4/3*c**2 + 0 + 4/3*c + 1/3*c**3.
c*(c + 2)**2/3
Let g be 1/4 + 15/36. Suppose -2*y - 1 = 2*v - 9, -4*y - 2*v = -12. Find b, given that g - 1/3*b**y + 1/3*b = 0.
-1, 2
Let f be (-2)/3 - (-308)/165. Factor 2/5*q**4 - 2/5*q**3 - f*q**2 + 4/5 + 2/5*q.
2*(q - 2)*(q - 1)*(q + 1)**2/5
Let b(g) be the second derivative of g**4/60 + 7*g**3/30 - 4*g**2/5 + 42*g. Factor b(y).
(y - 1)*(y + 8)/5
Let x(w) = w - 4. Let j be x(8). Solve 3*t**3 + 2*t**j - 3*t**3 = 0 for t.
0
Factor -11*q**2 + 10*q**2 - 25*q + 44 + 5*q**2 - 23*q.
4*(q - 11)*(q - 1)
Let g(u) = 4*u**2 - 4. Let m(i) = -i**4 - i**3 - 4*i**2 + i + 5. Let n(h) = 5*g(h) + 4*m(h). Solve n(r) = 0 for r.
-1, 0, 1
Let d(b) be the second derivative of b**7/252 - b**5/120 + b. Factor d(f).
f**3*(f - 1)*(f + 1)/6
Let j(d) be the first derivative of -d**3/3 - 5*d**2/2 - 4*d + 2. Let c be j(-3). Solve 3/2*h**4 - 3/2*h**c - 1/2*h + 5/2*h**3 - 2*h**5 + 0 = 0.
-1, -1/4, 0, 1
Let n(p) = -65*p**3 - 265*p**2 - 200*p + 75. Let t(o) = -32*o**3 - 133*o**2 - 100*o + 37. Let c(g) = -3*n(g) + 5*t(g). Determine d so that c(d) = 0.
-2, 2/7
Let l(s) be the third derivative of -s**6/54 - 17*s**5/135 - 8*s**4/27 - 8*s**3/27 + 9*s**2. Factor l(y).
-4*(y + 1)*(y + 2)*(5*y + 2)/9
Let b = -161 + 1779/11. Solve b*t + 12/11*t**2 + 2/11 + 8/11*t**3 + 2/11*t**4 = 0 for t.
-1
Let x(q) be the first derivative of 0*q**2 + 3 + 0*q**3 + 0*q + 0*q**4 - 1/25*q**5. Factor x(v).
-v**4/5
Factor -4/5*m**2 + 0 - 4/5*m - 1/5*m**3.
-m*(m + 2)**2/5
Let w(n) = -3*n**4 + n**3 - 2*n - 2. Let j(l) = 4*l**4 - 6*l**3 + 6*l + 3 - 3*l + 4*l**3. Let i(p) = 2*j(p) + 3*w(p). Factor i(t).
-t**3*(t + 1)
Let r(z) be the second derivative of -z**9/105840 + z**7/17640 + 7*z**4/12 - 3*z. Let b(i) be the third derivative of r(i). Let b(s) = 0. Calculate s.
-1, 0, 1
Let s(z) be the second derivative of 2/13*z**2 + 0 - 1/13*z**3 + 1/130*z**5 + 5*z + 0*z**4. Let s(t) = 0. Calculate t.
-2, 1
Factor -15*c**5 - 12*c**3 - 10*c**4 + 16*c + 8*c**2 + 2*c**5 + 11*c**5.
-2*c*(c - 1)*(c + 2)**3
Suppose -2*n**3 + 9*n**2 - 2*n**3 + 2*n - 3*n**3 + 2*n**3 = 0. What is n?
-1/5, 0, 2
Let s(z) be the first derivative of -z**6/12 - 2*z**5/5 - 5*z**4/8 - z**3/3 - 2. Factor s(r).
-r**2*(r + 1)**2*(r + 2)/2
Let x = 284 - 284. Find n, given that 2/7*n - 6/7*n**4 - 10/7*n**2 + 2*n**3 + x = 0.
0, 1/3, 1
Let k be 0/((-4)/(-8)*(-2 + 0)). Solve 0 + 2/3*y**3 + k*y**2 + 0*y = 0.
0
Let x be (1 + 1)/((-7)/(-14)). Suppose x*y + 4 = 12. Factor -q**3 - q**y - 1/2 + 3/2*q**4 + 3/2*q - 1/2*q**5.
-(q - 1)**4*(q + 1)/2
Factor 0*t**3 - 6/5*t**2 + 0 + 2/5*t**4 - 4/5*t.
2*t*(t - 2)*(t + 1)**2/5
Let f(v) be the third derivative of 0*v + 2/315*v**7 + 1/36*v**6 - 1/9*v**3 + 1/30*v**5 + 0 - 1/36*v**4 + v**2. Factor f(q).
2*(q + 1)**3*(2*q - 1)/3
Let i(c) be the first derivative of -3/4*c**2 + 0*c**3 + 0*c + 3/8*c**4 + 6. Find z such that i(z) = 0.
-1, 0, 1
Let y = -3112/5 - -623. Suppose -1/5*o**2 + 2/5 - 3/5*o**3 - 1/5*o**4 + y*o = 0. Calculate o.
-2, -1, 1
Let d(m) be the second derivative of 2*m**6/15 + 2*m**5/5 - 4*m**3/3 - 2*m**2 - 7*m. What is z in d(z) = 0?
-1, 1
Let r(i) = i**2 - i + 1. Let s(d) = 14*d**2 - 22*d + 18. Let l(o) = -7*o**2 + 11*o - 9. Let w(v) = 7*l(v) + 4*s(v). Let a(n) = 5*r(n) - w(n). Factor a(x).
-2*(x - 2)*(x - 1)
Factor -16/7*g**5 + 0*g + 4*g**4 - 4/7*g**2 - 8/7*g**3 + 0.
-4*g**2*(g - 1)**2*(4*g + 1)/7
Let s be (-6 + 0 - -2)/(-6). Determine f so that -s + 2/3*f**3 + 2*f - 2*f**2 = 0.
1
Let r(t) = t**2 - 4*t + 4. Let f be r(2). Let y(d) be the second derivative of -1/9*d**3 + 0*d**2 + f + d + 1/36*d**4. Let y(i) = 0. What is i?
0, 2
Let h = 8 - 7. Let j(w) = -w**2 + w + 1. Let o(v) = v - 4. Let m(f) = f - 1. Let t(l) = 3*m(l) - o(l). Let n(d) = h*j(d) - t(d). Factor n(r).
-r*(r + 1)
Let c(l) = -10*l**3 - 4*l**2 + 6*l + 4. Let j(v) = -v**4 + 21*v**3 + 8*v**2 - 11*v - 7. Let z(k) = 10*c(k) + 4*j(k). Determine i, given that z(i) = 0.
-3, -1, 1
Determine d so that -118*d - 143*d - 20 + 285*d - 4*d**2 = 0.
1, 5
Let a(k) = k**2 - 9*k - 2. Let x be a(9). Let h be -2 + ((-40)/6)/x. Find r such that -1/3*r**5 - 2*r**3 + h*r**4 + 4/3*r**2 + 0 - 1/3*r = 0.
0, 1
Let k(h) be the third derivative of -h**5/30 - h**4/66 + 9*h**2. Let k(v) = 0. What is v?
-2/11, 0
Let x(m) be the third derivative of m**5/30 - 3*m**4 + 108*m**3 + 56*m**2. Factor x(t).
2*(t - 18)**2
Factor 7*l - 10*l - l**2 + 2*l**2.
l*(l - 3)
Let k(c) be the first derivative of -1/9*c**3 - 3 - 2/3*c + 1/2*c**2. Factor k(u).
-(u - 2)*(u - 1)/3
Let o(s) = 0*s**2 + 1 + 0*s**2 - 2*s**3 - s**2 - s. Let l(q) = 2*q**3 + q**2 - 1. Let v(y) = 3*l(y) + 2*o(y). Factor v(h).
(h - 1)*(h + 1)*(2*h + 1)
Let i(l) be the first derivative of -l**6/9 + 26*l**5/15 - 23*l**4/3 - 20*l**3/9 + 175*l**2/3 + 250*l/3 + 15. Factor i(b).
-2*(b - 5)**3*(b + 1)**2/3
Solve 3*b**2 + 2*b**2 - 3*b**4 - 5*b**2 + 3*b**2 = 0 for b.
-1, 0, 1
Let t = 726/5425 + -3/217. Let a(q) be the third derivative of 0 - t*q**5 + 3*q**2 - 1/30*q**3 + 0*q + 1/10*q**4. Solve a(k) = 0 for k.
1/6
Suppose -3*h + 13 = -3*a + 5*a, 0 = -a - 4*h + 4. Factor -s + s**3 + s**4 - a*s + 8*s - s**2.
s*(s - 1)*(s + 1)**2
Let r(y) be the second derivative of 1/6*y**3 + 0 + 1/36*y**4 + 1/3*y**2 - 2*y. Factor r(z).
(z + 1)*(z + 2)/3
Let v(q) be the third derivative of q**6/180 - 7*q**2. Suppose v(f) = 0. What is f?
0
Let d be 6/9*3 + 1. Factor 3*q**4 + 4*q + q**4 + 56*q**2 + 17*q**d - 36*q**2.
q*(q + 2)**2*(4*q + 1)
Let i(j) = j**2 + j - 1. Let g(z) = -z**3 + z + 1. Let c(x) = -2*g(x) - 2*i(x). Let c(q) = 0. Calculate q.
-1, 0, 2
Let z(b) be the first derivative of -4*b**3/3 - 36*b**2 - 324*b + 37. Factor z(j).
-4*(j + 9)**2
Suppose 5*p - 2*k = 6, -3*k = -7*k + 8. Factor 2/5*m - 2/5*m**p + 4/5.
-2*(m - 2)*(m + 1)/5
Solve 259 - 259 + 18*m - 2*m**5 - 12*m**4 - 16*m**3 + 12*m**2 = 0 for m.
-3, -1, 0, 1
Let u(v) be the third derivative of 1/45*v**5 + 5/36*v**4 + 2/9*v**3 + 0*v + 0 - 2*v**2. Factor u(y).
2*(y + 2)*(2*y + 1)/3
Let m(j) be the third derivative of j**8/420 + j**7/350 - j**6/120 - j**5/100 + j**4/120 + 10*j**2. Find f such that m(f) = 0.
-1, 0, 1/4, 1
Suppose -2*i - 2*h = -12, 4*i + 3*h + 2*h = 27. Factor 5*o**2 - 4*o**2 + 0*o**2 - 5*o + 1 + i*o.
(o - 1)**2
Let c(a) be the third derivative of 0*a + 0 + 1/600*a**6 - 1/300*a**5 + 1/1050*a**7 + 4*a**2 - 1/120*a**4 + 0*a**3. Factor c(d).
d*(d - 1)*(d + 1)**2/5
Solve 0*w**2 - 2/7*w**3 + 1/7*w + 0 + 0*w**4 + 1/7*w**5 = 0.
-1, 0, 1
Let m(y) = -4*y**2 - 40*y. Let a(w) = -4*w**2 - 40*w. Let i(c) = -4*a(c) + 3*m(c). Factor i(v).
4*v*(v + 10)
Let j be (-1)/6 - (-20)/12. Let d(a) be the first derivative of -2*a**3 + j*a**2 - 3 + 3/4*a**4 + 0*a. Let d(y) = 0. What is y?
0, 1
Let k(u) be the second derivative of -u**6/150 + u**5/100 + u**4/60 - u**3/30 - 3*u. Solve k(w) = 0.
-1, 0, 1
Factor 10 - 4*s**2 + 5*s**3 - s**2 - 5*s - 5*s**2.
5*(s - 2)*(s - 1)*(s + 1)
Let f be -4 + (-123)/(-27) + 1/(-9). What is r in -2/3*r + 0*r**4 - 2/9*r**5 - f*r**2 + 8/9*r**3 + 4/9 = 0?
-2, -1, 1
Let i(d) be the third derivative of -3*d**6/80 - d**5/20 + 5*d**2. Factor i(x).
-3*x**2*(3*x + 2)/2
Let g(j) = 2*j**3 + j**2 - 2*j + 1. Let w be g(1). Suppose -6/5*r**3 - 2/5*r + 0 + 6/5*r**w + 2/5*r**4 = 0. Calculate r.
0, 1
Let m be 16/(-6)*(-24)/288. Find i such that 0 + m*i**3 + 4/9*i**2 + 2/9*i = 0.
-1, 0
Let r(l) be the first derivative of l**6/21 + 16*l**5/35 + 25*l**4/14 + 76*l**3/21 + 4*l**2 + 16*l/7 + 21. Factor r(s).
2*(s + 1)**2*(s + 2)**3/7
Let h = 0 + 4. Suppose 0 = -h*k + k + 9. Determine r so that 2*r**5 + 4*r - 2*r + 0*r**5 - 4*r**k = 0.
-1, 0, 1
Let h = 1025/3 - 340. Factor -2/3*p + 1/3*p**5 + 1/3*p**4 - h*p**2 - p**3 + 0.
p*(p - 2)*(p + 1)**3/3
Let q = -41 - -207/5. Factor 1/5 + 1/5*h**2 + q*h.
(h + 1)**2/5
Let i be (1 - 0)*((-58)/(-14) + -4). Factor -i*m**2 + 1/7*m**3 - 1/7*m + 1/7.
(m - 1)**2*(m + 1)/7
Let y = -8 - -11. Suppose 0 = -4*u - y*n + 28, -2*u - 4*n + 36 = 3*u. Factor -2*d**3 + 3*d + 3*d**4 - d**u - 3*d.
2*d**3*(d - 1)
Let 0*q**3 + 4*q**2 - 4*q**4 + 2*q + q**5 + 0*q**3 - 3*q**5 = 0. Calculate q.
-1, 0, 1
Let b(s) be the first derivative of -s**6/30 + s**5/5 - 7*s**4/20 - s**3/15 + 4*s**2/5 - 4*s/5 - 3. Find h such that b(h) = 0.
-1, 1, 2
Let a(b) be the third derivative of 5*b**8/336 + b**7/14 + b**6/8 + b**5/12 - 13*b**2. What is d in a(d) = 0?
-1, 0
Factor 