*c*(3*c - 1)/3
Let x(a) be the first derivative of -a**4/12 + 2*a**3/9 - a**2/6 - 10. Factor x(z).
-z*(z - 1)**2/3
Suppose -l - 25 = -2*r, -4*r + 2*l + 28 = -2*r. Let z = 13 - r. Suppose -u**3 - 1/3*u**4 - 1/3*u - u**z + 0 = 0. What is u?
-1, 0
Let w(i) be the second derivative of -3*i**5/140 + 5*i**4/28 - i**3/2 + 9*i**2/14 + 14*i. Factor w(x).
-3*(x - 3)*(x - 1)**2/7
Let t(l) = l**3 - 5*l**2 + l. Let j = -7 - -4. Let i(b) = 4*b**2 - 2*b. Let p(q) = j*i(q) - 2*t(q). Find h such that p(h) = 0.
-2, 0, 1
Let j(z) be the first derivative of -2/39*z**3 - 1/26*z**4 + 2 + 0*z + 0*z**2. Suppose j(b) = 0. What is b?
-1, 0
Suppose 2*z - 6 = 5*f + 15, 3*z + f + 11 = 0. Let i be (-4 - -7)/((-9)/z). Factor i + 0*y**2 - y + 1/3*y**3.
(y - 1)**2*(y + 2)/3
Factor 6/7*i**3 + 2/7*i**4 + 4/7*i**2 + 0*i + 0.
2*i**2*(i + 1)*(i + 2)/7
Let n(y) = -3*y + 9. Let b be n(3). Let m(r) be the second derivative of 0 + 0*r**3 - 1/12*r**7 - r - 1/20*r**5 + 3/20*r**6 + 0*r**2 + b*r**4. Factor m(h).
-h**3*(h - 1)*(7*h - 2)/2
Let j(k) = k**5 - 2*k**4 - k**3 + k**2 + k + 1. Let b(y) = -y**4 + y + 1. Let c be 5*(2 + 1 + -2). Suppose -c + 4 = -g. Let i(t) = g*j(t) - b(t). Factor i(w).
w**2*(w - 1)**2*(w + 1)
Let q = -255/7 - -2777/77. Let d = q - -41/22. Determine r, given that -1/2*r + 1/2*r**3 - 5/2*r**2 + 1 + d*r**4 = 0.
-1, 2/3, 1
Solve -25*i**4 + 66*i**2 - 600*i**2 - 924*i - 415*i**2 + 330*i**3 - 196 = 0.
-2/5, 7
Let d(x) be the second derivative of -x**6/20 + 9*x**5/20 - 13*x**4/8 + 3*x**3 - 3*x**2 - 13*x. Suppose d(j) = 0. Calculate j.
1, 2
Let x(c) = 8*c**4 - 80*c**3 - 54*c**2 - 18*c. Let f(y) = y**4 - 9*y**3 - 6*y**2 - 2*y. Let d(p) = -52*f(p) + 6*x(p). Factor d(a).
-4*a*(a + 1)**3
Let n(h) = 13*h**2 + 80*h + 73. Let x(v) = -6*v**2 - 40*v - 37. Let z(p) = 6*n(p) + 11*x(p). Let o(k) = -k - 1. Let g(i) = 4*o(i) + z(i). Factor g(j).
3*(2*j + 3)**2
Let g = -7 - -12. Let k be -2 + -1*8/(-3). Solve 0 + 4/3*r**2 + k*r**g - 2/3*r - 4/3*r**4 + 0*r**3 = 0.
-1, 0, 1
Factor 4/3 - 4/3*u**3 - 10/3*u**2 - 2/3*u.
-2*(u + 1)*(u + 2)*(2*u - 1)/3
Let i(h) be the second derivative of -h**7/273 + h**5/65 - h**3/39 - 2*h. Suppose i(m) = 0. What is m?
-1, 0, 1
Suppose -5*a + 18 = 3*l, -3*a + 26*l - 29*l + 6 = 0. What is b in -26/7*b**4 - 8/7 + a*b**5 - 66/7*b**3 + 34/7*b**2 + 24/7*b = 0?
-1, -2/3, 2/7, 1
Let p(l) = -l**3 - 2. Let s(v) = -v**3 - 1. Let o(d) = -5*p(d) + 8*s(d). Let g(k) = 14*k**3 + k**2 - 11. Let c(u) = 2*g(u) + 11*o(u). Factor c(b).
-b**2*(5*b - 2)
Let a = -9 - -8. Let l = a - -6. What is u in 7/5*u**3 + 3/5*u**l + 2/5*u**2 + 0 + 0*u + 8/5*u**4 = 0?
-1, -2/3, 0
Find t such that -3/8*t**4 + 1/2*t**2 + 0*t - 1/8*t**5 + 0 + 0*t**3 = 0.
-2, 0, 1
Factor 2*o**2 + 3*o + 0 + 0 - 5*o**2 + 6.
-3*(o - 2)*(o + 1)
Suppose -27 + 33 = 3*h. Factor 4/7 - 6/7*k + 2/7*k**h.
2*(k - 2)*(k - 1)/7
Let x(r) be the second derivative of 1/2*r**3 - 1/4*r**4 + 3*r**2 - r + 0. Solve x(m) = 0.
-1, 2
Let o(h) be the first derivative of 2*h**3/33 + h**2/11 - 4*h/11 - 2. Let o(n) = 0. Calculate n.
-2, 1
Let z(s) be the third derivative of s**6/24 - 5*s**4/8 + 5*s**3/3 + 12*s**2. Factor z(r).
5*(r - 1)**2*(r + 2)
Let n(j) be the first derivative of -3*j**4/8 + 3*j**3/2 - 6*j + 1. Factor n(g).
-3*(g - 2)**2*(g + 1)/2
Let i(s) = 35*s**2 + 5*s. Let a(j) = 9*j**2 + j. Let n(p) = 25*a(p) - 6*i(p). Factor n(l).
5*l*(3*l - 1)
Suppose -4*z = -z. Suppose -3*k + 2*n + 22 = 0, k + z*n + 4*n = -16. Solve 0 + 1/2*i + 3/4*i**k - 1/4*i**2 - i**3 = 0 for i.
-2/3, 0, 1
Let l be (-110)/(-50) - -2*(-2)/20. Solve 12/5*p - 48/5*p**l + 0 + 15*p**4 + 3*p**3 = 0.
-1, 0, 2/5
Let i(c) = -7*c**2 + 10*c - 13. Let p(q) = 4*q**2 - 5*q + 7. Let l(n) = 3*i(n) + 5*p(n). Suppose l(u) = 0. Calculate u.
1, 4
Let f(p) be the third derivative of -2*p**7/105 + p**6/30 + p**5/5 - p**4/6 - 4*p**3/3 + p**2. What is g in f(g) = 0?
-1, 1, 2
Let w = 7 - 7. Factor 3/4*h**3 + 1/4*h**4 + w + 1/4*h + 3/4*h**2.
h*(h + 1)**3/4
Let r(k) be the third derivative of k**6/720 + k**5/240 - 7*k**3/6 - 5*k**2. Let i(p) be the first derivative of r(p). Factor i(g).
g*(g + 1)/2
Let f(g) = -g**2 + 3*g - 1. Let y be f(3). Let q be (-1)/5*1*y. Find o, given that -q*o**2 + 0 - 1/5*o**4 + 2/5*o**3 + 0*o = 0.
0, 1
Let l = 23 - 19. Let p = 11 + -6. Factor 2*a + l*a**2 + 0*a**4 + 0*a**4 + 0*a - 2*a**p - 4*a**4.
-2*a*(a - 1)*(a + 1)**3
Let y(g) = g**2 + 8*g + 2. Let o be y(-8). Find p, given that 8*p - o - 2*p**2 + 0 - 5*p**2 - p**2 = 0.
1/2
Let k(r) be the third derivative of 0 + 0*r**3 - r**2 + 1/735*r**7 + 0*r - 1/420*r**6 + 1/84*r**4 - 1/210*r**5. Factor k(i).
2*i*(i - 1)**2*(i + 1)/7
Let r(q) = 6*q + 1. Let m be r(2). Suppose 4*o - m = 3. Factor -2 - 2*l**5 - 2*l**o + 7*l**2 + 4*l**3 + l - 3*l**2 - 3*l.
-2*(l - 1)**2*(l + 1)**3
Let n(s) be the second derivative of -1/21*s**3 - s + 1/21*s**4 + 1/70*s**5 + 0 + 0*s**2 - 2/105*s**6. Find f such that n(f) = 0.
-1, 0, 1/2, 1
Let k(l) = 5*l**2 - l - 2. Let j(a) = 6*a**2 - 3. Let s(x) = 2*j(x) - 3*k(x). Factor s(t).
-3*t*(t - 1)
Let z = 4 + -7/2. Let s(f) be the second derivative of -2*f + z*f**4 + 1/30*f**6 + 0 + 2/3*f**3 + 1/5*f**5 + 1/2*f**2. What is t in s(t) = 0?
-1
Let f(y) = -13*y**2 - 11*y + 5. Let q(o) = -7*o**2 - 5*o + 3. Let g(p) = 3*f(p) - 5*q(p). Solve g(z) = 0 for z.
-2, 0
Let u(h) be the third derivative of -1/160*h**6 - 1/48*h**5 + 1/840*h**7 - 2*h**2 + 0*h**3 + 0 - 1/48*h**4 + 0*h + 1/1344*h**8. Factor u(j).
j*(j - 2)*(j + 1)**3/4
Determine c, given that -188*c**4 + 368*c**4 + 2*c**3 - 2*c - 179*c**4 - 1 = 0.
-1, 1
Let k(p) = -2*p + 1. Let g be k(-1). Factor -4*v**g - 2*v**2 - 3*v**3 + v + 3*v**5 + 2*v**4 + 0*v**2 + 3*v**3.
v*(v - 1)*(v + 1)**2*(3*v - 1)
Solve -32/5*w**3 - 72/5*w + 0 - 4/5*w**4 - 84/5*w**2 = 0.
-3, -2, 0
Let o = 414/721 - 2/721. Let n = -3 - -6. Factor o*y**n - 4/7*y - 2/7*y**4 + 2/7*y**2 + 0.
-2*y*(y - 2)*(y - 1)*(y + 1)/7
Let v(s) be the third derivative of 9*s**8/112 - s**7/35 - 9*s**6/20 + s**5/5 + 9*s**4/8 - s**3 - 6*s**2. Suppose v(x) = 0. Calculate x.
-1, 2/9, 1
Suppose 17 = -11*c + 15*c - b, -5*b - 16 = 3*c. Let 0*d**c + 0 + 0*d - 3/4*d**4 - 3/4*d**5 + 0*d**2 = 0. Calculate d.
-1, 0
Let i = -183 - -1283/7. Factor -2/7*a**3 + 0 + i*a**2 + 4/7*a.
-2*a*(a - 2)*(a + 1)/7
Let i(g) be the second derivative of g**6/90 - g**5/15 + g**4/9 - g. Find t such that i(t) = 0.
0, 2
Let x = 3881/20 - 194. Let b(m) be the first derivative of -1/4*m + 1/6*m**3 - 3/8*m**2 + 1 - x*m**5 + 3/8*m**4 - 1/8*m**6. Let b(c) = 0. Calculate c.
-1, -1/3, 1
Let b = -2 + 2. Suppose -t - 17 = -3*f, b = -f + t - 6*t - 21. Factor 1/3*p**f + 0*p + 1/3*p**5 + 0*p**2 + 0*p**3 + 0.
p**4*(p + 1)/3
Let p(y) = -y**2 + 1. Let n be p(1). Let u(o) be the third derivative of 3*o**2 + 0 + n*o + 0*o**3 + 0*o**5 + 0*o**4 - 1/240*o**6. Factor u(z).
-z**3/2
Factor 5/2*y**4 + 15/2*y**2 + 0*y + 10*y**3 + 0.
5*y**2*(y + 1)*(y + 3)/2
Let b(c) be the third derivative of c**9/45360 - c**7/7560 - c**4/6 + c**2. Let h(g) be the second derivative of b(g). Factor h(j).
j**2*(j - 1)*(j + 1)/3
Let g(j) = 22*j**3 + j**2 - j + 1. Let b be g(1). Suppose b = 5*o + 3. Factor 0*s - 1/2*s**o + 0*s**3 + s**2 - 1/2.
-(s - 1)**2*(s + 1)**2/2
Let w(y) = y**3 + y + 1. Let o(i) = -9*i**3 - 3*i**2 - 11*i - 9. Let u = 24 + -48. Let q(x) = u*w(x) - 3*o(x). Suppose q(c) = 0. Calculate c.
-1
Let y(s) be the first derivative of -s**8/5880 - s**7/2940 + s**6/1260 + s**5/420 - 2*s**3/3 - 3. Let x(c) be the third derivative of y(c). Factor x(i).
-2*i*(i - 1)*(i + 1)**2/7
Let p(w) be the second derivative of -w**8/5600 - w**7/1260 - w**6/1800 + w**5/300 + w**4/6 + 4*w. Let j(z) be the third derivative of p(z). Solve j(i) = 0.
-1, 1/3
Let g(a) be the third derivative of a**7/2310 + a**6/1320 - a**5/132 + a**4/88 + 4*a**2. Suppose g(z) = 0. What is z?
-3, 0, 1
Let a = 22 - 17. Let s(u) be the first derivative of 1/6*u**6 - 1/2*u**2 + 2 + 0*u**4 + 2/3*u**3 - 2/5*u**a + 0*u. Factor s(b).
b*(b - 1)**3*(b + 1)
Let v(u) = -12*u**4 + 24*u**3 - 24*u + 26. Let g(l) = 4*l**4 - 8*l**3 + 8*l - 9. Let r(i) = -14*g(i) - 5*v(i). Factor r(n).
4*(n - 1)**3*(n + 1)
Let z = -172/7 + 565/21. Factor -5/3*g**2 + z*g - 2/3.
-(g - 1)*(5*g - 2)/3
Let r be (-42)/(-4) - 7/(-14). Let -r*z + 9*z + 6*z - 4*z**2 = 0. Calculate z.
0, 1
Let h(l) be the third derivative of l**5/15 - l**4/6 - 7*l**2. Factor