/2*d**3 + 1/20*d**5 + 2*d. Factor r(l).
(l - 2)*(l + 1)**2
Let h = -81 - -163/2. Factor -1/2*c**2 + 0 + h*c.
-c*(c - 1)/2
Factor -2/11*p**3 + 0*p + 0 + 4/11*p**4 - 2/11*p**5 + 0*p**2.
-2*p**3*(p - 1)**2/11
Let v(b) be the first derivative of -2/3*b - 3 + 2/3*b**4 - 4/3*b**3 - 2/15*b**5 + 4/3*b**2. Factor v(l).
-2*(l - 1)**4/3
Let n(o) be the third derivative of o**7/7 + 5*o**6/24 - 5*o**5/3 - 125*o**4/24 - 5*o**3 - 8*o**2. Find m such that n(m) = 0.
-3/2, -1, -1/3, 2
Let x = -164 + 657/4. Determine a so that -1/2*a**2 + 3/4*a - 1/4 - x*a**5 - 1/2*a**3 + 3/4*a**4 = 0.
-1, 1
Suppose 0 = -d + 4*q - 3*q + 5, 20 = -4*q. Solve -1/2*i + 2*i**2 + d = 0.
0, 1/4
Let c(h) be the third derivative of h**6/45 + h**5/20 - h**4/12 - h**3/2 - 2*h**2. Let s(b) be the first derivative of c(b). Factor s(k).
2*(k + 1)*(4*k - 1)
Let a(n) be the second derivative of n**5/110 - n**4/33 + 36*n. Suppose a(x) = 0. What is x?
0, 2
Let s = 3492/7 - 498. Factor 4/7*w**2 + s*w**3 + 0*w + 2/7*w**4 + 0.
2*w**2*(w + 1)*(w + 2)/7
Let s(d) be the first derivative of d**4/21 - 2*d**3/21 - 4*d**2/7 - 3*d - 1. Let f(n) be the first derivative of s(n). What is p in f(p) = 0?
-1, 2
Let x(a) = -8 + 45*a + a**3 - 16 + 9*a**2 + 5 - 10. Let u(o) = 4*o**2 + 22*o - 14. Let m(n) = 13*u(n) - 6*x(n). Let m(s) = 0. What is s?
-2, 2/3, 1
Let -7*p**2 + 0*p**4 - 4*p**5 + 3*p**4 + p**4 + 4*p**3 + 3*p**2 = 0. Calculate p.
-1, 0, 1
Factor -1/5*t + 2/5 - 1/5*t**2.
-(t - 1)*(t + 2)/5
Let o(c) = -8*c**4 + 2*c**3 + c**2 - 9*c - 7. Let a(s) = -s**4 - s - 1. Let q be 12/(-18) + 11/3. Let n(w) = q*o(w) - 21*a(w). Factor n(r).
-3*r*(r - 2)*(r - 1)*(r + 1)
Let -31/3*u**3 + 0 + 5/3*u**5 + 2*u**2 + 4*u**4 + 8/3*u = 0. What is u?
-4, -2/5, 0, 1
Suppose 1/6*g - 1/3*g**2 + 1/6*g**5 + 1/6 + 1/6*g**4 - 1/3*g**3 = 0. Calculate g.
-1, 1
Let w be 4/15 + 1/3. Solve 3/5*z**2 - 6/5 + w*z = 0 for z.
-2, 1
Solve 75/4*c**5 + 66*c**2 - 165/4*c**4 - 42*c**3 + 12 + 60*c = 0 for c.
-1, -2/5, 2
Let g(z) be the second derivative of 0 - 3*z - 1/6*z**4 + 1/3*z**2 + 1/15*z**5 + 0*z**3. Find p such that g(p) = 0.
-1/2, 1
Suppose -2*w - r = -6*r - 11, -5*r - 20 = -5*w. Let -82 + w*p**2 - 3*p**4 + 82 = 0. What is p?
-1, 0, 1
Let h = -5/16 + 31/48. Let g(d) be the second derivative of -25/21*d**7 + 0*d**3 - 3*d + 8/5*d**5 + 0*d**2 - 2/3*d**4 - h*d**6 + 0. Factor g(b).
-2*b**2*(b + 1)*(5*b - 2)**2
Let i = -2529/5 + 506. Let u = -2/105 + 13/21. Factor i*w**2 + 2/5 + u*w.
(w + 1)*(w + 2)/5
Suppose -7*d + 542 = 514. Factor -1/2 + f**2 + 0*f - 1/2*f**d + 0*f**3.
-(f - 1)**2*(f + 1)**2/2
Let s(q) be the first derivative of 2/3*q**3 - 2*q + 0*q**2 - 1. Determine x so that s(x) = 0.
-1, 1
Factor -1/7*d**3 + 1/7*d + 0 - 4/7*d**4 + 4/7*d**2.
-d*(d - 1)*(d + 1)*(4*d + 1)/7
Let j = 38 + -35. Factor -216*u**4 + 0 + 32/3*u**2 - 96*u**j - 126*u**5 + 32/3*u.
-2*u*(3*u + 2)**3*(7*u - 2)/3
Let m = -7 - -10. Find x, given that -12*x**2 - 4*x - 7 + 1 - m*x**3 - 11*x = 0.
-2, -1
Let x = 151/9 + -913/63. Let 0*l + x - 4/7*l**2 = 0. Calculate l.
-2, 2
Let n(i) be the first derivative of -3*i**5/20 + 3*i**4/4 + i**3/2 - 9*i**2/2 + 6*i - 1. Let v(o) be the first derivative of n(o). Let v(r) = 0. What is r?
-1, 1, 3
Factor 9/4*b - 3/2 - 3/4*b**3 + 0*b**2.
-3*(b - 1)**2*(b + 2)/4
Let t(m) be the second derivative of -m**4/4 + 5*m**3/2 + 27*m. Factor t(a).
-3*a*(a - 5)
Let h = 119 - 224. Let m be (-93)/h - (-9)/(-15). Factor 2/7 - 4/7*l**3 + m*l**5 - 4/7*l**2 + 2/7*l + 2/7*l**4.
2*(l - 1)**2*(l + 1)**3/7
Let j = -14 - -11. Let c be 2/j - 14/(-3). What is n in 0*n**2 - 2/9 + 4/9*n + 2/9*n**c - 4/9*n**3 = 0?
-1, 1
Let r(z) = -3*z**3 - 12*z**2. Let q(t) = 3*t**2 + 2*t**3 + 2*t**3 - 3*t**3. Let l(b) = 9*q(b) + 2*r(b). Solve l(m) = 0.
-1, 0
Suppose -3/5*b + b**2 - 1/5*b**3 - 9/5 = 0. Calculate b.
-1, 3
Suppose z = -0*z - 19. Let f be 8/28 + z/(-7). Let 6*b**f - 2*b**4 + 4*b**4 - 3*b**2 - 2*b**4 - 3*b**4 = 0. What is b?
0, 1
Let u(s) be the second derivative of -s**7/3360 + s**6/720 + s**5/120 + s**4/4 + 4*s. Let m(n) be the third derivative of u(n). What is x in m(x) = 0?
-2/3, 2
Let q(t) be the first derivative of 2/7*t**3 + 0*t - 1/7*t**2 - 3/14*t**4 - 1 + 2/35*t**5. Suppose q(w) = 0. What is w?
0, 1
Let x(a) = -5*a**3 + 13*a**2 - 14*a + 6. Let z(g) = -g**3 + g**2 - g + 1. Let o(r) = 3*x(r) - 6*z(r). Factor o(s).
-3*(s - 2)*(s - 1)*(3*s - 2)
Let g(j) be the first derivative of -j**7/70 - 3*j**6/40 - 3*j**5/20 - j**4/8 - 3*j**2/2 - 2. Let v(p) be the second derivative of g(p). Factor v(d).
-3*d*(d + 1)**3
Solve 4/5*t + 4/5 + 1/5*t**2 = 0 for t.
-2
Let d be ((-70)/(-84))/((-2)/(-12)). Suppose -4*q = q. Factor 1/3*a**d - 1/3*a**2 + q + a**3 + 0*a - a**4.
a**2*(a - 1)**3/3
Let i(l) = -l**3 + 4*l**2 - 1. Let y be i(2). Let k = 9 - y. Factor 2*j**k + 2/5*j**4 - 4/5*j - 8/5*j**3 + 0.
2*j*(j - 2)*(j - 1)**2/5
Let w(g) = 3*g + 2. Let u be w(2). Suppose 0 = 4*i - 5*t - 27, -3*i + u*i = 4*t + 27. Factor 1 + 3*d + i*d**2 + 0 + 0 + 0*d + d**3.
(d + 1)**3
Let o = 7 + -5. Factor -4*f + 3*f - 5 + o - f**2 - 3*f.
-(f + 1)*(f + 3)
Suppose 0 = 5*j - 4*j - 4. Factor -3*t + 11*t**2 - t**3 + 2 + j*t**3 + 1 - 14*t**2.
3*(t - 1)**2*(t + 1)
Suppose -d - 2208 = -7*d. Let t = d - 224. Let -81*f**4 - t*f**2 + 243*f**3 + 69/2*f - 3 - 243/2*f**5 = 0. What is f?
-2, 1/3
Let i(t) be the first derivative of -2*t**4/3 - 4*t**3/9 - t**2/9 + 5*t - 1. Let g(o) be the first derivative of i(o). Factor g(l).
-2*(6*l + 1)**2/9
Let a = 3/32 - -17/160. Suppose a*l**3 - 1/5*l + 1/5 - 1/5*l**2 = 0. What is l?
-1, 1
Let m(v) = -v**2 + 7*v - 4. Let s be m(6). Let -33*c**4 + 5*c**5 + 5*c**5 + 8*c**s + 8*c**3 + 7*c**4 = 0. What is c?
-2/5, 0, 1, 2
Let n(b) be the second derivative of 0 + 1/18*b**4 - 3*b + 4/3*b**2 + 4/9*b**3. Suppose n(x) = 0. Calculate x.
-2
Let d(i) be the third derivative of 27*i**7/70 + 3*i**6/10 + i**5/15 - 11*i**2. Suppose d(j) = 0. Calculate j.
-2/9, 0
Let f(v) be the first derivative of -v**3 + 24*v**2 - 192*v + 4. Factor f(m).
-3*(m - 8)**2
Let p = -46 + 51. Let c(d) be the first derivative of 1/18*d**6 - 1/12*d**4 + 0*d**2 - 4 + 1/15*d**p + 0*d - 1/9*d**3. Factor c(h).
h**2*(h - 1)*(h + 1)**2/3
Let j(v) be the second derivative of 1/8*v**2 + 1/48*v**4 + 0 - 1/12*v**3 - v. Suppose j(p) = 0. Calculate p.
1
What is l in 0 + 2/13*l**5 - 4/13*l**3 + 0*l**4 + 0*l**2 + 2/13*l = 0?
-1, 0, 1
Factor 4*n**2 + 2*n**4 + 166 - 6*n**3 - 166.
2*n**2*(n - 2)*(n - 1)
Let o be 1 - (-5)/(-10) - (-85)/34. Suppose 3/4*z**4 + 3/4 - 3/2*z**2 + 0*z**o + 0*z = 0. Calculate z.
-1, 1
Let n be 0*-2*(-3)/(-12). Suppose 2*g - 3*g + 2 = n. Factor 20*r**2 + 3 + g*r - 4 - 3.
2*(2*r + 1)*(5*r - 2)
Let v(c) be the second derivative of 1/10*c**6 + 0 + 5*c + 0*c**3 + 1/5*c**5 + 0*c**2 + 1/12*c**4. Solve v(d) = 0.
-1, -1/3, 0
Let n(s) = -5*s**5 + 11*s**3 + 11*s**2 + 11*s - 11. Let h(u) = u**5 - 2*u**3 - 2*u**2 - 2*u + 2. Let m(c) = -33*h(c) - 6*n(c). Determine k, given that m(k) = 0.
0
Let s(q) be the first derivative of -q**5 - 15*q**4/2 - 65*q**3/3 - 30*q**2 - 20*q - 28. Factor s(x).
-5*(x + 1)**2*(x + 2)**2
Let h(y) be the second derivative of 0 + 0*y**2 - 1/66*y**4 + 5*y - 1/33*y**3. Let h(m) = 0. What is m?
-1, 0
Let d be (-156)/(-45) - ((-24)/15)/(-2). Factor d*k + 2/3*k**2 + 8/3.
2*(k + 2)**2/3
Let l = -2/125 + 264/875. Factor -l*i**3 - 4/7*i**2 - 2/7*i + 0.
-2*i*(i + 1)**2/7
Let i(k) be the second derivative of 7/18*k**3 + 0 + 1/3*k**2 - 3*k - 1/9*k**4. Let i(g) = 0. What is g?
-1/4, 2
Let w(b) = -b**3 - 3*b**2 - 6*b. Let n(h) = -h**3 - 2*h**2 - 6*h. Let p(v) = -4*n(v) + 5*w(v). Let y be p(-6). Factor 0*d**2 + 0 + y*d - 2/5*d**4 - 2/5*d**3.
-2*d**3*(d + 1)/5
Let f(h) be the second derivative of -h**4/12 + h**3/3 - h**2/2 - 3*h. Suppose f(o) = 0. Calculate o.
1
Let o(w) be the first derivative of w**6/24 - 17. Determine a, given that o(a) = 0.
0
Let t(q) be the third derivative of -q**5/90 - 5*q**4/36 - 4*q**3/9 - 6*q**2. What is s in t(s) = 0?
-4, -1
Let u = -166 + 500/3. Solve -16/3*i**2 + 0*i + u*i**4 + 32/3 + 0*i**3 = 0 for i.
-2, 2
Let v(d) be the first derivative of -7*d**6/75 - d**5/25 + d + 4. Let q(i) be the first derivative of v(i). Solve q(b) = 0 for b.
-2/7, 0
Let k(r) = -6*r**5 + 18*r**4 - 11*r**3 + 13*r**2 - 7*r - 7. Let i(y) = 2*y**5 - 6*y**4 + 4*y**3 - 4*y**2 + 2*y + 2. Let s(w) = -14*i(w) - 4*k(w).