*l**2*(l - 1)*(4*l + 1)/11
Let a(p) be the second derivative of -p**6/60 - p**5/5 - p**4 - 8*p**3/3 + p**2 - 3*p. Let g(y) be the first derivative of a(y). Factor g(j).
-2*(j + 2)**3
Suppose -5*c + 0*c - 4*f - 16 = 0, -4*c + 12 = -3*f. Suppose d - 1 - 2 = c. Factor g**2 + 1 + d*g + 3*g - 4*g.
(g + 1)**2
Let x(r) be the first derivative of r**5/40 - r**3/8 + r**2/8 - 70. Solve x(h) = 0 for h.
-2, 0, 1
Let p(t) be the third derivative of 1/8*t**4 + 0*t - 1/6*t**3 + 0 + t**2 + 1/120*t**6 - 1/20*t**5. Let p(n) = 0. Calculate n.
1
Let v be (-20)/(-12) + -1 + 0. Let h(k) be the first derivative of v*k**2 + 2 + 2/3*k + 2/9*k**3. Determine i, given that h(i) = 0.
-1
Let c(f) be the first derivative of f**3/3 + 15*f**2/4 + 7*f/2 - 9. Factor c(s).
(s + 7)*(2*s + 1)/2
Let k(c) be the second derivative of c**7/210 - c**5/100 - 17*c. Factor k(u).
u**3*(u - 1)*(u + 1)/5
Let a(i) be the third derivative of -i**6/240 - i**5/30 - 5*i**4/48 - i**3/6 - 6*i**2. What is f in a(f) = 0?
-2, -1
Let a(u) be the first derivative of -1/50*u**5 - 1/3*u**3 - 2/15*u**4 + 1 + u - 2/5*u**2. Let t(v) be the first derivative of a(v). Factor t(n).
-2*(n + 1)**2*(n + 2)/5
Let u(p) be the third derivative of -p**5/360 - p**4/48 + 13*p**2. Solve u(d) = 0 for d.
-3, 0
Let j(g) be the first derivative of -g**5/20 + 3*g**4/16 + 6. Factor j(p).
-p**3*(p - 3)/4
Suppose 0*p = 3*p - 6. Suppose p*m = -5*x - 4, 0*x + 5*x + 6 = -3*m. What is a in 0*a**5 - 2*a**2 - 2*a**3 + 2*a**4 + x*a**2 + 2*a**5 = 0?
-1, 0, 1
Let i(m) be the first derivative of m**5/15 + m**4/6 - 4*m**3/9 - m**2/3 + m + 4. Determine h, given that i(h) = 0.
-3, -1, 1
Let m(j) be the third derivative of -j**6/30 - 2*j**5/15 - j**4/6 - 11*j**2. Factor m(i).
-4*i*(i + 1)**2
Let 6*h**2 - 4 - 1 + 5*h**3 - 3*h - 1 - 2*h**3 = 0. What is h?
-2, -1, 1
Let b(g) = 10*g - 7 + g**2 + 4*g**2 - 2 - 3*g**3 + 0. Let t(w) = -2*w**3 + 2*w**2 + 5*w - 5. Let c(x) = 6*b(x) - 11*t(x). Factor c(u).
(u + 1)*(2*u + 1)**2
Let u = -220530659/436 - -505806. Let r = u + 3/218. Factor -1/2 - 5/4*o**2 + r*o.
-(o - 1)*(5*o - 2)/4
Let w(c) = -c**3 - 3*c**2 - 5*c - 3. Let a be w(-3). Suppose -3*x - a = -4*z - 44, -5*z - 21 = x. Factor 3*k**3 - 2*k**x + 3*k**3 - k**2 + 3*k**2 - k - 5*k**3.
-k*(k - 1)*(k + 1)*(2*k - 1)
Suppose -2*c = -5*c. Suppose c = 4*f + 4*v - 12, -f + 3 = f + v. Factor 1/3*a**2 + 1/3*a + f.
a*(a + 1)/3
Let b = 6 - 2. Let j(o) be the second derivative of -1/7*o**3 - 2/7*o**2 + 0 - 1/42*o**b - o. Factor j(t).
-2*(t + 1)*(t + 2)/7
Determine c so that -2 - 2*c**2 - 5*c - 10*c**3 + 5*c**4 - c**5 + 1 + 12*c**2 + 2 = 0.
1
Let y(f) be the first derivative of f**6/3 - 6*f**5/5 + f**4 + 4*f**3/3 - 3*f**2 + 2*f - 39. Suppose y(z) = 0. Calculate z.
-1, 1
Let q(x) be the second derivative of x**4/3 - 2*x**2 + 12*x. Factor q(f).
4*(f - 1)*(f + 1)
Let y(t) be the first derivative of t**5/5 - 3*t**4/4 + 2*t**2 - 3. Find i, given that y(i) = 0.
-1, 0, 2
Let z(v) be the third derivative of 1/180*v**5 + 0 + 0*v + 0*v**3 + 2*v**2 - 1/36*v**4 + 1/360*v**6. Factor z(m).
m*(m - 1)*(m + 2)/3
Suppose 4*v + 5*p = 17, -2 = v + 4*p + 2. Suppose 0 = f - 5*f + 4*s + 8, 4*f - 2*s - v = 0. Factor 0 - 2/3*b**4 + 0*b - 2/3*b**f - 4/3*b**3.
-2*b**2*(b + 1)**2/3
Factor 0*o - 1/4*o**2 + 1/4.
-(o - 1)*(o + 1)/4
Let u be 4/(-8)*-18*1. Let m be u/(-3) + (-46)/(-6). Factor -4/3 - 2*w**3 - m*w - 16/3*w**2.
-2*(w + 1)**2*(3*w + 2)/3
Let v(c) be the first derivative of -c**6/480 + c**5/120 - c**4/96 - c**2/2 - 2. Let o(n) be the second derivative of v(n). Let o(a) = 0. What is a?
0, 1
Let z(n) be the third derivative of n**8/1512 + n**7/189 + n**6/60 + 7*n**5/270 + n**4/54 - 3*n**2. Suppose z(w) = 0. Calculate w.
-2, -1, 0
Solve 12/5 + 3/5*f**4 + 39/5*f**2 - 36/5*f - 18/5*f**3 = 0.
1, 2
Let t(f) be the first derivative of -9*f**4/26 - 16*f**3/13 - f**2 - 4*f/13 + 3. Let t(g) = 0. What is g?
-2, -1/3
Suppose -y + 10 - 29 = 0. Let b = y - -39/2. What is t in -3/4*t**3 + 1/4*t + 0 - b*t**4 + 0*t**2 = 0?
-1, 0, 1/2
Find v, given that v + 1/3*v**2 + 2/3 = 0.
-2, -1
Let s(r) = 15*r**3 - 9*r**2 + 21*r - 9. Suppose -5*p + 2 = -u, -u = 2*u - 2*p - 46. Let z(j) = -j**3 - j + 1. Let b(i) = u*z(i) + s(i). Solve b(d) = 0 for d.
-3, -1, 1
Let b(f) = -f - 1 + 0 + 0. Let c(i) = i**2 - 9*i - 6. Let u(x) = -6*b(x) + c(x). Solve u(d) = 0.
0, 3
Let f be 5/((-14)/((-112)/60)). Suppose 0*q**3 + 0*q + f*q**4 + 0*q**2 + 0 = 0. Calculate q.
0
Let i(b) be the second derivative of b**9/83160 + b**8/36960 - b**7/13860 - b**6/3960 + b**4/3 - b. Let h(d) be the third derivative of i(d). Factor h(u).
2*u*(u - 1)*(u + 1)**2/11
Let d(h) = -4*h**3 - 16*h**2 + 64*h - 56. Let i(b) = b**3 - b**2. Let a(z) = 2*d(z) + 12*i(z). Factor a(s).
4*(s - 7)*(s - 2)**2
Let j = 2355/14 - 339/2. Let d = -11/14 - j. What is h in -1/2*h + d*h**2 + 0 = 0?
0, 1
Let d(c) = c**3 + 9*c + 3. Let p be d(0). Factor 0 + 0*l**p - 2/5*l**2 + 2/5*l**4 + 0*l.
2*l**2*(l - 1)*(l + 1)/5
Let g be 46/437 - (-634)/114 - 3. Solve 2/3*q**2 - g*q + 8/3 = 0 for q.
2
Let r(y) = -y**2 - 11*y - 13. Let a be r(-9). Suppose 4*m - 3*m = a, -7 = -c - m. Factor -c*g**5 - 3*g**2 - 3*g**4 - g**2 - 2*g**4 + 3*g**5 + 8*g**3.
g**2*(g - 2)**2*(g - 1)
Let f(k) be the third derivative of 1/15*k**5 + 0*k**3 - 1/30*k**6 - 8*k**2 + 0*k**4 + 0*k + 0. Factor f(r).
-4*r**2*(r - 1)
Let q(x) be the third derivative of 6*x**2 + 0 + 1/8*x**4 - 1/5*x**3 + 1/200*x**6 - 1/25*x**5 + 0*x. Determine u, given that q(u) = 0.
1, 2
Let l(w) = -w + 10. Let i be l(5). Suppose 5*p = -o + 13, 5*o - 7 - 18 = -i*p. Factor p*u**2 - 5*u - 2 + 5*u.
2*(u - 1)*(u + 1)
Determine u so that 0 - 2/5*u**2 - 2*u**3 + 0*u = 0.
-1/5, 0
Let j = -46/3 + 101/6. Let a(z) = 10*z - 56. Let s be a(6). Factor -5/2*f**2 - j*f**3 + 1/2 + 3/2*f + 2*f**s.
(f - 1)**2*(f + 1)*(4*f + 1)/2
Let b(o) be the second derivative of -o**7/98 - o**6/70 + 3*o**5/28 + 5*o**4/28 - 2*o**3/7 - 6*o**2/7 - 7*o - 1. Let b(k) = 0. Calculate k.
-2, -1, 1, 2
Let g(k) be the third derivative of -k**7/240 + k**6/360 - 5*k**3/6 + 5*k**2. Let t(c) be the first derivative of g(c). Factor t(i).
-i**2*(7*i - 2)/2
Let b(v) = -3*v**2 - v**3 + 0 + 6*v**2 - 3. Let j(f) = -2*f**3 + 5*f**2 - 5. Let z(c) = -5*b(c) + 3*j(c). Let z(t) = 0. What is t?
0
What is x in 1/10*x**3 - 1/10*x + 0 + 0*x**2 = 0?
-1, 0, 1
Let o(k) be the third derivative of -2*k**7/525 - k**6/75 - k**5/75 + 2*k**2. Factor o(m).
-4*m**2*(m + 1)**2/5
Let m be 34/8 + 14/(-56). Let q be (-3)/(-9) - m/12. Let q*d + 1/2 - 1/2*d**2 = 0. Calculate d.
-1, 1
Let c(y) be the third derivative of y**2 - 1/180*y**5 + 0 + 0*y + 0*y**4 + 0*y**3. Solve c(t) = 0.
0
Let l(o) = 4*o - 9*o**2 + 10*o**2 - 3*o. Let x(b) = -15*b**2 - 21*b. Let g(u) = -12*l(u) - x(u). Factor g(j).
3*j*(j + 3)
Let k(i) be the first derivative of -i**5/90 + i**4/6 - i**3 - 3*i**2/2 + 3. Let m(r) be the second derivative of k(r). Factor m(n).
-2*(n - 3)**2/3
Determine m, given that -19*m**3 - 21*m**3 - 23*m**3 + 58*m**3 = 0.
0
Suppose -r + 32 = r. Suppose r = 3*h + h. Factor 0 + 0*g**3 + 2/5*g**2 + 0*g - 2/5*g**h.
-2*g**2*(g - 1)*(g + 1)/5
Let j(u) = u**3 + 2*u**2. Let s be 14/(-6) - (-2)/6. Let v be j(s). Factor -1/4*m**3 + 0 + v*m**2 + 1/4*m.
-m*(m - 1)*(m + 1)/4
Suppose -2*s = 6 + 2. Let l be -2 + 4/(-2 - s). Find g such that l*g**4 + 2*g**2 - g**3 - 3*g**3 + 2*g**4 = 0.
0, 1
Let f = 7 + -4. Factor 3*i + 2*i - 2*i - 2*i**f - i.
-2*i*(i - 1)*(i + 1)
Let o = -367 + 1837/5. Factor 2/5*g**3 - o*g - 2/5 + 2/5*g**2.
2*(g - 1)*(g + 1)**2/5
Let i(k) be the first derivative of k**7/735 - k**6/210 + k**5/210 - k**2 + 3. Let g(x) be the second derivative of i(x). Let g(o) = 0. Calculate o.
0, 1
Find q such that -24/7 + 6/7*q**2 + 18/7*q = 0.
-4, 1
Let c(f) be the first derivative of -f**5/360 - f**4/72 - f**3/36 - 4*f**2 - 7. Let s(p) be the second derivative of c(p). Determine x so that s(x) = 0.
-1
Let t(d) be the first derivative of 14*d**5/85 + 8*d**4/17 + 22*d**3/51 + 2*d**2/17 - 2. Find n, given that t(n) = 0.
-1, -2/7, 0
Let n(c) be the second derivative of -c**8/13440 + c**7/2520 + c**6/480 - c**4/4 + 2*c. Let q(g) be the third derivative of n(g). Factor q(r).
-r*(r - 3)*(r + 1)/2
Let a(q) be the third derivative of -q**6/900 + q**4/60 - q**3/3 + 3*q**2. Let z(u) be the first derivative of a(u). Solve z(l) = 0.
-1, 1
Let j be (