12))/(-1). Suppose -4*t - 11 = 3*w - k, 0 = -t - 5*w - 23. Factor -2*s**t + 8/5 - 16/5*s.
-2*(s + 2)*(5*s - 2)/5
Let i(o) = 366*o**3 + o**2 - 4*o + 4. Let j be i(1). Let d = j - 1831/5. Solve -d*n**2 - 4/5*n**3 + 2/5*n**5 + 2/5*n + 2/5*n**4 + 2/5 = 0.
-1, 1
Factor 57835*y**2 + 1410*y**3 + 80055*y - 9012*y + 4*y**4 + 14161 - 453*y**3.
(y + 1)*(y + 119)**2*(4*y + 1)
Let t = 11/4064 + 16179/28448. Let b be (-5)/7 - (-2)/2. Factor -t*h + b*h**2 - 6/7.
2*(h - 3)*(h + 1)/7
Let g(m) be the third derivative of m**7/1260 + m**6/72 + 13*m**5/360 - m**4/6 - 3173*m**2 - 1. Factor g(t).
t*(t - 1)*(t + 3)*(t + 8)/6
Let s(w) be the first derivative of -1/9*w**3 + 0*w**2 + 185 - 7/36*w**6 + 0*w - 8/15*w**5 - 11/24*w**4. Let s(j) = 0. What is j?
-1, -2/7, 0
Let h be (2 + 48/(-18))/(10/(-9651)). Let n = h + -643. Find r such that 8/5*r**4 + 0 + 8/5*r**2 + 2/5*r**5 + 12/5*r**3 + n*r = 0.
-1, 0
Let b = -2822791/13 + 217141. Factor 2/13*w**2 + b*w - 44/13.
2*(w - 1)*(w + 22)/13
Suppose 278/7*v - 16 - 9/7*v**5 + 397/7*v**2 - 71*v**3 - 513/7*v**4 = 0. Calculate v.
-56, -1, 1/3, 2/3
Let k(g) be the first derivative of -24*g**5/25 + 879*g**4/5 + 1818*g**3 + 13785*g**2/2 + 11550*g - 10639. Find d, given that k(d) = 0.
-5/2, 154
Let q(s) = -2*s**2 - 5*s - 6. Suppose 113*u - 70 = 118*u. Let k(c) = -4*c**2 - 9*c - 14. Let x(m) = u*q(m) + 6*k(m). Factor x(f).
4*f*(f + 4)
Let b(o) = -o**3 - o - 1. Let r(m) = -44*m**2 - 17*m**3 - 19*m**3 - 2*m**3 - 40*m**2 - 66*m - 18. Let f(k) = -2*b(k) + r(k). Factor f(c).
-4*(c + 1)*(3*c + 2)**2
Let u(q) be the first derivative of 7 - 1/4*q**4 + 18*q + 0*q**3 + 27/2*q**2. Let t(p) be the first derivative of u(p). Factor t(m).
-3*(m - 3)*(m + 3)
Let b(k) be the second derivative of k**6/12 - 21*k**5/20 - 7*k**4/2 + 10*k**3/3 + 131*k - 3. Factor b(w).
w*(w - 10)*(w + 2)*(5*w - 2)/2
Let i(q) = -q**3 + 5*q**2 + 1. Let z(c) = 38*c**3 + 182*c**2 - 90*c + 1. Let m(w) = -i(w) + z(w). Factor m(t).
3*t*(t + 5)*(13*t - 6)
Factor 23667 + 800*m - 2*m**2 + 92760 + 5*m**2 + 382*m.
3*(m + 197)**2
Suppose 22 + 14 = 8*m + m. Let w(j) be the third derivative of 0 + 0*j**3 + 0*j - m*j**2 + 1/30*j**6 + 1/105*j**7 + 0*j**4 + 0*j**5. Factor w(s).
2*s**3*(s + 2)
Let j(v) be the first derivative of v**5/60 + 2*v**4/3 + 72*v**2 - 83. Let l(y) be the second derivative of j(y). What is z in l(z) = 0?
-16, 0
Let m be 3 - 1*(4 - 5). Suppose -45*i = -43*i - m. Let -25*f**5 - 23*f**4 - 30*f**3 + 9*f**i - 4*f**2 + 5*f**5 + 68*f**4 = 0. Calculate f.
0, 1/4, 1
Let q = 6 + -3. Let c be 0 - q - (-7 - -4). Factor -2/11*g**4 + c*g + 8/11*g**3 + 0 - 6/11*g**2.
-2*g**2*(g - 3)*(g - 1)/11
Suppose 0 = -3*n - 3*n + 66. Factor n*i**3 - 28*i**3 + 44*i + 16*i**3 + 26*i - 20*i - 49*i**2.
-i*(i - 1)*(i + 50)
Let p = 33760 - 33756. Find n such that 1/4*n**2 + p + 2*n = 0.
-4
Let y be (1 - 2 - 1)/((-33)/(-154)*-7). Let b(d) be the first derivative of 0*d + 0*d**2 + y*d**3 + 22 - 2/5*d**5 - 1/2*d**4. Solve b(t) = 0.
-2, 0, 1
Let h(i) be the first derivative of -6*i**5/5 + 262*i**4 + 1910*i**3 + 2718*i**2 - 6480*i + 10284. Suppose h(t) = 0. Calculate t.
-3, 2/3, 180
Let x(p) be the first derivative of -p**4/12 - 19*p**3/3 - 25*p**2/3 + 112*p - 6553. Factor x(d).
-(d - 2)*(d + 3)*(d + 56)/3
Let k(l) = -3*l + 10. Let d be k(2). Suppose -4 = -d*s + 2*i, -s + 7 = -0*s + i. Factor -4*v**3 + v + v + v**2 - 4*v**s + 5*v**3.
-v*(v - 1)*(3*v + 2)
Solve 1/3*y**5 - 35/3*y**2 - 17/6*y**4 + 7*y - 3/2 + 26/3*y**3 = 0.
1/2, 1, 3
Let s(f) = -194*f + 18044. Let m be s(93). Suppose 39/8 - 39/8*w**m - 3/8*w + 3/8*w**3 = 0. What is w?
-1, 1, 13
Let v(n) be the second derivative of -4/13*n**2 + 0 + 20/39*n**3 - 2/13*n**5 + 3/65*n**6 - 5/78*n**4 + 17*n. Solve v(s) = 0 for s.
-1, 2/9, 1, 2
Let h be (-1)/(-5)*10650/852*((-249)/(-45) - 1). Solve -5/3*y**3 + 14/3 - 1/6*y**4 + 17/2*y**2 - h*y = 0 for y.
-14, 1, 2
Let d = -84 + 88. Find x, given that 12 - 2*x**d - 3*x**4 - 32*x**3 - 8*x + 2*x**4 + 2*x**4 - 11*x**2 + 40*x**3 = 0.
-1, 1, 2, 6
Let l be 2/(-6) - (-9 - (-1160)/12). Let t be (-143)/l - 3/(-8). Solve 4/3*u**t + 2*u - 4/3 - 2*u**3 = 0 for u.
-1, 2/3, 1
Let z = 4350/7 + -620. Let u = 226 - 1580/7. Factor 8/7 + z*k + u*k**2.
2*(k + 1)*(k + 4)/7
What is h in 482 + 1594 + 7273914*h + 2*h**2 - 7274272*h = 0?
6, 173
Let q(d) be the third derivative of 20*d**2 - 3 + 4/21*d**3 - 1/7*d**4 + 0*d - 1/140*d**6 + 11/210*d**5. Factor q(i).
-2*(i - 2)*(i - 1)*(3*i - 2)/7
Let q(u) be the first derivative of 0*u**2 + 2/3*u**6 + 8/5*u**5 + 0*u + 80 - 15*u**4 - 48*u**3. Let q(j) = 0. What is j?
-3, 0, 4
Factor 864/5 - 3/5*n**2 - 861/5*n.
-3*(n - 1)*(n + 288)/5
Factor -128/3*d + 2/3*d**3 + 4*d**2 + 64.
2*(d - 4)*(d - 2)*(d + 12)/3
Let p(c) be the third derivative of c**6/60 - 19*c**5/6 - c**4/12 + 95*c**3/3 - 16*c**2 - 8*c. Factor p(s).
2*(s - 95)*(s - 1)*(s + 1)
Let b(g) be the first derivative of 47 + 0*g - 1/16*g**4 - 15/8*g**2 - 4/3*g**3. Determine z, given that b(z) = 0.
-15, -1, 0
Let z(b) = -b**3 - 56*b**2 + 69*b - 2724. Let t be z(-58). Factor 2/7*j**3 - 2/7*j - 6/7*j**t + 6/7.
2*(j - 3)*(j - 1)*(j + 1)/7
Suppose 5*u + 25 = -2*k, -4*k = -5*u - 5 - 20. Suppose -9 = -7*m + 4*m. Let 21*b**m + k*b**4 + b**2 - 21*b**3 - b**4 = 0. Calculate b.
-1, 0, 1
Let q(i) be the first derivative of -i**4/16 - i**3/2 + 72*i**2 - 1080*i - 11778. Let q(s) = 0. Calculate s.
-30, 12
Let c(q) be the third derivative of -9/5*q**3 + 0 - 726/25*q**5 + 9*q**2 + 2662/75*q**6 + 99/10*q**4 + 0*q. What is f in c(f) = 0?
3/22
Let t(j) be the first derivative of j**6/8 + 12*j**5/5 + 117*j**4/8 + 36*j**3 + 243*j**2/8 - 2545. What is h in t(h) = 0?
-9, -3, -1, 0
Let p(m) be the third derivative of -m**8/168 + 13*m**7/105 - 53*m**6/60 + 83*m**5/30 - 7*m**4/2 - 39*m**2. Let p(a) = 0. What is a?
0, 1, 2, 3, 7
Let b(t) = -t**3 - 47*t**2 + 42*t - 284. Let m be b(-48). Let r be 48 + 2/(-4)*-4. Factor -49*g**5 + 4*g**2 + 2*g**m - 4*g**2 + r*g**5.
g**4*(g + 2)
Let x = -58 - -60. Factor -10*m - 2 + 2*m**2 + 2*m**2 - 5*m**x + 18*m + 22.
-(m - 10)*(m + 2)
Let n(y) = 15*y**2 + 155*y - 170. Let x(r) = 8*r**2 + 78*r - 86. Let l(f) = -3*n(f) + 5*x(f). Determine c so that l(c) = 0.
-16, 1
Let g(z) be the first derivative of 5*z**4/4 - 3335*z**3 + 2505000*z**2 - 5000000*z + 4343. Factor g(u).
5*(u - 1000)**2*(u - 1)
Let l = -2/199 - -1457/125171. Let o = 631/1258 - l. Factor 1/2*j**3 + 1/4*j**4 - 1/4 - o*j + 0*j**2.
(j - 1)*(j + 1)**3/4
Let w(y) be the first derivative of -4/3*y**3 + 8*y**2 + 20*y + 42. Factor w(k).
-4*(k - 5)*(k + 1)
Let f(a) be the third derivative of a**8/336 - a**7/70 - a**6/60 + a**5/10 + a**4/24 - a**3/2 + 530*a**2. Factor f(q).
(q - 3)*(q - 1)**2*(q + 1)**2
Let p(o) = 20*o - 176. Let w be p(9). Let v(d) be the second derivative of 5*d + 1/39*d**3 + 0 + 1/78*d**w + 0*d**2. Determine t so that v(t) = 0.
-1, 0
Let n(o) be the second derivative of 119*o + 0 - 124/15*o**3 - 1922/5*o**2 - 1/15*o**4. Find d such that n(d) = 0.
-31
Let a(s) be the second derivative of -23/15*s**3 + 11/60*s**4 + 4/5*s**2 + 299*s + 0. Solve a(r) = 0 for r.
2/11, 4
Let u(v) = v**4 - 3*v**3 + v**2 + 39*v - 20. Let w(h) = 3*h**4 - 8*h**3 - h**2 + 116*h - 59. Let b(m) = 17*u(m) - 6*w(m). Find s such that b(s) = 0.
-7, 1, 2
Determine u, given that -6*u**2 - u**3 - 4*u**2 + 1166*u - 1183*u - 8 = 0.
-8, -1
Let i = 98 - 44. Suppose -10*d**4 - i*d**2 - 63*d**2 + 14*d**3 + 111*d**2 + 2*d**5 = 0. Calculate d.
0, 1, 3
Let l(b) = -4*b**2 + 2046*b + 1048. Let a(g) = 28*g**2 - 14322*g - 7344. Let h(f) = 6*a(f) + 44*l(f). Factor h(k).
-4*(k - 512)*(2*k + 1)
Let t be -4*((-10)/4)/5. Let h be 9/t*92/207. Solve 6*g**5 - 2*g**4 - h*g**5 + 0*g**4 - 6*g**5 = 0.
-1, 0
Let k be (-1782)/(-165) + 36/90. What is h in 36/5*h - k - 4/5*h**3 + 24/5*h**2 = 0?
-2, 1, 7
Suppose -6*p - 41*p**4 + 2*p**5 + 7*p**3 + 7*p**2 + p**5 - 4*p**3 - 4*p**5 + 38*p**4 = 0. Calculate p.
-3, -2, 0, 1
Let r(o) be the first derivative of -o**7/21 - o**6/15 + o**5/5 - 52*o + 93. Let u(q) be the first derivative of r(q). Factor u(v).
-2*v**3*(v - 1)*(v + 2)
Let i = 4104 + -4101. Let t(s) be the second derivative of -2/3*s**i - 5/24*s**4 + 0 - 1/40*s**5 - 5*s - s**2. Solve t(p) = 0 for p.
-2, -1
Let j(p) be the first derivative of -p**7/280 + 7*p**6/120 - 11*p**5/40 + 5*p**4/8 + 46*p**3 + 36. Let o(x) be the third derivativ