*i + 2*y**4 + 2*y + 0*y**2.
2*y*(y + 1)**3
Let q(g) be the third derivative of g**6/360 - g**5/80 + g**4/48 + 2*g**3/3 - 3*g**2. Let r(i) be the first derivative of q(i). Solve r(y) = 0 for y.
1/2, 1
Let u(j) = 48*j**4 - 303*j**3 + 405*j**2 - 177*j + 39. Let p(b) = -24*b**4 + 152*b**3 - 202*b**2 + 89*b - 19. Let y(z) = 9*p(z) + 4*u(z). Factor y(q).
-3*(q - 5)*(2*q - 1)**3
Let i(t) be the third derivative of -1/6*t**4 + 0 + 0*t**3 - 3*t**2 + 0*t - 1/15*t**6 - 3/10*t**5. Suppose i(p) = 0. Calculate p.
-2, -1/4, 0
Let a(m) be the first derivative of -m**4/18 + 2*m**3/9 - 7. Factor a(b).
-2*b**2*(b - 3)/9
Find g such that 8/9*g**3 + 4/3*g**2 + 8/9*g + 2/9*g**4 + 2/9 = 0.
-1
Let t(p) = -15*p**2 + 48*p + 63. Let g(n) = 3*n - n + n + 4 - n**2. Let v(b) = 33*g(b) - 2*t(b). Factor v(l).
-3*(l - 2)*(l + 1)
Factor -77*h - 17*h**2 - 15*h**3 + 161*h - 4*h**2 + 36.
-3*(h - 2)*(h + 3)*(5*h + 2)
Suppose -y = -0*s - 3*s + 10, 0 = -5*s + 3*y + 22. Factor -2*l**2 - 2*l - 2*l + s*l + 4*l.
-2*l*(l - 1)
Suppose 2*f = 5*m + 3 - 7, -4 = -4*f + 4*m. Factor -6 + 2 - f*z + 6 + z**3.
(z - 1)**2*(z + 2)
Let v = -2 - -7. Let j(k) be the third derivative of 1/72*k**4 - 1/9*k**3 + 0 - k**2 + 0*k + 1/180*k**v. Find x such that j(x) = 0.
-2, 1
Let h(s) be the third derivative of 3*s**6/40 - 2*s**5/5 + s**4/2 - 4*s**2. Factor h(p).
3*p*(p - 2)*(3*p - 2)
Suppose 0 = -58*v + 59*v - 3. Factor 4/3 + 8*h**2 + 8/3*h**v + 6*h.
2*(h + 2)*(2*h + 1)**2/3
Let i(b) be the second derivative of 0 + b - 2/27*b**4 + 2/9*b**2 - 1/27*b**3 + 1/30*b**5. Let i(o) = 0. Calculate o.
-2/3, 1
Factor 2/9 + 16/9*h**4 - 19/9*h - 56/9*h**3 + 19/3*h**2.
(h - 2)*(h - 1)*(4*h - 1)**2/9
Let j(v) = -8*v**2 - 72*v - 400. Let g(p) = 9*p**2 + 70*p + 400. Let n(i) = -4*g(i) - 5*j(i). Factor n(f).
4*(f + 10)**2
Let u(y) = -6*y**2 - 11*y - 14. Let b(c) = c**2 + c + 1. Let n(i) = -5*b(i) - u(i). Suppose n(q) = 0. What is q?
-3
Let a(c) be the third derivative of -1/120*c**7 - 1/48*c**4 + c**2 + 5/1344*c**8 - 1/160*c**6 + 0 + 0*c + 0*c**3 + 7/240*c**5. Solve a(r) = 0.
-1, 0, 2/5, 1
Let p(b) = b**3 + b + 4. Let d = -3 - -3. Let r be p(d). Factor -q**3 + 2*q**4 + 5*q**3 + 2*q**3 + r*q**2.
2*q**2*(q + 1)*(q + 2)
Suppose d = -2*u + 8, -4*d = 2*u + 1 - 3. Let s be (-23)/(-5) + d/(-5). Factor -2/5*w**3 + 1/5*w + 0*w**2 + 0 + 0*w**4 + 1/5*w**s.
w*(w - 1)**2*(w + 1)**2/5
Suppose -3*l = 5*r + 41, -r - 6 = 3*l + 7. Let q = 10 + r. Factor u**4 + u - 1 + 0*u**q + u - 2*u**3.
(u - 1)**3*(u + 1)
Let b(n) be the third derivative of 0*n**5 - 1/420*n**7 + 0*n + 0*n**3 + 0*n**4 + 1/1344*n**8 + 1/480*n**6 + 0 - 7*n**2. Factor b(p).
p**3*(p - 1)**2/4
Let h(r) be the third derivative of r**9/60480 - r**8/6720 + r**7/1680 - r**6/720 + r**5/15 + 3*r**2. Let s(i) be the third derivative of h(i). Factor s(v).
(v - 1)**3
Let d(w) = w**2 + 12*w - 16. Let l(y) = 6*y**2 + 84*y - 111. Let g(q) = 27*d(q) - 4*l(q). Factor g(k).
3*(k - 2)**2
Suppose -q = 4*s - 6, s - 4*q - 6 = 2*s. What is w in -2/7 - 6/7*w - 6/7*w**s - 2/7*w**3 = 0?
-1
Let j = 2 + 1. Find y such that -3*y**4 - 3*y**3 + 6*y**3 + 4*y**2 - y**2 - 6*y + j*y**3 = 0.
-1, 0, 1, 2
Let p(c) = c**3 - 4*c**2 + 5. Let u be p(4). Factor 3*h**4 - 2*h**u + 10*h**3 - h**4 - 2*h**2 - 9 + 1 - 16*h.
-2*(h - 2)**2*(h + 1)**3
Find r such that -3*r**4 - r**4 + 3*r**3 - r**4 - 8*r**3 = 0.
-1, 0
Let v(b) = -14*b**5 - 51*b**4 - 54*b**3 - 31*b**2 + b + 5. Let k(j) = 14*j**5 + 50*j**4 + 54*j**3 + 30*j**2 - 4. Let y(d) = -5*k(d) - 4*v(d). Factor y(o).
-2*o*(o + 1)**3*(7*o + 2)
Let m = 3/262 - -515/786. Determine b so that 4/9*b - 2/3*b**3 + 14/9*b**4 - m*b**5 + 0 - 2/3*b**2 = 0.
-2/3, 0, 1
Let y(i) be the second derivative of i**5/90 + i**4/36 + i**2 - 3*i. Let k(d) be the first derivative of y(d). Let k(m) = 0. What is m?
-1, 0
Let v(i) be the second derivative of -i**7/7 + 2*i**6/3 - 6*i**5/5 + i**4 - i**3/3 + 4*i. Suppose v(j) = 0. What is j?
0, 1/3, 1
Let l(f) = -11*f - 85. Let d be l(-8). Factor -5/4*a**2 - 3/4*a + 3/4*a**d + a**4 + 1/4.
(a - 1)*(a + 1)**2*(4*a - 1)/4
Factor 0 + 6/7*t**2 + 8/7*t**3 + 0*t + 2/7*t**4.
2*t**2*(t + 1)*(t + 3)/7
Solve 2/7*a**3 + 6/7*a**2 + 2/7 + 6/7*a = 0 for a.
-1
Let d(l) be the first derivative of -l**7/2520 - l**6/1080 + l**3/3 + 3. Let q(t) be the third derivative of d(t). Let q(r) = 0. What is r?
-1, 0
Let u be 4/(-7) + 180/21. Let 9*i**2 + 3*i**3 - 20 + 0*i**2 + u = 0. Calculate i.
-2, 1
Let i(r) be the second derivative of r + 1/72*r**4 + 1/90*r**5 + 1/360*r**6 + 0*r**3 + 0 + 1/2*r**2. Let s(a) be the first derivative of i(a). Factor s(n).
n*(n + 1)**2/3
Let d(h) be the first derivative of h**6 + 16*h**5/5 + 7*h**4/2 + 4*h**3/3 - 11. Suppose d(w) = 0. What is w?
-1, -2/3, 0
Let o(w) be the second derivative of 3*w**5/4 + w**4/12 - 2*w**3 - 2*w**2 + 22*w. What is k in o(k) = 0?
-2/3, -2/5, 1
Suppose 25 = -4*l - 15. Let v be ((-8)/l)/(6/15). Factor 0 + 0*c - 2/7*c**4 - 2/7*c**3 + 0*c**v.
-2*c**3*(c + 1)/7
Let j(d) be the first derivative of -1/15*d**3 + 0*d + 1/5*d**2 + 2. Determine o, given that j(o) = 0.
0, 2
Let n(m) be the second derivative of 5*m**7/42 - 2*m**6/3 - 3*m**5/4 + 85*m**4/6 - 130*m**3/3 + 60*m**2 - 50*m. Factor n(l).
5*(l - 2)**3*(l - 1)*(l + 3)
Let r(t) be the second derivative of -t**4/90 - t**3/15 + 2*t**2/3 + 24*t. Factor r(o).
-2*(o - 2)*(o + 5)/15
Solve -2/7*v - 2/7*v**2 + 0 = 0.
-1, 0
Let v(w) be the first derivative of -3 + 0*w + 0*w**2 + 3/2*w**4 - w**3 - 3/5*w**5. Solve v(q) = 0 for q.
0, 1
Let r(f) = f**3 - 2*f**2. Let i be r(2). Suppose -2*g + 4*y - 20 = i, -3*g + 6*g = -y + 5. Find t such that g - 1/2*t - 1/2*t**2 = 0.
-1, 0
Let v = 1/6 - 0. Let g(c) be the second derivative of -1/9*c**3 + 1/36*c**4 + v*c**2 + 0 - 3*c. Factor g(t).
(t - 1)**2/3
Suppose 3*s + 5*x = -s + 31, -3*s = 2*x - 18. Factor n - 1/4*n**s - 1/2*n**3 - 1 + 3/4*n**2.
-(n - 1)**2*(n + 2)**2/4
Let l(o) be the third derivative of o**6/900 + o**5/150 + 4*o**3/3 - 7*o**2. Let u(p) be the first derivative of l(p). Factor u(w).
2*w*(w + 2)/5
Let f(q) be the first derivative of 25*q**6/8 + 21*q**5/2 + 207*q**4/16 + 7*q**3 + 3*q**2/2 - 13. Solve f(r) = 0.
-1, -2/5, 0
Let t(p) = -17*p**5 + 48*p**4 - 105*p**3 + 89*p**2 - 15*p. Let f(z) = -4*z**5 + 12*z**4 - 26*z**3 + 22*z**2 - 4*z. Let y(h) = -18*f(h) + 4*t(h). Factor y(k).
4*k*(k - 3)*(k - 1)**3
Let w = 15 - 21. Let k(h) = -h**3 - 7*h**2 - 5*h + 6. Let r be k(w). Determine t, given that 2/5*t**2 + 0 + r*t = 0.
0
Let g(s) be the second derivative of 0 + 1/15*s**4 + 0*s**3 - 2/5*s**2 - 4*s. Solve g(x) = 0.
-1, 1
Let y(r) = -r**2 + 1. Let q(s) = 16*s**4 - 40*s**3 + 14*s**2 + 13*s - 3. Let w(g) = -q(g) - 5*y(g). Determine n, given that w(n) = 0.
-1/4, 1, 2
Factor 1/2*j**2 - 1/6*j**4 - 5/6*j + 1/6*j**3 + 1/3.
-(j - 1)**3*(j + 2)/6
Let u(f) be the third derivative of -3*f**8/4480 - f**7/840 + f**6/480 - f**4/8 - 6*f**2. Let z(j) be the second derivative of u(j). Factor z(s).
-3*s*(s + 1)*(3*s - 1)/2
Find m such that 52*m**3 + 38/7*m**2 - 8/7 + 42*m**4 - 40/7*m = 0.
-1, -2/7, 1/3
Find s, given that -13 + 16 + 0*s**2 - 2*s**2 - 5 - 4*s = 0.
-1
Let d(f) be the third derivative of f**9/20160 + f**8/6720 - f**5/30 - f**2. Let y(n) be the third derivative of d(n). Find m such that y(m) = 0.
-1, 0
Let m(k) be the third derivative of 0*k**3 - 2*k**2 - 1/30*k**5 - 1/210*k**7 + 0 + 0*k + 1/40*k**6 + 0*k**4. Find h such that m(h) = 0.
0, 1, 2
Factor -3*p + 9/2 + 1/2*p**2.
(p - 3)**2/2
Let g(r) = r**4 - 2*r**2 - 4*r + 1. Let v(d) = -4*d + d + 2*d. Suppose 4*c = 12, c - 5 - 1 = 3*w. Let y(x) = w*g(x) + 4*v(x). Factor y(n).
-(n - 1)**2*(n + 1)**2
Let x = 19 - 30. Let m(t) = t + 13. Let o be m(x). Determine p so that 1/4*p - 5/2*p**o - 5/4*p**5 + p**3 + 1/2 + 2*p**4 = 0.
-1, -2/5, 1
Solve 12/7*g**3 - 12/7 + 3/7*g**4 + 9/7*g**2 - 12/7*g = 0.
-2, -1, 1
Let v = 0 - -3. Let n = -5/12 + 49/60. Factor 0 + 0*t + 4/5*t**4 + 0*t**2 + 2/5*t**v + n*t**5.
2*t**3*(t + 1)**2/5
Let x = 2/23 - -235/207. Let r = x - 5/9. Find i, given that 0 + r*i**2 + 4/3*i = 0.
-2, 0
Let i = -22 - -25. Factor 0*y**i + 0*y + 1/2*y**4 + 0*y**2 + 1/2*y**5 + 0.
y**4*(y + 1)/2
Let q(n) = -2*n**4 - 11*n**3 - 3*n**2 + 11*n - 5. Let y(m) = -3*m**4 - 21*m**3 - 6*m**2 + 21*m - 9. Let h(u) = 9*q(u) - 5*y(u). Let h(o) = 0. What is o?
-1, 0, 1, 2
Let u(a) = a**2 + 15*a + 51. Let f be u(-10). F