t a be (18 + -20)/(5/(-4)). Let h(n) = n**3 + 5*n**2. Let v be h(-5). Find i, given that v*i - a + 2/5*i**2 = 0.
-2, 2
Let j(a) be the second derivative of a**4/150 + 9*a**3/25 - 121*a. Factor j(m).
2*m*(m + 27)/25
Let u(f) be the second derivative of f**7/980 - f**6/1260 - f**5/140 + f**4/84 - 29*f**3/6 + 28*f. Let a(c) be the second derivative of u(c). Factor a(o).
2*(o - 1)*(o + 1)*(3*o - 1)/7
Let m(l) be the first derivative of -l**6/6 - 26*l**5/5 - 48*l**4 - 96*l**3 + 912. Factor m(h).
-h**2*(h + 2)*(h + 12)**2
Let t be 9*(14 - 1162/84). Determine v so that 0 + t*v**4 + 6*v + 12*v**2 + 15/2*v**3 = 0.
-2, -1, 0
Let t(n) be the third derivative of n**5/40 + 3*n**4 + 144*n**3 - 40*n**2. Factor t(k).
3*(k + 24)**2/2
Let b(z) = 33*z**3 + 180*z**2 - 648*z + 396. Let k(s) = 130*s**3 + 720*s**2 - 2595*s + 1585. Let w(l) = -15*b(l) + 4*k(l). Solve w(p) = 0 for p.
-10, 4/5, 2
Let v(a) be the third derivative of -a**7/14 - a**6/6 + 25*a**5/12 - 65*a**4/12 + 20*a**3/3 + 6*a**2. Suppose v(j) = 0. Calculate j.
-4, 2/3, 1
Let b(p) be the first derivative of -4/13*p**2 + 6/13*p + 2/39*p**3 + 15. Factor b(i).
2*(i - 3)*(i - 1)/13
Let h(z) be the second derivative of -z**5/4 - 95*z**4/12 - 125*z**3/3 - 80*z**2 + z + 2. Factor h(p).
-5*(p + 1)*(p + 2)*(p + 16)
Let f(q) be the second derivative of -3*q**5/100 - 3*q**4/20 + 6*q**2/5 - q + 2. What is u in f(u) = 0?
-2, 1
Let m be (-19 + 18)/(1*5/(-10)). Factor -8/9*c**3 + 8/9*c - 2/3 + 2/9*c**4 + 4/9*c**m.
2*(c - 3)*(c - 1)**2*(c + 1)/9
Let v be (2/9)/((-5)/(-45)). Let s(y) = y**3 - y**2 - 2*y + 4. Let b be s(v). Factor 5*q**b + 3*q**3 - 5*q**4 - 2*q**5 - q**3.
-2*q**3*(q - 1)*(q + 1)
Let j(m) be the first derivative of 6*m**2 - 4*m**4 + 0*m - 8/5*m**5 + 2/3*m**6 + 8/3*m**3 + 14. Factor j(d).
4*d*(d - 3)*(d - 1)*(d + 1)**2
Suppose -58*f = 419*f - 0 - 0. Solve f + 1/5*q**3 + 0*q + 3/5*q**2 = 0.
-3, 0
Let c = -832 + 834. Factor 12/5*p + 2/5*p**c + 18/5.
2*(p + 3)**2/5
Let z(t) be the first derivative of -14/9*t**2 - 2/27*t**3 + 31 + 0*t. Factor z(d).
-2*d*(d + 14)/9
Let u(m) be the first derivative of 45 - 16*m - 6*m**2 + 4/3*m**3. Factor u(q).
4*(q - 4)*(q + 1)
Let h(q) = -6*q**2 + 9*q - 3. Let i(f) be the first derivative of -13*f**2 + 8*f + 7 + 17/3*f**3. Let v(a) = 8*h(a) + 3*i(a). Solve v(y) = 0.
0, 2
Let u = 623 - 616. Let y(o) be the third derivative of 0*o**3 + 45/14*o**u - 13/4*o**6 - 1/5*o**5 + 0 + o**4 - 12*o**2 + 0*o. Factor y(c).
3*c*(5*c - 2)**2*(9*c + 2)
Suppose a = -5*k - 4*a + 5, -2*k + 3*a = -7. Let b be (-216)/114 + 2 + -55*1/(-19). What is z in 0*z**k + 0 - 1/8*z**b + 1/2*z = 0?
-2, 0, 2
Let o(b) be the second derivative of b**4/4 - b**3/2 - 45*b**2 - 237*b. Factor o(q).
3*(q - 6)*(q + 5)
Let m(p) be the second derivative of -p**5/10 + p**4 + p**3/3 - 6*p**2 - 75*p - 2. Factor m(b).
-2*(b - 6)*(b - 1)*(b + 1)
Let l(f) be the third derivative of 1/30*f**6 + 25/18*f**3 + 0 + 1/630*f**7 + 15*f**2 + 23/90*f**5 + 5/6*f**4 + 0*f. Find v, given that l(v) = 0.
-5, -1
Let f be ((-1184)/(-180))/8 + 24/40*-1. Factor f*w**2 + 2/3 - 8/9*w.
2*(w - 3)*(w - 1)/9
Let i be 5/((-15)/12) + -52. Let p = i - -61. Determine j so that 0 + 0*j**2 + 0*j + 0*j**3 - 2/3*j**4 - 1/3*j**p = 0.
-2, 0
Solve -10/7*i**2 - 64/7*i + 2/7*i**3 - 72/7 = 0.
-2, 9
Let l(u) = -2*u**2 - 467*u + 53824. Let x(f) = -3*f**2 - 933*f + 107648. Let t(n) = -5*l(n) + 3*x(n). Factor t(g).
(g - 232)**2
Let x(a) = -40*a**2 + 156*a + 52. Let g(h) = -117*h**2 + 469*h + 155. Let w(b) = 4*g(b) - 11*x(b). Solve w(q) = 0.
-2/7, 6
Let z(a) = 3*a**2 - 43*a + 88. Let c(d) = 3*d**2 - 45*d + 87. Let s(j) = -2*c(j) + 3*z(j). What is h in s(h) = 0?
3, 10
Let d = -330 + 2971/9. Let z(a) be the second derivative of 0*a**2 - d*a**3 + 0 + 1/18*a**4 + 7*a. Determine r, given that z(r) = 0.
0, 1
Let j be 329/84 + (-3 - 148/(-48)). Let -1/5*h + 3/5 - 1/5*h**5 + 3/5*h**j + 2/5*h**3 - 6/5*h**2 = 0. What is h?
-1, 1, 3
Let o(z) = -2*z**2 - 9*z - 4. Let t be o(-4). Suppose 2 - 4 = -4*u - s, -s = -4*u - 2. Solve u + 1/4*i**2 + t*i = 0.
0
Let h(y) = -5*y**3 - 2 + 9 - 5*y**2 + 5*y + 2*y**2 + 4*y**3. Let j(m) = -m - 1. Let w(c) = 4*h(c) + 28*j(c). Factor w(d).
-4*d*(d + 1)*(d + 2)
Suppose -5/2*v**3 + 0 + 0*v - v**2 - 2*v**4 - 1/2*v**5 = 0. Calculate v.
-2, -1, 0
Let l(b) be the third derivative of 1/24*b**4 + 0*b + b**2 + 0 - 3/140*b**5 + 1/168*b**6 - 1/21*b**3 - 1/1470*b**7. Solve l(j) = 0 for j.
1, 2
Let t(b) be the second derivative of -b**6/120 - 3*b**5/16 - 61*b**4/48 - 7*b**3/8 + 49*b**2/4 + 376*b. Factor t(o).
-(o - 1)*(o + 2)*(o + 7)**2/4
Let r(y) = 2*y**4 - 20*y**3 - 13*y**2 + 7*y + 24. Let q(n) = -n**4 + n**3 - n**2 + n. Let g(c) = -5*q(c) - r(c). Determine o, given that g(o) = 0.
-2, 1
Factor 2/9*u**3 + 56/9 + 34/9*u**2 + 88/9*u.
2*(u + 1)*(u + 2)*(u + 14)/9
Factor 240/7*n**2 + 36/7*n**3 + 2/7*n**4 + 750/7 + 100*n.
2*(n + 3)*(n + 5)**3/7
Let y(h) be the third derivative of h**7/42 + 19*h**6/120 + 19*h**5/50 + 13*h**4/30 + 4*h**3/15 + h**2 + 10*h. Determine d so that y(d) = 0.
-2, -1, -2/5
Factor -33/2*j + 9/4 + 4*j**4 + 97/4*j**2 + 22*j**3.
(j + 3)**2*(4*j - 1)**2/4
Factor 27/2*j**2 + 0 + 1/2*j**4 - 13/2*j - 15/2*j**3.
j*(j - 13)*(j - 1)**2/2
Let i be 1860/124 - 12*1. Let -1/4*s**4 + 0 + 1/4*s + 3/4*s**i - 3/4*s**2 = 0. What is s?
0, 1
Factor 6/5*l**3 - 9*l**2 + 12/5*l + 3/5*l**4 + 12.
3*(l - 2)**2*(l + 1)*(l + 5)/5
What is u in 18*u**3 + 234*u**4 - 117*u**4 - 114*u**4 + 12*u + 27*u**2 = 0?
-4, -1, 0
Suppose 3*q = 2*z - 4 - 12, 4*q + 26 = 5*z. Let l(y) be the third derivative of y**z + 0*y + 0 + 1/2*y**3 - 1/6*y**4 + 1/60*y**5. What is j in l(j) = 0?
1, 3
Let j(n) be the third derivative of -n**8/112 - n**7/70 + n**6/40 + n**5/20 - n**2 - 27*n. Factor j(d).
-3*d**2*(d - 1)*(d + 1)**2
Let r(v) be the third derivative of -5*v**2 - 135/2*v**3 + 0 - 15/4*v**4 - 1/12*v**5 + v. Factor r(j).
-5*(j + 9)**2
Let y(c) = 8*c**3 + 2*c. Let r(i) = 15*i**3 + 3*i. Let v be 21/4 + (-1)/4. Suppose 2*n - n + 9 = 0. Let q(b) = n*y(b) + v*r(b). Factor q(u).
3*u*(u - 1)*(u + 1)
Let y(i) = -i**2 - 17*i + 394. Let m be y(-30). Solve -m*c**2 - 10/3*c + 2/3 = 0 for c.
-1, 1/6
Let d be -9 + (8 - -6) - (10 + -10). Suppose -4/5*o**3 + 2/5 - 2/5*o**d - 6/5*o**4 + 4/5*o**2 + 6/5*o = 0. Calculate o.
-1, 1
Let n(r) be the second derivative of r**6/75 + 7*r**5/50 - 17*r**4/30 + 3*r**3/5 + r - 20. Find a such that n(a) = 0.
-9, 0, 1
Suppose 3*d - 69 + 57 = 0. Let s(u) be the first derivative of 2/25*u**5 + 4 + 0*u - 1/5*u**d + 2/15*u**3 + 0*u**2. Factor s(i).
2*i**2*(i - 1)**2/5
Let b(s) be the first derivative of 98*s - 7 + 2/3*s**3 - 14*s**2. Factor b(g).
2*(g - 7)**2
Let m(h) be the second derivative of 7*h**6/57 + 81*h**5/190 + h**4/57 - 12*h**3/19 + 8*h**2/19 + 46*h - 1. Solve m(n) = 0.
-2, -1, 2/7, 2/5
Let p = -14 + 5. Let y be 1/(3/p) + 19. Determine u so that -44*u**2 - 12*u**5 + 28*u**4 + 5*u + u**3 + y + 11*u**3 - 5*u = 0.
-1, -2/3, 1, 2
Suppose -9*d - 9 = 9. Let c(b) = 3*b**2 + 3*b - 6. Let q(z) = -4*z**2 - 3*z + 7. Let m(f) = d*q(f) - 3*c(f). Determine x, given that m(x) = 0.
-4, 1
Suppose -11*m - 12 = -45. Factor m - 11*o + 3*o**3 + 55*o**2 + 50*o**2 - 100*o**2.
(o - 1)*(o + 3)*(3*o - 1)
Let x(y) be the second derivative of -y**6/30 - y**5/5 + 7*y**4/4 - 2*y**3/3 - 14*y**2 + 741*y. Factor x(a).
-(a - 2)**2*(a + 1)*(a + 7)
Let t(r) be the third derivative of 0*r + 3/100*r**5 + 0 - r**2 - 1/40*r**6 - 1/1680*r**8 + 0*r**3 + 1/150*r**7 + 0*r**4. Let t(n) = 0. Calculate n.
0, 1, 3
Let p(m) = 12*m**2 - 4*m - 24. Let h(n) be the first derivative of 4*n**3/3 - n**2/2 - 8*n - 4. Let f(y) = 8*h(y) - 3*p(y). Factor f(q).
-4*(q - 2)*(q + 1)
Suppose 0 = 4*p - 2*c - 20, 3*c + 12 = p - 3. Factor -56/15*l**p - 32/15 - 32/15*l + 2/3*l**4 + 32/5*l**2.
2*(l - 2)**3*(5*l + 2)/15
Suppose -2306*p = -2302*p. Factor 0*n + p*n**4 + 0*n**2 + 0 + 0*n**3 - 1/3*n**5.
-n**5/3
Determine h, given that -3/5*h**5 + 0*h + 0*h**2 + 6/5*h**4 - 3/5*h**3 + 0 = 0.
0, 1
Let m = -17917 + 17917. Factor -12/7*a - 3/7*a**4 + m - 15/7*a**3 - 24/7*a**2.
-3*a*(a + 1)*(a + 2)**2/7
Let x be 2*(4 + (-15)/6). Suppose -x*y + y + y = 0. Factor 3/4*w**3 + y - 1/4*w - 1/2*w**2.
w*(w - 1)*(3*w + 1)/4
Factor -1/3*f**4 + 1/3*f**2 + 0*f + 1/6*f**5 + 0 - 1/6*f**3.
f**2*(f - 2)*(f - 1)*(f + 1)/6
Suppose -5*b + 7*z = 49, 10*b - 2*z + 14 = 12*