30808 + -12/3851. Determine m so that 3/2 + 1/4*m**3 + 21/8*m**2 - v*m**4 - 4*m = 0.
-3, 2/3, 1, 2
Let d be 4/5*(-2)/4 - (-46)/15. Factor -22/9*w + 2/9*w**2 - d.
2*(w - 12)*(w + 1)/9
Let c(h) be the third derivative of -h**6/600 + h**5/10 + 31*h**4/120 - 3162*h**2. What is f in c(f) = 0?
-1, 0, 31
Let k(f) = f**2 + 26*f + 156. Let g be k(-19). Factor 71 + 18*q**2 + 27*q + 2*q**3 - g + 25*q.
2*(q + 2)*(q + 3)*(q + 4)
Let a(l) be the third derivative of -1/240*l**6 + 0 + 1/30*l**5 + 1/3*l**4 - 16/3*l**3 + 48*l + 3*l**2. Factor a(q).
-(q - 4)**2*(q + 4)/2
Find u such that -392000*u - 3*u**3 + 2551*u**2 - 486*u**2 - 2*u**3 + 0*u**3 + 735*u**2 = 0.
0, 280
Let i(g) be the first derivative of 99 + 24*g**2 + 2*g**4 + 36*g - 44/3*g**3. Find r such that i(r) = 0.
-1/2, 3
Let g(n) be the second derivative of 3*n**5/140 - 95*n**4/28 - n**3/14 + 285*n**2/14 - 12646*n. Factor g(z).
3*(z - 95)*(z - 1)*(z + 1)/7
Suppose 334*v - 8 = 332*v. Suppose -5*p = -v*i - 4, 0 = 2*i + 4*p - 14 - 10. Factor 3/2*t**3 - 2*t**i + 0 + 0*t + 1/2*t**5 + 0*t**2.
t**3*(t - 3)*(t - 1)/2
Determine b so that -8*b**4 - 12 - 2*b**5 + 1018*b**2 + 997*b**2 - 1995*b**2 + 2*b + 0*b = 0.
-3, -2, -1, 1
Suppose 6*j - 2*j = 8. Find x, given that -174*x**2 + 176*x + 70 + 344*x**2 - 154*x**j + 414 = 0.
-11/2
Let i(o) be the first derivative of -o**3/18 - 43*o**2/6 - 164*o/3 - 2570. Factor i(g).
-(g + 4)*(g + 82)/6
Factor 27/5*l**2 - 3/5*l**3 + 81 + 243/5*l.
-3*(l - 15)*(l + 3)**2/5
Let n = -797412 + 797412. Factor 0*o + n + 1/2*o**3 + 1/4*o**2.
o**2*(2*o + 1)/4
Let d(p) be the third derivative of 1/20*p**5 - 27*p**2 + 0 + 1/2*p**3 + 0*p - 1/4*p**4. Factor d(n).
3*(n - 1)**2
Let y(q) = 19235*q - 96172. Let a be y(5). Factor 37*k**2 + 12 + 13*k**a + 1/3*k**4 + 109/3*k.
(k + 1)**3*(k + 36)/3
Let m(p) be the third derivative of 1/180*p**5 + 0 - 4*p + 6*p**2 + 1/18*p**4 + 0*p**3. Factor m(q).
q*(q + 4)/3
Let w(l) be the third derivative of 1/70*l**7 + 0*l + 9/4*l**4 + 3 + 27/20*l**5 + 1/4*l**6 + 0*l**3 - 4*l**2. Factor w(z).
3*z*(z + 1)*(z + 3)*(z + 6)
Let q(s) = -s**3 - s**2 + s + 2. Suppose -f - 3 = 2*y + 7, 8 = -2*f. Let v(k) = k**3 + 7*k**2 - 11*k + 6. Let j(d) = y*q(d) + v(d). Factor j(i).
2*i*(i - 1)*(2*i + 7)
Let d(q) = -2*q**2 + q. Let l(y) = -2*y**3 + 2*y**2 + 30*y + 32. Let i = -43 - -41. Let k(r) = i*l(r) - 4*d(r). Factor k(g).
4*(g - 4)*(g + 1)*(g + 4)
Determine v so that -1/5*v**3 - 11/5*v - 1/10*v**4 - 28/5 + 33/10*v**2 = 0.
-7, -1, 2, 4
Determine b so that 508/7*b**2 + 2850/7*b**3 - 48*b + 0 + 1982/7*b**4 - 24/7*b**5 = 0.
-1, -2/3, 0, 1/4, 84
Let y be 0 + (-29)/(4002/(-92)). Suppose -14/3*p + 20 - y*p**2 = 0. What is p?
-10, 3
Solve -39*b**2 - 27/2 + 9/2*b**4 - 6*b**3 + 54*b = 0 for b.
-3, 1/3, 1, 3
Let f = 49/2 - 24. Let z(s) = 167*s + 4511. Let x be z(-27). Find h such that -2/5 - 1/10*h**x - f*h = 0.
-4, -1
Let i(z) be the second derivative of -2*z**7/21 + 8*z**6/5 + 11*z**5 - 650*z**4/3 - 1000*z**3 + 10000*z**2 + 319*z. Let i(a) = 0. What is a?
-5, 2, 10
Let l be ((-16)/5)/(-4) + (-28288)/260. Let k be (-16)/(-72)*l/(-48). Factor 1/2*r + 0*r**2 - k*r**3 - 1/4 + 1/4*r**4.
(r - 1)**3*(r + 1)/4
Factor 2*v**4 - 5*v**3 - 9*v**3 + 20 + 30*v**2 - 26*v - 12.
2*(v - 4)*(v - 1)**3
Let a(q) be the third derivative of -q**7/210 - 3*q**6/20 - 4*q**5/3 + 3*q**4/4 + 27*q**3/2 + 3*q**2 - 496*q. Determine h so that a(h) = 0.
-9, -1, 1
Solve -92*b**5 + 260*b**3 + 93*b**5 + 9*b**4 - 246*b**3 = 0 for b.
-7, -2, 0
Determine p so that -284/3 + 1/6*p**3 - 23*p**2 - 94*p = 0.
-2, 142
Let b(a) be the first derivative of -3*a**5/5 + 7*a**4/4 + a**3/3 - 7*a**2/2 + 2*a - 5594. Suppose b(j) = 0. Calculate j.
-1, 1/3, 1, 2
Let a = -2015 - -1910. Let j be ((-672)/a)/(7/5). Factor 4/7*o**2 + 0 - j*o.
4*o*(o - 8)/7
Let v(p) be the second derivative of p**4/30 + 306*p**3/5 + 917*p**2/5 - 6353*p + 2. What is n in v(n) = 0?
-917, -1
Suppose 36543*y = 36702*y. Factor -7/2*w**5 + 0*w**2 + 0*w - 22*w**4 - 6*w**3 + y.
-w**3*(w + 6)*(7*w + 2)/2
Let n = 72630 - 72630. Suppose -1/3*y - 1/3*y**4 - y**2 + n - y**3 = 0. Calculate y.
-1, 0
Let a(r) be the first derivative of r**5/50 + r**4/30 + 279*r + 217. Let g(m) be the first derivative of a(m). Factor g(y).
2*y**2*(y + 1)/5
Let n be (-40)/90*((-78)/13 - 219/(-38)). What is s in n*s**2 + 54/19*s - 56/19 = 0?
-28, 1
Let x be -42*(-34)/3927*11. Let r(o) be the second derivative of 0*o**2 + 7/6*o**x + 0 + 2/5*o**5 - 2/3*o**3 - 30*o. Solve r(z) = 0.
-2, 0, 1/4
Let f(z) be the third derivative of -11/21*z**3 + 0*z - 1/1176*z**8 - 31/105*z**5 + 19/210*z**6 + 52*z**2 + 0 + 43/84*z**4 - 1/105*z**7. Factor f(q).
-2*(q - 1)**4*(q + 11)/7
Suppose -13*s + 4*s = -27. Suppose 0 = -b - q - 2, 0*q + s*q = 4*b - 20. Factor 12*t + 20 + 38*t + 5*t**b + 105.
5*(t + 5)**2
Let f = -262232 - -262234. Determine y, given that 2/7*y + 12/7 - 2/7*y**f = 0.
-2, 3
Let 5 - 15*i**3 + 255*i**2 - 5*i**4 + 235 + 15*i**3 - 490*i = 0. What is i?
-8, 1, 6
Let q(b) be the first derivative of -b**4/4 + 45*b**3 + 1910. Factor q(s).
-s**2*(s - 135)
Let g(k) be the first derivative of -9/4*k**2 + 4*k + 1/6*k**3 + 273. Factor g(z).
(z - 8)*(z - 1)/2
Let p(u) = 22*u**3 - 42089*u**2 + 39340174*u - 12261005618. Let s(m) = 7*m**3 - 14029*m**2 + 13113389*m - 4087001873. Let o(h) = -2*p(h) + 7*s(h). Factor o(k).
5*(k - 935)**3
Let l(k) = -2280*k**5 - 936*k**4 + 116*k**3 + 136*k**2 - 4*k. Let p(x) = x**5 + x**4 + x**3 + 4*x**2. Let o(r) = -l(r) + 24*p(r). Factor o(a).
4*a*(3*a + 1)**2*(8*a - 1)**2
Let h(t) be the first derivative of 7/12*t**3 + 2*t**2 - 16*t - 116 + 1/32*t**4. Determine l, given that h(l) = 0.
-8, 2
Let d(i) be the first derivative of 2*i**5/5 + 49*i**4/6 - 304*i**3/9 - 5714. Factor d(p).
2*p**2*(p + 19)*(3*p - 8)/3
Let g(w) be the second derivative of 137*w**5/20 - 823*w**4/6 + 826*w**3 - 36*w**2 - 880*w. Let g(o) = 0. Calculate o.
2/137, 6
Suppose -2423*q - h - 53 = -2438*q, -3*q - h + 19 = 0. Factor 1/2*w**q + 0*w - 7*w**2 - 13/2*w**3 + 0.
w**2*(w - 14)*(w + 1)/2
Let m(w) = -7696*w - 577187. Let u be m(-75). Factor -63/5*o + 1/5*o**4 + 127/5*o**2 - u*o**3 + 0.
o*(o - 63)*(o - 1)**2/5
Let d(u) be the second derivative of -7/9*u**3 - 1/90*u**5 + 4/27*u**4 + 2*u**2 + u + 4. Solve d(n) = 0 for n.
2, 3
Let v(w) be the first derivative of -45/2*w**2 - 55/4*w**4 + 35*w**3 - 5*w + 105. Solve v(j) = 0 for j.
-1/11, 1
Let a(g) be the first derivative of g**6/6 - 83*g**5/25 + 301*g**4/20 - 301*g**3/15 + 3*g**2/5 + 72*g/5 - 924. Determine r, given that a(r) = 0.
-2/5, 1, 3, 12
Let u be 93/(56823/(-26))*-47. Factor 0 + 4/9*i + 2/9*i**u.
2*i*(i + 2)/9
Let t = 175122 + -175122. Solve 22/7*x**2 + 18/7*x**3 - 2/7*x**5 + 8/7*x + 2/7*x**4 + t = 0 for x.
-1, 0, 4
Let r(i) be the second derivative of 11*i**5/70 + 299*i**4/42 - 254*i**3/21 - 8*i**2 + 1203*i. Determine o, given that r(o) = 0.
-28, -2/11, 1
Let l = -1789/2355 + 452/471. Factor 3/5 - l*c**2 - 2/5*c.
-(c - 1)*(c + 3)/5
Suppose 9*c - 10*c = 2. Let i be c + 12/(-9)*-3. Find s such that 3*s**2 + 2*s**2 - s**i - 4*s = 0.
0, 1
Factor -1/3*c**4 - 10*c + 0 - 43/3*c**2 - 14/3*c**3.
-c*(c + 1)*(c + 3)*(c + 10)/3
Factor -3750*k + 0 - 32/3*k**5 + 4550*k**2 - 10681/6*k**3 + 728/3*k**4.
-k*(k - 2)**2*(8*k - 75)**2/6
Let y be 27/15 - 3/(-15). Let a(o) = -o**3 - o + 1. Let k(w) = w**3 + 2 - 6*w**3 + 67*w**2 - 70*w**2 + 4*w. Let f(n) = y*a(n) - k(n). Factor f(m).
3*m*(m - 1)*(m + 2)
Let t = 81/1298 - 1/59. Let v(u) be the second derivative of -15*u + 3/22*u**4 + t*u**5 + 7/33*u**3 + 2/11*u**2 + 1/165*u**6 + 0. Factor v(n).
2*(n + 1)**3*(n + 2)/11
Let w(v) be the second derivative of -8*v**3 + 2/15*v**6 - 3/5*v**5 + 0*v**2 + 22*v - 16/3*v**4 - 1. Factor w(q).
4*q*(q - 6)*(q + 1)*(q + 2)
Let d be (-432)/(-80) - 2/5. Suppose -d*l + 2*l = -9. Let -6*u**l + u**3 - 4 - 6*u**2 + 12 + 3*u**3 = 0. Calculate u.
-2, 1
Suppose 8*a = 3*a + 4*j + 41, 5*a = -4*j + 9. Suppose s - 5*w - 30 + a = 0, -s = w - 19. Let -3*v**3 - 17*v - 96 - s*v**2 - v**3 + 92 = 0. Calculate v.
-4, -1/2
Factor 21/8 + 1/8*r**5 + 27/4*r**3 + 47/4*r**2 + 73/8*r + 13/8*r**4.
(r + 1)**3*(r + 3)*(r + 7)/8
Let h(q) be the third derivative of 49*q**6/90 - 77*q**5/45 + 121*q**4/72 - 2657*q**2. Solve h(c) = 0.
0, 11/14
Let v(a) be the first derivative of -2*a**3/21 - 208*a**2/7 - 414*a/7 + 6313. Factor v(x).
-