tive of 1/20*t**5 + 1/90*t**x + 0*t**2 + 1/18*t**3 + 1/12*t**4 + 2*t + 0. Solve z(p) = 0 for p.
-1, 0
Factor q**4 + q**2 + 5*q**4 - 5*q**4 + 10*q**3 - 8*q**3.
q**2*(q + 1)**2
Suppose 0 = -4*o - 2*o + 24. Let r(g) be the third derivative of 0*g - 1/420*g**6 - g**2 + 0*g**5 + 0*g**3 + 0 + 0*g**o. Factor r(k).
-2*k**3/7
Let m(w) = 3*w**2 + 16*w - 27. Let g(i) = i**2 + 1. Let l(x) = 5*g(x) - m(x). Factor l(y).
2*(y - 4)**2
Let z(y) be the first derivative of -y**5/40 - y**4/24 + 4*y - 6. Let c(d) be the first derivative of z(d). Factor c(p).
-p**2*(p + 1)/2
Suppose 5*z - v - 10 = 4*z, 4*z - 67 = -5*v. Let g = 17 - z. Find p such that -2/9*p**g + 2/9*p**2 + 0 - 2/9*p + 2/9*p**3 = 0.
-1, 0, 1
Factor -3*b - 3 - 3/4*b**2.
-3*(b + 2)**2/4
Let i be 10/(-175)*(-2 - 3). Let g(z) be the first derivative of -32/35*z**5 - i*z - 10/7*z**2 - 20/7*z**4 - 22/7*z**3 + 2. Factor g(s).
-2*(s + 1)**2*(4*s + 1)**2/7
Let g(d) be the second derivative of d**6/150 - d**5/20 + d**4/10 + 2*d**3/15 - 4*d**2/5 + d. Find s, given that g(s) = 0.
-1, 2
Let n(y) = y**2 + y - 2. Let k(b) = -6*b**2 - 6*b + 11. Let a(u) = -2*k(u) - 11*n(u). Factor a(t).
t*(t + 1)
Let o(b) be the third derivative of b**8/504 + b**7/45 + b**6/12 + b**5/10 - 56*b**2 + 1. Factor o(q).
2*q**2*(q + 1)*(q + 3)**2/3
Factor -2/11*v**4 + 0 + 2/11*v**2 + 2/11*v**3 - 2/11*v.
-2*v*(v - 1)**2*(v + 1)/11
What is i in -1/3*i**3 + i**2 - i + 1/3 = 0?
1
Let n be (12/(-14))/((-6)/42). Let k(f) = f**3 - 6*f**2 - 2*f + 14. Let g be k(n). Factor -2/5*q**g - 4/5*q + 0.
-2*q*(q + 2)/5
Let g = 8/211 + 33111/422. Let b = 388 + -753/2. Determine k, given that -k + 0 - b*k**2 - 47*k**3 - g*k**4 - 42*k**5 = 0.
-1, -1/3, -2/7, -1/4, 0
Suppose 4*z - 1 = -2*q - 3, 2*q + 2*z - 4 = 0. Let d be (-3)/(-4)*(-1 + q). Let d*h**4 - 2*h**4 + h**4 - 2*h**2 = 0. Calculate h.
-1, 0, 1
Find b such that -4*b**2 - 13/5*b - 2/5 - 9/5*b**3 = 0.
-1, -2/9
Let t(n) = -n**3 + 5*n**2 + n - 3. Let c be t(5). Let d(b) be the first derivative of c + 0*b + 4/15*b**3 + 0*b**2 - 1/10*b**4. Factor d(s).
-2*s**2*(s - 2)/5
Let c(v) = 2*v**2 - 8*v. Let q(s) = -2*s**2 + 8*s. Let a(p) = -5*c(p) - 6*q(p). Suppose a(i) = 0. What is i?
0, 4
Let f be -2*39/6 + 3. Let d be (-4 - -2)*f/55. Factor d*q**2 + 2/11*q**3 - 4/11 - 2/11*q.
2*(q - 1)*(q + 1)*(q + 2)/11
Suppose 5*s + 3*b - 6 = b, -3*s + 2 = 2*b. Suppose -3*q - s*q + 60 = 0. Factor -2*x**4 + 4*x + 8*x**3 - 2 - 5*x - q*x**2 + 9*x.
-2*(x - 1)**4
Let i(v) be the third derivative of v**6/20 - 4*v**5/15 + v**4/4 + 2*v**3/3 + 9*v**2. Suppose i(w) = 0. What is w?
-1/3, 1, 2
Let a = -4 - -11. Let q = a + -7. Suppose q*b + 2/5*b**2 + 0 + 2/5*b**3 = 0. What is b?
-1, 0
Let m(l) be the third derivative of -l**4/24 - l**3/6 + l**2. Let h be m(-6). Solve h*o - 4*o + 0*o**2 - o**2 = 0.
0, 1
Let t be (-2 - 17/(-3))*-1 - -4. Factor -h**3 + 2/3*h + 0 + 1/3*h**5 + t*h**4 - 1/3*h**2.
h*(h - 1)**2*(h + 1)*(h + 2)/3
Let x(z) be the first derivative of -6*z**3/19 - 3*z**2/19 + 4*z/19 + 6. Factor x(a).
-2*(3*a - 1)*(3*a + 2)/19
Let t(n) be the third derivative of 5*n**8/336 - n**7/21 + n**5/6 - 5*n**4/24 - 9*n**2 - 2. Factor t(i).
5*i*(i - 1)**3*(i + 1)
Let w(p) be the first derivative of -3/7*p**3 + 7 + 0*p - 3/7*p**2 + 3/14*p**4. Factor w(k).
3*k*(k - 2)*(2*k + 1)/7
Suppose 2*k + 2*b = 4, 0*k - 5 = 5*k + 2*b. Let i(h) = -3*h**3 - h**2 - h + 1. Let n(x) = -2*x**3 - x**2 - x + 1. Let z(o) = k*i(o) + 4*n(o). Factor z(y).
(y - 1)**2*(y + 1)
What is o in -4/3 + 10/9*o**2 + 26/9*o = 0?
-3, 2/5
Let c(r) be the third derivative of 0*r + 1/30*r**5 + 6*r**2 - 1/3*r**3 + 1/60*r**6 + 0 - 1/12*r**4. Suppose c(b) = 0. Calculate b.
-1, 1
Let g(h) be the second derivative of -h**5/120 + h**4/24 + h**3/36 - h**2/4 - 10*h. Factor g(n).
-(n - 3)*(n - 1)*(n + 1)/6
Let d = 180/7 + -893/35. Factor -3/5*m - 2/5 - d*m**2.
-(m + 1)*(m + 2)/5
Factor 2 + 2 + 2*t**3 - 18*t + 12*t.
2*(t - 1)**2*(t + 2)
Let m be (-549)/(-108) - (-5)/(-1). Let r(v) be the second derivative of -1/12*v**4 - 3*v + m*v**3 + 1/2*v**2 - 1/40*v**5 + 0. Solve r(d) = 0 for d.
-2, -1, 1
Let a be (-86)/(-110) - (-7 - 79/(-11)). Determine k, given that 0 - 1/5*k**5 + a*k**4 + 0*k + 0*k**2 - 2/5*k**3 = 0.
0, 1, 2
Let d(l) be the first derivative of 1 + 0*l**2 - 3/2*l**4 + 0*l + 2/3*l**3 + 6/5*l**5 - 1/3*l**6. Factor d(r).
-2*r**2*(r - 1)**3
Let t(b) = b**3 - 4*b**2 - 2*b - 11. Let c be t(5). Factor -v**3 - 10 - 3 - c*v + 5*v**3 + 8*v**2 + 5.
4*(v - 1)*(v + 1)*(v + 2)
Let s = 7/106 + 39/212. Determine t, given that 1/4*t - 1/2 + s*t**2 = 0.
-2, 1
Let p(j) = -2*j**2 + 5*j + 1. Let z(s) = s**2 - s. Let y(m) = -p(m) - 3*z(m). Factor y(u).
-(u + 1)**2
Factor -1/4*v**2 + 1/4 + 0*v.
-(v - 1)*(v + 1)/4
Let r(b) be the first derivative of -8*b - 2/3*b**3 + 1 + 4*b**2. Determine o so that r(o) = 0.
2
Let n = 236/5 + -47. Let i(x) be the second derivative of 1/3*x**7 + 0 + 0*x**3 + x + 0*x**4 + n*x**5 + 3/5*x**6 + 0*x**2. What is u in i(u) = 0?
-1, -2/7, 0
Let o(u) = -2*u - 10. Let p be o(-5). Let h(a) be the third derivative of a**2 - 1/180*a**5 + 0*a**3 + 0*a**4 + 0 + p*a. Let h(y) = 0. Calculate y.
0
Let u = -759 - -761. Suppose 1/3*h**3 + h**u + 2/3*h + 0 = 0. What is h?
-2, -1, 0
Let u(v) be the first derivative of 1/60*v**6 + 0*v - 1/12*v**4 + 0*v**3 - 3 - 3/2*v**2 + 0*v**5. Let i(s) be the second derivative of u(s). Factor i(q).
2*q*(q - 1)*(q + 1)
Let r = 11 - 33. Let h = 156/7 + r. Factor h*k - 2/7*k**2 + 4/7.
-2*(k - 2)*(k + 1)/7
Suppose 3*o = 4 - 52. Let v be (9/108)/((-6)/o). Let v*b + 0*b**2 + 0 - 2/9*b**3 = 0. What is b?
-1, 0, 1
Let w(y) = -y + 1. Let m(z) = 2*z**3 - 6*z**2 + 4*z. Let c(d) = m(d) - 2*w(d). Solve c(b) = 0 for b.
1
Let k(v) be the first derivative of -v**5 + 20*v**3/3 - 13. Factor k(i).
-5*i**2*(i - 2)*(i + 2)
Let d(j) = -20*j - 16. Let n be d(-1). Let 8/5*q**n - 12/5*q**2 + 0 + 8/5*q - 12/5*q**3 = 0. What is q?
-1, 0, 1/2, 2
Let m(w) be the first derivative of w**4/36 + 4*w**3/27 + w**2/6 + 11. Factor m(k).
k*(k + 1)*(k + 3)/9
Let y(n) be the second derivative of n**7/840 - n**6/240 + n**4/48 - n**3/24 - n**2/2 - 3*n. Let d(c) be the first derivative of y(c). Factor d(r).
(r - 1)**3*(r + 1)/4
Suppose 0*p - 2*p = 0. Let n(k) be the first derivative of 1/3*k**6 + 0*k**2 + 1 - 2/5*k**5 + 0*k**4 + p*k**3 + 0*k. Solve n(u) = 0 for u.
0, 1
Let r(o) be the third derivative of -o**6/360 - o**5/120 + o**4/12 + o**3/6 + o**2. Let y(z) be the first derivative of r(z). Suppose y(g) = 0. Calculate g.
-2, 1
Suppose -2*w = -k - 20, w + 8 - 28 = -2*k. Let r = 15 - w. Solve 2/3*u**5 + 4/3*u**r - 2/3 - 2*u + 2*u**4 - 4/3*u**2 = 0 for u.
-1, 1
Let i(r) be the third derivative of r**8/80640 - r**7/10080 + r**6/2880 + r**5/30 + r**2. Let l(s) be the third derivative of i(s). Factor l(b).
(b - 1)**2/4
Let t be (-10)/(-4)*(-36)/(-45). Let o be 2/(-3) - (t - 3). Factor 0*l - 4/3 + l**2 + o*l**3.
(l - 1)*(l + 2)**2/3
Let i = -50 - -50. Let b(c) be the third derivative of 4/5*c**5 - 7/40*c**6 - 3*c**2 + 0*c + c**3 - 11/8*c**4 + i. Factor b(d).
-3*(d - 1)**2*(7*d - 2)
Let r(i) be the second derivative of -i**6/50 - 3*i**5/100 + i**4/20 + i**3/10 - 18*i. Factor r(v).
-3*v*(v - 1)*(v + 1)**2/5
Let s(q) be the first derivative of 0*q**5 - 1/30*q**4 - 2*q + 0*q**2 + 1/75*q**6 + 3 + 0*q**3. Let i(p) be the first derivative of s(p). Factor i(j).
2*j**2*(j - 1)*(j + 1)/5
Suppose 0 = 2*t - t - 1. Let r be t/2 - (-17)/2. Factor -2*n - 13*n**3 - 2 + r*n**2 + 3*n + 5*n**4 + 0*n**3.
(n - 1)**3*(5*n + 2)
Let a be -2 + (-3 - 51/(-6)). Suppose 0 = -8*u + 6*u. Factor a*o**2 + u - o - 5/2*o**3.
-o*(o - 1)*(5*o - 2)/2
Suppose -5*g - 14 = h, -g + 8 = 2*h - 0. Factor -3*o**2 + h*o**2 - 3*o**2 - o**3.
-o**3
Let m = 262 + -7859/30. Let n(y) be the second derivative of -1/9*y**4 - 1/18*y**3 - m*y**5 + 1/42*y**7 + 2/45*y**6 + y + 0*y**2 + 0. Solve n(v) = 0.
-1, -1/3, 0, 1
Let d(b) be the first derivative of -2*b**6/15 - b**5/5 + b**4/3 + 2*b**3/3 + 5*b + 8. Let n(z) be the first derivative of d(z). Factor n(s).
-4*s*(s - 1)*(s + 1)**2
Let k = -4 - -20. Suppose -2*r + n = -n - 6, -3*r - 4*n + k = 0. Solve -2/7*t**r + 2/7*t**2 + 0 + 6/7*t**5 - 10/7*t**3 + 4/7*t = 0.
-1, -2/3, 0, 1
Let d be (-2)/(-3) - 12/18. Let c(h) = h**2 + 3 - 4 + d*h**2 + 0*h**2. Let k(y) = y**2 - 1. Let v(r) = 5*c(r) - 3*k(r). Factor v(a).
2*(a - 1