e c(-6). What is r in 32/3*r**3 + 8/3*r**q + 14*r**4 + 0 + 6*r**5 + 0*r = 0?
-1, -2/3, 0
Find o such that -1/6*o**3 + 1/6*o**5 + 0*o - 1/6*o**2 + 1/6*o**4 + 0 = 0.
-1, 0, 1
Let k(m) = -3*m - 6. Let i be k(-3). Suppose i*u = u. Factor -1/5*g**4 - 1/5*g**3 + 1/5*g + 1/5*g**2 + u.
-g*(g - 1)*(g + 1)**2/5
Let y(a) be the first derivative of -1/3*a**3 + 3 + 3*a**2 - 9*a. Factor y(z).
-(z - 3)**2
Suppose 12 = 2*d + d. Let b = -2 + d. Factor -1/2*n**4 + 3/2*n**3 - n**b + 0*n + 0.
-n**2*(n - 2)*(n - 1)/2
Let i be (-8)/40 + (-13)/(-60). Let c(o) be the third derivative of 0*o**3 + i*o**5 + 0*o + 0 - 1/30*o**6 - 1/168*o**8 + 1/42*o**7 + o**2 + 0*o**4. Factor c(k).
-k**2*(k - 1)**2*(2*k - 1)
Let z(n) = n**2 - 13*n + 15. Let a be z(13). Let x be (-2)/a*(-100)/15. Factor -8/3*h + 14/9*h**2 - x.
2*(h - 2)*(7*h + 2)/9
Let f(p) be the first derivative of p**5/5 - p**4/2 + p**3/3 + 15. Factor f(x).
x**2*(x - 1)**2
Let u(m) be the third derivative of m**6/1440 + m**5/80 + 3*m**4/32 + m**3/2 + 4*m**2. Let r(i) be the first derivative of u(i). Suppose r(n) = 0. Calculate n.
-3
Let w(i) be the third derivative of i**6/420 - i**4/28 + 2*i**3/21 - 12*i**2. Factor w(j).
2*(j - 1)**2*(j + 2)/7
Let u(r) be the third derivative of -3*r**2 + 0 + 1/3*r**3 - 1/30*r**5 + 0*r + 0*r**4. Find l such that u(l) = 0.
-1, 1
Determine b, given that -10/9*b**3 - 2/9*b**4 + 0 - 16/9*b**2 - 8/9*b = 0.
-2, -1, 0
Suppose -d = -0 - 4. Let b(l) = -10*l**2 - 6*l - 1. Let y(o) = 11*o + 10*o**2 - 8*o + 3*o. Let k(u) = d*b(u) + 5*y(u). Factor k(r).
2*(r + 1)*(5*r - 2)
Let c(q) = -q - 14. Let g be c(-12). Let n be 0 + 1/((-5)/g). Factor 0*j + 2/5*j**2 - n.
2*(j - 1)*(j + 1)/5
Let w(c) be the second derivative of c**6/15 + c**5/5 - c**4/6 - 2*c**3/3 + 6*c. Factor w(g).
2*g*(g - 1)*(g + 1)*(g + 2)
Let c(s) = -9*s**4 - 21*s**3 - 3*s**2 - 9*s + 9. Let i(n) = 5*n**4 + 10*n**3 + n**2 + 4*n - 4. Let z(t) = 4*c(t) + 9*i(t). Solve z(x) = 0.
-1, 0, 1/3
Suppose -3*m + 6*m = 12. Let c be m - (14/6 + 1). Factor 0 + 2/3*k**3 + 0*k + c*k**2.
2*k**2*(k + 1)/3
Suppose -x + 3 = 2, -3*o = 2*x - 17. Let l be (12/15)/(2/o). Determine s, given that 0 + 0*s - 7*s**5 + 15/4*s**4 - 1/2*s**3 + 0*s**l = 0.
0, 1/4, 2/7
Suppose 0 = -l - 12 + 14. Factor -m**3 + 9*m**l + 4*m**3 - 12 + 2*m - 2*m.
3*(m - 1)*(m + 2)**2
Let k be (4 - 1) + 1 + 0. Let u(c) = -2*c**3 + 8*c**3 - k*c**4 + 2*c**4 + 2*c**5 + 6*c**4. Let i(t) = t**4 + t**3. Let x(g) = 6*i(g) - u(g). Factor x(v).
-2*v**4*(v - 1)
Let g(k) = k**3 + 38*k**2 + 38*k + 39. Let l be g(-37). Factor 0*y**4 + 0*y**l + 0*y + 2/9*y**3 - 2/9*y**5 + 0.
-2*y**3*(y - 1)*(y + 1)/9
Let f(n) be the second derivative of n**9/15120 - n**7/2100 + n**5/600 + n**3/2 + 4*n. Let h(v) be the second derivative of f(v). Suppose h(c) = 0. What is c?
-1, 0, 1
Suppose 0 = -4*g + 6 + 10. Factor 2 + k**3 - g*k**2 - 2*k**2 - k + 4*k**2.
(k - 2)*(k - 1)*(k + 1)
Let m(l) be the first derivative of l**4/3 - 2*l**3/3 - 2*l**2/3 + 6. Find g, given that m(g) = 0.
-1/2, 0, 2
Let q(o) be the second derivative of o**7/630 - o**6/90 + o**5/60 + o**4/18 - 2*o**3/9 - 5*o**2/2 + 2*o. Let m(x) be the first derivative of q(x). Factor m(i).
(i - 2)**2*(i - 1)*(i + 1)/3
Factor 4/7 - 3/7*a**3 - 1/7*a**2 + 12/7*a.
-(a - 2)*(a + 2)*(3*a + 1)/7
Find w, given that -2/5*w**3 + 2/5*w - 1/5 + 0*w**2 + 1/5*w**4 = 0.
-1, 1
Let f(r) be the first derivative of -r**5/60 + r**4/36 + r + 2. Let c(j) be the first derivative of f(j). Find x, given that c(x) = 0.
0, 1
Let w = 4 + -4. Suppose -p - 3 = 3*s - 5, -10 = 3*s + 4*p. Suppose y**2 + 2*y + w*y**s + 4 - 3*y**2 = 0. What is y?
-1, 2
Let r(n) be the first derivative of -1/9*n**3 + 1/3*n - 4 + 0*n**2. Factor r(x).
-(x - 1)*(x + 1)/3
Let b = -436 + 438. Factor -3 - 33/2*i + 39/2*i**b.
3*(i - 1)*(13*i + 2)/2
Let o(a) = 120*a**5 + 135*a**4 + 85*a**3 + 35*a - 35. Let w(v) = 7*v**5 + 8*v**4 + 5*v**3 + 2*v - 2. Let d(k) = 2*o(k) - 35*w(k). Find u such that d(u) = 0.
-1, 0
Let c(a) = a**5 + 6*a**4 + 9*a**3 - 4*a**2. Let s(t) = -t**5 - t**4 + t**3 - t**2. Let x(b) = -c(b) + 4*s(b). Factor x(r).
-5*r**3*(r + 1)**2
Let t(v) be the third derivative of v**8/23520 + v**7/4410 + v**6/2520 + 7*v**4/24 - 5*v**2. Let d(c) be the second derivative of t(c). Solve d(u) = 0 for u.
-1, 0
What is u in 9/4*u - 3/4*u**2 + 0 - 5/4*u**3 - 1/4*u**4 = 0?
-3, 0, 1
Let l(t) = 2*t**2 + 2*t - 1. Let z be l(-2). Let c be (84/(-105))/(z/(-5)). Factor 3/2*q**4 + 0 - 1/2*q**3 + 2/3*q - c*q**2.
q*(q + 1)*(3*q - 2)**2/6
Suppose 2*f + 2 - 6 = 0. What is i in -63*i + 4 - 4*i**f + 63*i = 0?
-1, 1
Let p be (-4)/2 + (0 - -3). Let q be ((-65)/20)/(p/(-4)). Factor 2 + 5*i**3 + q*i**3 + 6*i**2 - 16*i - 10.
2*(i - 1)*(3*i + 2)**2
Let c(y) be the second derivative of y**4/3 + 4*y**3 - 14*y**2 - 28*y. Let c(s) = 0. What is s?
-7, 1
Let b(d) be the first derivative of -d**6/21 + 6*d**5/35 - d**4/14 - 2*d**3/7 + 2*d**2/7 + 5. What is c in b(c) = 0?
-1, 0, 1, 2
Let h(w) be the first derivative of -w**6/6 + 2*w**5/5 - w**4/4 + 16. Determine l, given that h(l) = 0.
0, 1
Let b(u) be the second derivative of 1/48*u**4 + 1/6*u**3 - 4*u + 3/8*u**2 + 0. Factor b(p).
(p + 1)*(p + 3)/4
Let v be 114/22 - 8/44. Suppose v*o - 2*o = -9. Let l(j) = -7*j**2 + j - 7. Let i(w) = -4*w**2 + w - 4. Let t(m) = o*l(m) + 5*i(m). Let t(g) = 0. What is g?
-1
Factor -2/13 + 2/13*d**2 + 2/13*d**3 - 2/13*d.
2*(d - 1)*(d + 1)**2/13
Let w be (-20)/(-15)*(-15)/(-10). Factor 27/4*c**3 - 18*c**4 - 3/4*c**w + 0 + 12*c**5 + 0*c.
3*c**2*(c - 1)*(4*c - 1)**2/4
Suppose 7*t = 3*t + 12. Solve 3/2*k**t + 0 + k**2 + 1/4*k + k**4 + 1/4*k**5 = 0.
-1, 0
Let w(p) be the first derivative of p**6/15 + 2*p**5/25 - p**4/10 - 2*p**3/15 - 7. Solve w(c) = 0.
-1, 0, 1
Let v be 1*(-9)/(-3) + 2. Let y = 89 + -797/9. Factor 0*x**3 + 2/9*x + 0 + 4/9*x**4 - 2/9*x**v - y*x**2.
-2*x*(x - 1)**3*(x + 1)/9
Let y = 871/14 - 62. Let b(r) be the second derivative of 0 + 0*r**2 - 1/49*r**7 - 2/21*r**3 - y*r**4 - 3/14*r**5 - 11/105*r**6 + 3*r. Solve b(j) = 0.
-1, -2/3, 0
Let b be -2*1/(-6) + 93/45. Factor -84/5*o + 147/5*o**2 + b.
3*(7*o - 2)**2/5
Let t(q) = -3*q**2 - 8*q. Let z(w) = 4*w**2 + 12*w. Let v(n) = -8*t(n) - 5*z(n). Solve v(u) = 0 for u.
-1, 0
Suppose 0 = 2*b - 11 + 3. Factor -b*r**4 - 6*r**3 - r**4 + 2*r - 2*r**3 - r**2.
-r*(r + 1)**2*(5*r - 2)
Let n(p) be the first derivative of -p**6/8 + 3*p**5/20 + 9*p**4/16 - 5*p**3/4 + 3*p**2/4 - 10. Factor n(d).
-3*d*(d - 1)**3*(d + 2)/4
Solve 0*a - 4/11*a**2 - 8/11*a**4 + 18/11*a**3 + 0 = 0 for a.
0, 1/4, 2
Let c(v) be the second derivative of -9*v**6/10 - 12*v**5/5 + v**4 - 15*v. Factor c(w).
-3*w**2*(w + 2)*(9*w - 2)
Let z(p) be the first derivative of -3*p**4/4 + 8*p**3 - 15*p**2/2 - 150*p - 10. Determine j so that z(j) = 0.
-2, 5
Let o be 15/10*(1 + -3). Let d = o - -5. Solve d*r**3 - 7*r**2 - 3*r**3 + 4*r + 3*r**2 + 2*r**3 = 0.
0, 2
Factor 0 - 16/15*x**2 + 2/15*x**3 + 32/15*x.
2*x*(x - 4)**2/15
Let i be (-1)/10*(-34 - (-14)/(-7)). Find u such that -8/5 - 74/5*u**2 - 12*u**3 - 8*u - i*u**4 = 0.
-1, -2/3
Suppose 0 = 23*k - 19*k - 8. Let z(p) be the third derivative of -1/30*p**5 + 0*p + 1/6*p**4 + 0 - 2*p**k - 1/3*p**3. Suppose z(q) = 0. Calculate q.
1
Factor 4/5*d**2 + 2/5*d + 2/5*d**3 + 0.
2*d*(d + 1)**2/5
Let r(m) = m**4 - m**3 + m**2 - m - 1. Let q(o) = -o**5 + o**4 - 6*o**3 + 6*o**2 - o + 5. Let w(t) = -q(t) - 4*r(t). Suppose w(i) = 0. What is i?
1
Determine k, given that 6 + 24 + 72*k - 3 + 48*k**2 = 0.
-3/4
Let v(k) be the third derivative of 0*k - 1/240*k**6 - 1/12*k**3 - k**2 + 1/48*k**4 + 0 + 1/120*k**5. Factor v(w).
-(w - 1)**2*(w + 1)/2
Let k be (2 - -1) + -7 + 6. Factor -3 + 9*h**2 - 7*h**2 - 5*h**k - 3 - 9*h.
-3*(h + 1)*(h + 2)
Let m be 12/8 + 178/(-120). Let w(o) be the third derivative of 0*o + 0 + o**2 - m*o**4 - 1/15*o**3 - 1/100*o**6 + 1/30*o**5. Factor w(i).
-2*(i - 1)**2*(3*i + 1)/5
Let s(w) = -8*w**2 - 8*w. Let o(x) = -15*x**2 - 16*x. Let j = -14 - -21. Let l(u) = j*s(u) - 4*o(u). Factor l(m).
4*m*(m + 2)
Solve 0 - 2/9*s**2 + 4/9*s = 0.
0, 2
Let b(f) = 7*f**2 + 2*f - 2. Suppose -2*t + t - 4 = 0. Let o(k) = 8*k**2 + 2*k - 2. Let y(c) = t*b(c) + 3*o(c). Let y(w) = 0. What is w?
-1, 1/2
Let j = -12037 + 168249/14. Let h = 39/2 + j. Factor h*c**2 - 6/7*c + 4/7.
2*(c - 2)*(c - 1)/7
Let p(w) = -10*w**3 - 16*w**2 - 34*w - 4. Let f