+ v**3/9 - 11*v. Determine u, given that c(u) = 0.
-1/4, 0, 1
Let r(q) be the second derivative of q**4/30 + 2*q**3/15 - 11*q. Solve r(w) = 0.
-2, 0
Suppose 4*s - x - 42 = -2*x, -5*x + 12 = 2*s. Suppose 5*g - v = 13, 2*v + 3 + s = 4*g. Factor 1/2 - 1/2*m**g + 1/2*m - 1/2*m**3.
-(m - 1)*(m + 1)**2/2
Let r be -1 - (-12)/9 - (-32)/12. Let x(w) be the first derivative of 4/15*w**5 + 0*w - 1/6*w**2 + 2/3*w**r - 2 - 3/4*w**4. Factor x(m).
m*(m - 1)**2*(4*m - 1)/3
Let v(j) be the first derivative of -1/3*j**3 - 1 + 1/2*j**2 - 1/4*j**4 + j. Factor v(a).
-(a - 1)*(a + 1)**2
Factor -31*h + 4 + 3*h**2 + 23*h + h**2.
4*(h - 1)**2
Let n(a) be the third derivative of -1/3*a**3 + 0*a**4 + 0 + 1/1080*a**6 + 1/180*a**5 - 2*a**2 + 0*a. Let z(k) be the first derivative of n(k). Factor z(o).
o*(o + 2)/3
Let k(w) be the third derivative of -w**6/900 + w**5/90 - 2*w**4/45 + 4*w**3/45 + 4*w**2. Factor k(r).
-2*(r - 2)**2*(r - 1)/15
Let s(a) be the second derivative of -2*a**6/135 + 11*a**5/180 + a**4/36 + 5*a. Let s(c) = 0. What is c?
-1/4, 0, 3
Suppose -u + 4*u - 15 = 0. Suppose -2*m = -7 + 1. Let -128/5*l**4 + 4/5 - 36/5*l**2 + 2*l - 128/5*l**m - 42/5*l**u = 0. What is l?
-1, -1/3, 2/7
Let p(d) = -20*d**2 - 49*d - 18. Let w(o) = -7*o**2 - 17*o - 6. Let g(u) = 6*p(u) - 17*w(u). Find r such that g(r) = 0.
-3, -2
Let d(l) be the third derivative of -l**7/2520 - l**6/540 - l**5/360 - l**3/6 - 3*l**2. Let p(g) be the first derivative of d(g). Solve p(o) = 0 for o.
-1, 0
Let j(m) = -m**3 + 11*m**2 - 3*m + 33. Let f be j(11). Determine z, given that f*z + 0 - 7/3*z**3 + 3*z**4 - 2/3*z**2 = 0.
-2/9, 0, 1
Factor 0 + 2/13*b - 4/13*b**2 + 2/13*b**3.
2*b*(b - 1)**2/13
Let c(v) be the first derivative of v**4/6 - 2*v**3/3 + v**2 - 2*v/3 - 6. Factor c(j).
2*(j - 1)**3/3
Let j(o) be the first derivative of -o**4/20 + o**3/5 - o**2/5 - 5. Factor j(r).
-r*(r - 2)*(r - 1)/5
Let w be ((-6)/5)/(9/(-30)). Let c = -36 - -37. Factor 5/4*r**w - 15/4*r**2 - 1/2*r**3 + 4*r - c.
(r - 1)**2*(r + 2)*(5*r - 2)/4
Let b(r) be the first derivative of -4/9*r + 0*r**3 - 1/18*r**4 + 1/3*r**2 + 1. Factor b(o).
-2*(o - 1)**2*(o + 2)/9
Factor 0 + 2/15*a**2 - 2/15*a**3 - 2/15*a**4 + 2/15*a.
-2*a*(a - 1)*(a + 1)**2/15
Let w(p) be the third derivative of -p**8/10080 + p**6/360 + p**5/30 - p**2. Let f(x) be the third derivative of w(x). Factor f(j).
-2*(j - 1)*(j + 1)
Let -6*x + 15 + 3*x**4 + 15*x**2 - 15 - 12*x**3 = 0. Calculate x.
0, 1, 2
Factor 3*c**2 - 3*c**4 + 0*c**3 + 0 + 3/2*c**5 - 3/2*c.
3*c*(c - 1)**3*(c + 1)/2
Let a(p) = p**2 + 8*p + 2. Let n be a(-8). Suppose 0 = 4*h, -3*g + 4*g + 2*h = n. What is t in -2*t + t**g + 4 - 7*t**2 + 0*t = 0?
-1, 2/3
Let a(m) = 3*m - 1 + 0*m - m - m**2. Let g be a(1). Factor g*n**2 + 1/2*n**3 - 1 - 3/2*n.
(n - 2)*(n + 1)**2/2
Factor -8/3*j**2 + 2/3 + 5/3*j**3 + 1/3*j.
(j - 1)**2*(5*j + 2)/3
Find j such that -2/11*j - 2/11 - 6/11*j**3 + 10/11*j**2 = 0.
-1/3, 1
Let n(d) be the third derivative of d**5/20 + d**4/4 - 13*d**3/6 - 5*d**2. Let j(g) = -4*g**2 - 6*g + 14. Let o(y) = 4*j(y) + 5*n(y). Factor o(h).
-(h - 3)**2
Let d be 3 + 106/105 - (0 + 4). Let u(z) be the second derivative of d*z**6 + 0*z**4 + 0*z**2 - z + 1/70*z**5 + 0 + 0*z**3. Factor u(o).
2*o**3*(o + 1)/7
Factor 3/5 + 3/5*w**4 - 6/5*w**2 - 6/5*w**3 + 3/5*w + 3/5*w**5.
3*(w - 1)**2*(w + 1)**3/5
Let h(g) be the third derivative of 0*g - 1/8*g**4 + 1/40*g**6 + 0 - 1/30*g**5 + 1/3*g**3 - g**2. Factor h(y).
(y - 1)*(y + 1)*(3*y - 2)
Factor -2 - 5*p + 5*p**2 - 10*p**2 + 10*p**2 - 28.
5*(p - 3)*(p + 2)
Let y = -4 + 4. Suppose -3*l + y*n - 3*n + 18 = 0, 4*l = 2*n. Factor 3*p**3 - 2*p**2 - l*p**3 + p**2.
p**2*(p - 1)
Let t(r) = -r + 8. Let u be t(-7). Factor 7*o - 4 - 11*o**3 - 4 + u*o**3 - 19*o.
4*(o - 2)*(o + 1)**2
Let u(m) be the second derivative of -m**6/80 + m**5/40 + m**4/96 - m**3/24 + 3*m. Factor u(w).
-w*(w - 1)**2*(3*w + 2)/8
Let t(b) be the first derivative of 0*b - 2/3*b**3 + 2*b**2 + 6. Factor t(n).
-2*n*(n - 2)
Factor -3/2*m**2 - 1/2*m**3 + 0*m + 0.
-m**2*(m + 3)/2
Determine h so that 6 - 4*h**3 + 4 - 32*h**2 - 10 - 28*h = 0.
-7, -1, 0
Let b(i) = -18*i**2 - 26*i - 9. Let w(o) = 19*o**2 + 27*o + 9. Let j(y) = -3*b(y) - 2*w(y). Factor j(g).
(4*g + 3)**2
Suppose d - 2*x + 5 = 0, 1 + 44 = 5*d + 4*x. Let b(h) be the first derivative of -4*h + 3 + 2/5*h**d + 1/2*h**4 - 2*h**3 - 5*h**2. Find l, given that b(l) = 0.
-1, 2
Let b = -23 - -23. Let k(t) be the first derivative of -1/7*t**2 - 1/14*t**4 + 4/21*t**3 + 1 + b*t. Factor k(o).
-2*o*(o - 1)**2/7
Let i(m) be the first derivative of 2 - 3*m**2 - 9/4*m**4 + 0*m - 5*m**3. Determine y, given that i(y) = 0.
-1, -2/3, 0
Let q(d) be the first derivative of -2*d**3/21 + 2*d**2/7 + 6*d/7 - 2. Factor q(y).
-2*(y - 3)*(y + 1)/7
Let z be (1 + -2 - -2)*(-1 + 1). Factor -2/3*t**5 + 4/3*t**2 + 0*t + 2*t**3 + 0 + z*t**4.
-2*t**2*(t - 2)*(t + 1)**2/3
Let v(y) be the second derivative of y**6/15 + y**5/6 + 7*y**4/54 + y**3/27 - 8*y. What is x in v(x) = 0?
-1, -1/3, 0
Let q = 41 + -38. Suppose -q*c + 3*g - 7 = -8*c, g = 3*c - 7. Solve 2/3*d + 0 - 1/3*d**3 - 1/3*d**c = 0.
-2, 0, 1
Let n = -11 + -9. Let f be (-72)/n - 10/(-25). Factor 6/5*h**3 - 3/5 - 3/5*h**f - 3/5*h - 3/5*h**5 + 6/5*h**2.
-3*(h - 1)**2*(h + 1)**3/5
Let l(a) be the second derivative of 5*a**7/42 - 3*a**6/5 + 11*a**5/10 - 2*a**4/3 - a**3/2 + a**2 - 5*a. Suppose l(f) = 0. What is f?
-2/5, 1
Let u(t) be the first derivative of 0*t**2 + 1/9*t**3 + 0*t - 1/12*t**4 + 3. Factor u(j).
-j**2*(j - 1)/3
Let x(k) = k**3. Let j(l) = -l**4 + 7*l**3 + l**2. Let d(y) = 5*j(y) - 35*x(y). Suppose d(t) = 0. What is t?
-1, 0, 1
Suppose 2/7*p**3 + 0*p**2 + 0 - 2/7*p = 0. Calculate p.
-1, 0, 1
Suppose 0 + 9 = 3*p. What is k in k**p + 63*k - 63*k - k**5 = 0?
-1, 0, 1
Let v(u) = u**3 - 4*u**2 - 13*u + 10. Let l be v(6). Let j be ((-3)/4)/(12/(-8)). Factor j*g - 1/2*g**3 - 1/4*g**l + 0*g**2 + 1/4.
-(g - 1)*(g + 1)**3/4
Let r = -246 + 5905/24. Let b(d) be the second derivative of 0*d**4 + 0*d**2 + d - r*d**3 + 1/80*d**5 + 0. Determine f so that b(f) = 0.
-1, 0, 1
Let n(k) be the first derivative of k**4/8 - k**3/3 - 3. Factor n(l).
l**2*(l - 2)/2
Let z = -3156/5 + 621. Let f = z + 12. Factor -f + 6/5*v - 1/5*v**2.
-(v - 3)**2/5
Let g(a) be the first derivative of 3 - 1/2*a**2 + 1/3*a**3 + a. Let u(n) = n**2 + 5. Let k(r) = -3*g(r) + u(r). Factor k(c).
-(c - 2)*(2*c + 1)
Factor 1/6*x**3 - 1/6*x + 0*x**2 + 0.
x*(x - 1)*(x + 1)/6
Let r(i) be the first derivative of 3*i**4/20 - 2*i**3/5 + 9. Factor r(b).
3*b**2*(b - 2)/5
Suppose -4*x + 4*s = 12, 3*x + 2*s - 16 = -0. Let u = 15/8 - 89/56. Factor 0 + u*b**x + 2/7*b.
2*b*(b + 1)/7
Let p(x) be the first derivative of 9*x**4/8 + 2*x**3 - 11*x**2/4 + x + 14. Factor p(v).
(v + 2)*(3*v - 1)**2/2
Let n(f) be the third derivative of 0 + 7/12*f**4 + 1/12*f**6 + 0*f + 2/3*f**3 + 1/105*f**7 + 2*f**2 + 3/10*f**5. Factor n(u).
2*(u + 1)**3*(u + 2)
Suppose 1 = 4*k - 7. Factor 0 + r**k + 1/2*r**3 + 1/2*r.
r*(r + 1)**2/2
Let v(r) be the third derivative of -r**7/15 + 4*r**6/15 - 11*r**5/30 + r**4/6 + 23*r**2. Factor v(o).
-2*o*(o - 1)**2*(7*o - 2)
Let n(i) = 8*i + 10. Let p be n(-3). Let h be (-130)/(-35) + (-4)/p. Factor -2/3*l**2 + 0*l**3 + 0*l + 1/3*l**h + 1/3.
(l - 1)**2*(l + 1)**2/3
Let h(k) = -3*k**3 + 3*k. Let o(c) = 12*c**2 - 12*c**2 + 2*c**3 - 2*c. Let w(v) = -3*h(v) - 5*o(v). Solve w(j) = 0.
-1, 0, 1
Let y(h) be the first derivative of h**6/3 + 5. Suppose y(r) = 0. What is r?
0
Let r(o) be the third derivative of o**6/840 - o**4/56 + o**3/21 + 3*o**2. Factor r(c).
(c - 1)**2*(c + 2)/7
Let n be (-2)/8*128/(-56). Let c be (-1)/(-3) - 46/(-42). Factor c*h**2 + 0 - n*h.
2*h*(5*h - 2)/7
Let j(o) be the first derivative of -o**6/18 + o**4/6 - o**2/6 + 6. Factor j(m).
-m*(m - 1)**2*(m + 1)**2/3
Let h = 5 - 2. Suppose -8 = -h*x - 2*n, 2*x - 3*x - n + 3 = 0. Factor 1/3*m**3 + m - 1/3 - m**x.
(m - 1)**3/3
Let g(z) be the first derivative of -z**6/20 - 3*z**5/20 + z**4/8 + z**3/2 - 4*z - 3. Let q(l) be the first derivative of g(l). Let q(p) = 0. What is p?
-2, -1, 0, 1
Let b(r) be the second derivative of 3/14*r**3 + 0 + 1/7*r**2 + 6*r + 1/12*r**4. Suppose b(t) = 0. Calculate t.
-1, -2/7
Let b(o) = o**3 + 15*o**2 + 16*o + 31. Let h be b(-14). Let v(p) be the first derivative of 3/2*p**4 - 3/5*p**5 - 