**3 + 5*j**2 - 20*j = 0. Calculate j.
-3, 1
Let w(d) be the third derivative of -d**7/252 - 11*d**6/720 - d**5/180 - d**2 + 10. Factor w(y).
-y**2*(y + 2)*(5*y + 1)/6
Let a(p) = 21*p - 12. Let d be a(9). Factor s**3 + 87 - d + 90.
s**3
Let z = 32 - 30. Let t(y) be the first derivative of 1/16*y**4 - 4 + 1/4*y**3 + 3/8*y**z + 1/4*y. Factor t(x).
(x + 1)**3/4
Let n = 21 + -46. Let s(z) = -10*z**3 + 2*z**2 - 3*z - 3. Let g(y) = -80*y**3 + 15*y**2 - 25*y - 25. Let x(w) = n*s(w) + 3*g(w). Determine a so that x(a) = 0.
0, 1/2
Suppose 17*h = 10*h + 84. Factor 8*c + h*c + 3 + 8 + 4*c**2 + 13.
4*(c + 2)*(c + 3)
Let r(c) be the second derivative of -c**5/20 + 7*c**4/6 - 11*c**3/6 - 13*c**2/2 - 5*c. Let l be r(13). Factor -l*n + 2*n**2 + 4*n + n.
2*n*(n - 4)
Let r(k) be the first derivative of 0*k**2 - 1/9*k**4 - 20 + 0*k + 1/54*k**6 - 4/27*k**3 + 1/45*k**5. Factor r(v).
v**2*(v - 2)*(v + 1)*(v + 2)/9
Let d(m) = -2*m**2 - m - 3. Let u(z) = -5*z**2 - 3*z - 8. Let g(p) = -8*d(p) + 3*u(p). Let r(k) = 4*k**2 - 4*k - 4. Let v(l) = -2*g(l) + r(l). Factor v(j).
2*(j - 2)*(j + 1)
Let p = 2882 + -2880. Factor 3/7*d - 2/7*d**p + 0 - 1/7*d**3.
-d*(d - 1)*(d + 3)/7
Let q be 4/(-8) + 15/2. Suppose -8 = -4*z + 3*c + q, -6 = -2*c. What is n in 2*n**2 + z*n**2 - 2*n + 0*n = 0?
0, 1/4
Let k(b) be the second derivative of -2*b**5/15 - b**4/6 + 4*b**3/9 + b**2 + 8*b - 5. Find j such that k(j) = 0.
-1, -3/4, 1
Let x(v) be the third derivative of 5*v**8/336 + v**7/6 - v**6/12 - 23*v**5/6 + 325*v**4/24 - 125*v**3/6 + 291*v**2. Factor x(b).
5*(b - 1)**3*(b + 5)**2
Factor 2*p**3 + 0 + 6/5*p**2 - 2/5*p**5 + 0*p + 2/5*p**4.
-2*p**2*(p - 3)*(p + 1)**2/5
Let w(a) = 644*a + 7105. Let j be w(-11). Determine p so that -j*p + 3/2*p**2 + 147/2 = 0.
7
Let g = -287 - -339. Suppose 0 = -11*d + 3 + g. Suppose 15/4*o**4 + 21/4*o**2 + 3/4*o**d + 3/2*o + 0 + 27/4*o**3 = 0. Calculate o.
-2, -1, 0
Suppose -17 = -2*p - 2*p - g, 2*p = -5*g + 31. Let c(h) be the first derivative of 4/3*h**3 - p*h**4 - 2/3*h**6 + 0*h**2 + 5 + 12/5*h**5 + 0*h. Factor c(z).
-4*z**2*(z - 1)**3
Factor -30/7*f**2 - 3/7 + 15/7*f + 3/7*f**5 - 15/7*f**4 + 30/7*f**3.
3*(f - 1)**5/7
Let m(v) be the first derivative of 30/7*v - 18 + 15/7*v**3 + 3/28*v**4 + 69/14*v**2 - 3/35*v**5. Find a, given that m(a) = 0.
-2, -1, 5
Suppose o - 132 = 4*o + 5*x, -4*x = 3*o + 132. Let j be o/(-33) - (1 - 1). Solve -4/3*i**2 - j*i + 0 = 0 for i.
-1, 0
Suppose -4 - 6 = -5*a. Suppose -4*y = -a*y - 32. Factor -4 + y*x**3 + 2*x**2 + 2*x**2 - 12*x - 4*x**3.
4*(x - 1)*(x + 1)*(3*x + 1)
Let h(s) be the first derivative of -s**5/10 - s**4 + s**3/6 + 2*s**2 - 52. Factor h(z).
-z*(z - 1)*(z + 1)*(z + 8)/2
Suppose 2*f + 4 = 4*g + 2, 0 = -3*g + 5*f - 9. Find d such that 13*d**2 + 27*d**2 - g*d**3 - 3*d**3 = 0.
0, 8
Let v(o) = -o**3 - 30*o**2 - 56*o + 3. Let w be (0 + (3 - 17))/((-1)/(-2)). Let x be v(w). Find a such that 0*a**4 - 2/3*a**x + 0*a + 0 + 2/3*a**5 + 0*a**2 = 0.
-1, 0, 1
Let d(c) be the third derivative of -c**8/5040 + 11*c**7/7560 + c**6/540 - 19*c**5/30 + 40*c**2. Let u(q) be the third derivative of d(q). Factor u(p).
-2*(p - 2)*(6*p + 1)/3
Let y(c) be the first derivative of c**6/12 - 3*c**5/5 - 3*c**4/8 + 26*c**3/3 - 15*c**2 + 15. Suppose y(a) = 0. What is a?
-3, 0, 2, 5
Factor -4897/4*q**2 - 1/4*q**4 + 69/2*q**3 - 1156 + 2346*q.
-(q - 68)**2*(q - 1)**2/4
Let z(y) be the first derivative of -29*y**6/12 + 17*y**5/2 - 81*y**4/8 + 23*y**3/6 + y**2/2 - 192. Find d, given that z(d) = 0.
-2/29, 0, 1
Let y(q) = q**2 + 10*q + 12. Let a be y(-9). Suppose -2*z + 1 = -a*s, 4*z - 40 = -2*s - 14. Factor 2*u**4 - 7*u**2 + 0*u**2 - u + s*u**2 - u**5 + 2*u**3 + 2.
-(u - 2)*(u - 1)**2*(u + 1)**2
Let v(y) be the first derivative of -4*y**3/3 + 111*y**2 + 112*y - 182. Suppose v(s) = 0. Calculate s.
-1/2, 56
Let k = 2414 - 2414. Factor -4/11*z + 2/11*z**2 + k.
2*z*(z - 2)/11
Let x(r) be the second derivative of -r**5/110 - 5*r**4/66 - 7*r**3/33 - 3*r**2/11 - 296*r. Factor x(b).
-2*(b + 1)**2*(b + 3)/11
Let m(i) be the third derivative of -1/180*i**6 + 0*i**4 + 0*i - 2*i**2 + 0 - 1/20*i**5 - 1/2*i**3. Let j(c) be the first derivative of m(c). Factor j(o).
-2*o*(o + 3)
Factor 17*k**5 - 6*k**3 + 6*k**5 - 21*k**5 - 4*k**2.
2*k**2*(k - 2)*(k + 1)**2
Let l(p) be the first derivative of -2*p**3/15 - 54*p**2/5 - 1458*p/5 - 21. Factor l(z).
-2*(z + 27)**2/5
Let k(x) = -6*x**3 - 30*x**2 + 6*x + 30. Let a(d) = -9*d**3 - 45*d**2 + 9*d + 45. Let p(s) = -5*a(s) + 7*k(s). Suppose p(u) = 0. Calculate u.
-5, -1, 1
Let i(c) be the first derivative of -c**4/16 - 5*c**3/4 - 6*c**2 + 16*c - 89. Factor i(f).
-(f - 1)*(f + 8)**2/4
Let a = -5 - 1. Let y be 1*(-3)/a - 15/110. Let -y*n - 10/11*n**2 + 14/11*n**3 + 0 = 0. What is n?
-2/7, 0, 1
Let o(r) be the first derivative of -r**6/180 + r**5/15 + 11*r**3/3 - 4. Let s(q) be the third derivative of o(q). Factor s(x).
-2*x*(x - 4)
Let m(h) = -37*h**2 + 398*h + 130. Let x(y) = -56*y**2 + 598*y + 194. Let w(z) = -7*m(z) + 5*x(z). Suppose w(s) = 0. What is s?
-2/7, 10
Let d(y) = -y**3 - 14*y**2 + 14*y - 13. Let s be d(-15). Let x be 11*2/1*s. Factor 20*k**3 + 1 + 48*k + 17 - 34 + x*k**2 - 140*k**3 - 100*k**4.
-4*(k + 1)**2*(5*k - 2)**2
Suppose 3*p - 121 = -127. Let m(n) = -n**3 - 24*n**2 - 65*n - 56. Let g(w) = 15*w**3 + 384*w**2 + 1041*w + 897. Let j(r) = p*g(r) - 33*m(r). Factor j(z).
3*(z + 2)*(z + 3)**2
Solve -15*w**2 + 28*w**3 - 61*w**3 - 125 - 75*w + 32*w**3 = 0.
-5
Suppose 69*z = 11*z + 174. Let r(x) be the first derivative of -1/4*x**2 - 1/6*x**z - 2 + 0*x. Suppose r(u) = 0. What is u?
-1, 0
Let m = -1340 + 1342. Factor -4/3 - 1/3*r**m + 5/3*r.
-(r - 4)*(r - 1)/3
Solve 0*s + 1/7*s**2 - 6/7*s**3 + 5/7*s**4 + 0 = 0 for s.
0, 1/5, 1
Let g = -11 - -16. Suppose g*a**2 + 14*a**4 + 2*a**2 - 16*a**4 - 5*a**2 = 0. Calculate a.
-1, 0, 1
Suppose 158*c + 18 = 161*c - 3*k, c + 5*k + 12 = 0. Factor 0*n - 3/2*n**2 + 0 - 1/4*n**c.
-n**2*(n + 6)/4
Let r be 6/33 + 5/(220/124). Solve 6*d**r + 2 + 3*d**3 - 4*d**3 - 15*d + 8 = 0 for d.
-2, 1
Find h, given that 84 - 155*h + 75*h - 2*h**2 + 102*h = 0.
-3, 14
Factor -2/7*j**2 + 20/7 + 18/7*j.
-2*(j - 10)*(j + 1)/7
Let f = -52 + 55. Let l(z) be the first derivative of 5*z**2 - 9 + 4*z - 14/3*z**f. Suppose l(s) = 0. Calculate s.
-2/7, 1
Let k = -504 - -3530/7. Suppose -2/7*q**2 + 9/7*q**3 - 9/7*q + k = 0. What is q?
-1, 2/9, 1
Suppose 40/3*a + 14/15*a**5 - 8/5*a**4 + 28/5*a**2 - 106/15*a**3 + 16/5 = 0. What is a?
-2, -1, -2/7, 2, 3
Let f(a) = -3*a**2 + 16*a - 9. Let o(c) = -4*c**2 + 18*c - 9. Let j(k) = -5*f(k) + 4*o(k). What is h in j(h) = 0?
-9, 1
Let c(l) = -7*l**3 + 10*l**2 + l + 8. Let g = 0 - -3. Let a(o) = -22*o**3 + 29*o**2 + 2*o**g + 2*o + 0*o**3 + 23. Let t(j) = -6*a(j) + 17*c(j). Factor t(f).
(f - 2)*(f - 1)**2
Let c(x) = -7*x**2 - 13*x + 65. Let l(v) = 12*v**2 + 26*v - 131. Let f(y) = 10*c(y) + 6*l(y). Let f(t) = 0. What is t?
-17, 4
Let x(w) = 2*w**4 - 268*w**3 + 4614*w**2 - 8444*w + 4098. Let v(s) = 7*s**4 - 1074*s**3 + 18457*s**2 - 33774*s + 16393. Let n(f) = 2*v(f) - 9*x(f). Factor n(y).
-4*(y - 32)**2*(y - 1)**2
Suppose 0 = 4623*r - 4644*r. Solve 0 + 0*f**2 - 1/5*f**4 + r*f - 2/5*f**3 = 0.
-2, 0
Suppose -29*p + 25*p - 18 = 2*h, -5*h - 15 = 5*p. Factor 0 - 3*a**3 + 15/2*a**2 - h*a.
-3*a*(a - 2)*(2*a - 1)/2
Let j(t) be the second derivative of t**4/12 + t**3/6 - 69*t. Find v such that j(v) = 0.
-1, 0
Let b(a) be the second derivative of 0 + 16/7*a**2 + 1/35*a**5 + 2/7*a**4 + 10*a + 8/7*a**3. Factor b(m).
4*(m + 2)**3/7
Suppose 4*o + 0*o - 16 = 0. Suppose 5*d + 2*z = 20, z - o = -d + 3*z. Factor -3/5 - 6/5*m**3 + 9/5*m**d - 6/5*m**2 + 9/5*m - 3/5*m**5.
-3*(m - 1)**4*(m + 1)/5
Solve -2/7*q**3 + 0 - 128/7*q + 32/7*q**2 = 0 for q.
0, 8
Let k(m) be the first derivative of 5/18*m**3 + 5/6*m - 20 - 5/6*m**2. Factor k(i).
5*(i - 1)**2/6
Let k(q) be the first derivative of -28/39*q**3 - 6/65*q**5 + 16/13*q - 1/2*q**4 + 4/13*q**2 + 2. Suppose k(w) = 0. What is w?
-2, -1, 2/3
Let d(u) be the first derivative of 25*u**3/9 - 65*u**2/3 + 25*u/3 + 3. What is b in d(b) = 0?
1/5, 5
Suppose -3*r + 0*l + 3*l - 24 = 0, l + 4 = -2*r. Let i(s) = -s**2 - 2*s + 8. Let q be i(r). Find u such that 3/2*u + q + 3/2*u**2 = 0.
-1, 0
Let n be -4 + 1 - (0 - 11). Factor -14*s - 6*s - 9*s + n + 4*s**2 + 17*s.
4*(s - 2)*(s