3*r**3*(r - 1)*(r + 1)/2
Let y = -1 - -2. Let z(w) be the first derivative of 15*w**2/2 - 24*w + 51. Let v(b) = -b**2 + b - 1. Let q(f) = y*z(f) + 3*v(f). Factor q(n).
-3*(n - 3)**2
Let o(x) be the second derivative of x**4/24 + x**3/12 - 2*x. Factor o(g).
g*(g + 1)/2
Factor 18*a - 3*a**2 + 3 - 18*a.
-3*(a - 1)*(a + 1)
Factor -i**4 + 1/6*i**5 + 2/3*i + 13/6*i**3 + 0 - 2*i**2.
i*(i - 2)**2*(i - 1)**2/6
Let d(j) be the first derivative of -1/20*j**4 + 1/5*j**2 + 1/15*j**3 + 0*j + 1. Factor d(b).
-b*(b - 2)*(b + 1)/5
Let a(v) be the second derivative of 0*v**2 - 1/21*v**3 - 3/70*v**5 - 3*v - 3/35*v**6 + 5/42*v**4 + 0. Let a(p) = 0. What is p?
-1, 0, 1/3
Let k = 109/2 - 54. Let s(y) be the second derivative of 1/20*y**5 + 0*y**4 + 0 - y**2 + y - k*y**3. Suppose s(o) = 0. Calculate o.
-1, 2
Let f(v) be the first derivative of -v**6/6 - v**5/5 + v**4/2 - 20. Factor f(h).
-h**3*(h - 1)*(h + 2)
Let n(y) be the first derivative of -2*y + 7 - 1/6*y**3 - y**2. Suppose n(s) = 0. Calculate s.
-2
Let m(k) be the first derivative of 4 - 12*k**2 + 26/3*k**3 + 2/5*k**5 + 8*k - 3*k**4. Factor m(a).
2*(a - 2)**2*(a - 1)**2
Let g(s) be the first derivative of -s - 9/10*s**5 - 8/5*s**2 + 1 + 4/15*s**3 + 7/5*s**4. Let p(q) be the first derivative of g(q). Suppose p(u) = 0. What is u?
-2/5, 2/3
Let g(b) be the first derivative of -4*b**5/5 - 4*b**4 - 20*b**3/3 - 4*b**2 - 8. Factor g(u).
-4*u*(u + 1)**2*(u + 2)
Let i(l) be the second derivative of l**8/20160 + l**4/12 + l. Let v(d) be the third derivative of i(d). Solve v(r) = 0 for r.
0
Let o(h) be the second derivative of -2*h**4 - h + h**3 + 2*h**2 + 7/10*h**5 + 0. Factor o(t).
2*(t - 1)**2*(7*t + 2)
Let a(m) = -m**3 + 11*m**2 + 2*m - 20. Let u be a(11). Determine q so that 2/9*q - 4/9 + 2/3*q**u - 2/9*q**4 - 2/9*q**3 = 0.
-2, -1, 1
Let m(u) = -u**2 + 6*u + 18. Let d be m(8). Suppose -4*c = -9 + 1. Determine o, given that -2*o**2 - 2*o**d + 2*o**2 + o**c = 0.
0
Factor 351*o + 6*o**2 - 4 - 3*o**2 - 351*o + o**3.
(o - 1)*(o + 2)**2
Suppose -3/4*v**2 - 3*v - 3 = 0. Calculate v.
-2
Let t(l) be the third derivative of l**9/5040 - l**7/420 + l**5/40 + l**4/8 + 7*l**2. Let d(p) be the second derivative of t(p). Factor d(v).
3*(v - 1)**2*(v + 1)**2
Let l(o) be the first derivative of 1/20*o**5 + 0*o**2 - 1/6*o**3 - 1/30*o**6 + 1/12*o**4 + 2 + 2*o. Let a(z) be the first derivative of l(z). Factor a(t).
-t*(t - 1)**2*(t + 1)
Suppose -2*i - i = -18. Let y(r) be the first derivative of 0*r + 0*r**5 + r**4 - r**2 - 1/3*r**i + 3 + 0*r**3. Factor y(h).
-2*h*(h - 1)**2*(h + 1)**2
Let d(s) be the third derivative of -s**10/120960 + s**9/30240 - s**7/5040 + s**6/2880 - s**4/12 + s**2. Let p(v) be the second derivative of d(v). Factor p(c).
-c*(c - 1)**3*(c + 1)/4
Let s be -5 + (-8)/(-2) + 4. Find p such that -2/9*p**s + 2 - 2/3*p - 10/9*p**2 = 0.
-3, 1
Let q(x) = -x**4 - 4*x**3 - 27*x**2 - 34*x - 16. Let m(r) = r**3 + r**2 + r. Let d(o) = -30*m(o) + 5*q(o). What is i in d(i) = 0?
-4, -1
Suppose 13*t = -t. Factor t*z - 2/5*z**2 + 8/5.
-2*(z - 2)*(z + 2)/5
Let k be (-2)/4*(-26)/39. Let m(u) be the first derivative of -2*u + 3/2*u**2 + 1 - k*u**3. Let m(h) = 0. What is h?
1, 2
Let t = -4 + 0. Let j(x) = -x**2 - 6*x - 6. Let q be j(t). Factor 0 + 4*m**2 - 2*m**2 - 2*m**3 - 2 + q*m.
-2*(m - 1)**2*(m + 1)
Suppose -13*k + 8 = -31. Solve -2/3*y**k - 2/9*y**4 - 4/9*y**2 + 0 + 0*y = 0 for y.
-2, -1, 0
Let p = -13 - -24. Factor -p*z - 3*z**4 + 8*z**3 + 14*z + z**3 - 9*z**2.
-3*z*(z - 1)**3
Suppose 5*b + 2*g = -0*g, g = 0. Let f be 2/10*(2 + b). Let 4/5*x + 0 - f*x**2 = 0. Calculate x.
0, 2
Find m such that -2646/5*m**5 - 6768/5*m**3 - 736/5*m + 3232/5*m**2 + 64/5 + 6804/5*m**4 = 0.
2/7, 2/3
Let w(p) be the second derivative of -2*p**7/105 - p**6/120 + p**5/5 + 11*p**4/24 + p**3/3 - p**2 + 2*p. Let u(c) be the first derivative of w(c). Factor u(l).
-(l - 2)*(l + 1)**2*(4*l + 1)
Let l(y) be the first derivative of -y**7/2520 - y**6/540 - y**5/360 + y**3 - 10. Let u(i) be the third derivative of l(i). Let u(r) = 0. Calculate r.
-1, 0
Let l(g) = 6*g**3 - 6*g**2 - 9*g - 3. Let b(r) = -7*r**3 + 6*r**2 + 9*r + 4. Let j(d) = -3*b(d) - 4*l(d). What is i in j(i) = 0?
-1, 0, 3
Let o(s) be the first derivative of s**3 - 15*s**2/2 + 28. Determine z, given that o(z) = 0.
0, 5
Let a(g) = 8*g**4 - 12*g**3 + 8*g**2 + 16*g - 20. Let w(z) = z**4 + z**3 - 2. Let m(d) = a(d) - 4*w(d). Find v such that m(v) = 0.
-1, 1, 3
Suppose -3*g + 2*q - 5 - 3 = 0, 5*g + 2*q = 8. Let r be g - -1*(6 - 2). Factor r*t - 4*t**3 + 2*t**5 + 2 - 4*t**5 + 2*t - 6*t**4 + 4*t**2 + 0*t**3.
-2*(t - 1)*(t + 1)**4
Suppose 12*c - 10*c - 38 = 0. Solve -4*l**4 + 29*l**3 - 14*l**3 - c*l**3 = 0 for l.
-1, 0
Suppose -4*p + 6 = 5*t - 5, 5*p - 1 = -2*t. Find j, given that 15*j**2 - 3*j**2 - 19*j**t + 15*j**3 - 16 = 0.
-1, 2
Let b(y) be the first derivative of 0*y**4 + 0*y + 0*y**2 - 5 - 2/55*y**5 + 2/33*y**3. Factor b(w).
-2*w**2*(w - 1)*(w + 1)/11
Let b(j) = j**2 + 4*j + 6. Let l(p) = p**2 + 4*p + 7. Let t(k) = -4*b(k) + 3*l(k). Solve t(s) = 0.
-3, -1
Let t(p) be the first derivative of -p**8/5880 + p**7/2940 + p**6/1260 - p**5/420 - 2*p**3 - 4. Let k(v) be the third derivative of t(v). Factor k(n).
-2*n*(n - 1)**2*(n + 1)/7
Let q(s) be the first derivative of s**6/60 + 3*s**5/20 + 3*s**4/8 - 6*s - 1. Let c(k) be the first derivative of q(k). Let c(b) = 0. What is b?
-3, 0
Suppose -3*o - 8 = -2*o. Let q(g) = -g**2 - 8*g + 3. Let w be q(o). Factor 2 + 1 + d**w - 3*d - 1.
(d - 1)**2*(d + 2)
Let i = 10248/1895 - 3/379. Factor -i*x**3 + 3/5 + 3*x + 9/5*x**2.
-3*(x - 1)*(3*x + 1)**2/5
Let l(d) be the first derivative of d**4/22 + d**3/33 - 2*d - 2. Let a(f) be the first derivative of l(f). Suppose a(k) = 0. What is k?
-1/3, 0
Let z(d) be the second derivative of 1/48*d**4 + 0 + 0*d**2 + 0*d**3 + 4*d + 1/80*d**5. Factor z(x).
x**2*(x + 1)/4
Suppose -3*i + 9 = -0. Factor 2*z**4 + 3*z**3 - i*z**3 - 3*z**2 + z**2.
2*z**2*(z - 1)*(z + 1)
Factor 3 + 106*k**5 + 3*k**3 + 14*k**2 - 9*k**3 - 105*k**5 - k**4 - 11*k.
(k - 1)**4*(k + 3)
Suppose 5*a + 14 = -2*j, 27 = -4*a + 11. Factor -3/4*t**4 + 9/4*t**5 + 0 + 0*t - 3/2*t**j + 0*t**2.
3*t**3*(t - 1)*(3*t + 2)/4
Suppose 5*c = 2*i - 18, 0 = -5*c - 0*c - 10. Suppose -3*x + w = -w - i, -2*w = 5*x - 28. Solve -3*z**5 - 4*z**x - 4*z**3 + z**5 - 2*z**4 = 0.
-2, -1, 0
Let f(j) be the second derivative of 5*j**4/12 - 10*j**3/3 - 25*j**2/2 + 18*j. Factor f(w).
5*(w - 5)*(w + 1)
Let h(v) be the first derivative of 1/4*v**4 + 0*v**3 - 3 - 1/2*v**2 + 0*v. Factor h(p).
p*(p - 1)*(p + 1)
Determine t so that 0 - 2 + 5 + 12*t**2 - 7*t + 19*t = 0.
-1/2
Find a such that -14/5*a**5 - 22/5*a**3 + 4/5*a**2 + 0*a + 32/5*a**4 + 0 = 0.
0, 2/7, 1
Suppose -1/4*l + 0 - 1/4*l**2 = 0. Calculate l.
-1, 0
Let x(j) be the second derivative of -1/2*j**2 + 3*j + 0 - 1/12*j**4 - 1/3*j**3. Solve x(n) = 0 for n.
-1
Let q(z) be the third derivative of z**6/480 - z**4/96 + 2*z**2. Suppose q(k) = 0. What is k?
-1, 0, 1
Factor 1/5*y**4 + 0 - 1/5*y**5 + 11/5*y**2 + 4/5*y + 9/5*y**3.
-y*(y - 4)*(y + 1)**3/5
Let q(f) be the third derivative of -f**6/360 - f**5/60 - f**4/36 + 10*f**2. Factor q(k).
-k*(k + 1)*(k + 2)/3
Let d be (-30)/(-225)*(13 + -3). Suppose -1/3*i**4 + i**2 + 2/3*i**3 - 4/3 - d*i = 0. Calculate i.
-1, 2
Factor 4*a - a + 8 - 2 - 3*a**2.
-3*(a - 2)*(a + 1)
Let g(j) be the first derivative of j**4/14 + 8*j**3/21 + 5*j**2/7 + 4*j/7 - 2. Factor g(f).
2*(f + 1)**2*(f + 2)/7
Let w be (1/((-2)/4))/2. Let l = w + 7/5. Factor -l*z**3 - 1/5*z**4 + 0*z**2 + 2/5*z + 1/5.
-(z - 1)*(z + 1)**3/5
Suppose 23*f + 6*f - 174 = 0. Find q such that -f*q**3 + 0 + 18*q**2 - 18*q + 2/3*q**4 = 0.
0, 3
Let l(s) be the second derivative of -s**8/168 - s**7/105 + s**6/60 + s**5/30 + s**2 - 3*s. Let q(v) be the first derivative of l(v). Factor q(j).
-2*j**2*(j - 1)*(j + 1)**2
Let o(v) be the second derivative of v**7/42 - v**5/10 + v**3/6 - 9*v. Factor o(p).
p*(p - 1)**2*(p + 1)**2
Find t such that -64*t**3 - 8*t - 26*t**4 - 69*t**2 + 25*t**2 - 2*t**4 = 0.
-1, -2/7, 0
Factor -b**3 + 2*b**3 - 3*b**2 - 3*b**2 + 0*b**2.
b**2*(b - 6)
Suppose -2*u = j, -42*u + 46*u - 3*j = 0. Factor u + k**2 - 1/2*k**3 - 1/2*k.
-k*(k - 1)**2/2
Let o = 29 - 29. Let l(g) be the second derivative of -1/15*g**3 + 1/30*g**4 + 0*g**2 + o + g. Su