2/7*k**2.
4*k*(k - 1)**3/7
Let t be 2/8*(12 + -3 + -7). Solve 0*k - 11/4*k**2 + 9/4*k**3 + 1 - t*k**4 = 0.
-1/2, 1, 2
Let r be 2/(-2)*8/(-24). Factor -4/3*z + r - 5/3*z**2.
-(z + 1)*(5*z - 1)/3
Let s(k) = -1. Let m(v) = -2*v**2 - 10*v - 18. Let p(b) = -m(b) + 10*s(b). Factor p(t).
2*(t + 1)*(t + 4)
Let x(a) be the second derivative of 1/70*a**5 + 1/21*a**3 + 1/21*a**4 - a + 0*a**2 + 0. Factor x(r).
2*r*(r + 1)**2/7
Let -5*r**2 + 8/3*r**3 - 8/3*r - 1/3*r**4 + 16/3 = 0. What is r?
-1, 1, 4
Let 8/7*y + 0 + 12/7*y**4 + 32/7*y**3 + 4*y**2 = 0. What is y?
-1, -2/3, 0
Let j = 557/2685 - 4/537. Factor -2/5*d**5 + 1/5*d**4 + 0*d + j*d**3 + 0*d**2 + 0.
-d**3*(d - 1)*(2*d + 1)/5
Let s = -211 - -216. Solve 0 + 6*u**4 - 4/5*u - 12/5*u**2 - 5*u**s + 11/5*u**3 = 0 for u.
-2/5, 0, 1
Let k = 105 + -148. Let n = -40 - k. Factor -1/5*h**2 + 1/5*h**n + 0*h - 1/5*h**5 + 0 + 1/5*h**4.
-h**2*(h - 1)**2*(h + 1)/5
Let p(k) be the second derivative of k**5/30 - k**4/3 - 10*k + 2. Factor p(a).
2*a**2*(a - 6)/3
Factor -6*t**2 + 8 - 7*t + 42*t**2 - 16*t - 21*t.
4*(t - 1)*(9*t - 2)
Let a = 48 - 335/7. Suppose 2*r - 2 = r. Factor -a*o**r + 0*o - 1/7*o**4 + 0 - 2/7*o**3.
-o**2*(o + 1)**2/7
Let z = -6 + 10. Suppose 20*f**5 + 4*f**z - 20*f**3 - 12*f**4 + 5*f**2 + 4*f**2 - f**2 = 0. Calculate f.
-1, 0, 2/5, 1
Suppose w + 0*w = 5. Let u(z) be the first derivative of 2/21*z**3 - 2 + 1/7*z**4 + 2/35*z**w + 0*z + 0*z**2. Factor u(h).
2*h**2*(h + 1)**2/7
Determine w so that 0*w - 3/4*w**4 - 5/4*w**3 + 0 + 1/2*w**2 = 0.
-2, 0, 1/3
Factor 6 + 2 - 3*f**2 - 3*f - 5 + 3*f**3.
3*(f - 1)**2*(f + 1)
Let g be (-10 + 16/(-8))*1/(-2). Determine j so that -6*j + 9/2*j**2 - g = 0.
-2/3, 2
Find b, given that -3/7*b**2 - 24/7*b - 45/7 = 0.
-5, -3
Let t(n) be the second derivative of n**7/21 - 7*n**6/45 + n**5/6 - n**4/18 + 2*n. Suppose t(z) = 0. Calculate z.
0, 1/3, 1
Let g = 91 - 88. Let q(b) be the third derivative of 0*b + 0*b**3 + 1/30*b**4 - 1/150*b**6 - 1/150*b**5 + 1/525*b**7 + 0 + g*b**2. Factor q(n).
2*n*(n - 2)*(n - 1)*(n + 1)/5
Suppose -3*k = -6*k + 15. Suppose -t - 10 = -k*v, 4*v + 0*t = -4*t + 8. Factor -8/11*g**v - 4/11*g**4 + 10/11*g**3 + 0 + 2/11*g.
-2*g*(g - 1)**2*(2*g - 1)/11
Let c(x) be the first derivative of 4*x**5/5 + 20*x**4 + 168*x**3 + 392*x**2 - 1372*x + 28. Let c(d) = 0. What is d?
-7, 1
Let i(q) be the second derivative of 1/21*q**4 + 0*q**2 - 1/21*q**3 - 6*q - 1/70*q**5 + 0. Factor i(s).
-2*s*(s - 1)**2/7
Suppose -27 = -6*g + 3*g. Suppose -x - 2*p = -2*x + g, -20 = -2*x + 2*p. Find l, given that 18*l**2 + l + 8 - 14*l - x*l = 0.
2/3
Let x(q) be the first derivative of -3*q**4/28 - 4*q**3/7 + 15*q**2/14 + 14. Factor x(h).
-3*h*(h - 1)*(h + 5)/7
Let a = 124 + -122. Let g = -21/4 - -71/12. Let a*v + g*v**2 + 4/3 = 0. Calculate v.
-2, -1
Let v(o) be the second derivative of 0*o**3 + 0*o**2 + 0 - o + 1/42*o**4. Factor v(c).
2*c**2/7
Let z(v) be the third derivative of -v**7/2268 + v**6/1080 + v**5/270 + v**4/8 + 2*v**2. Let s(i) be the second derivative of z(i). Factor s(t).
-2*(t - 1)*(5*t + 2)/9
Let o(y) = -85*y**3 - 77*y**2 - 23*y + 1. Let l(j) = 86*j**3 + 76*j**2 + 22*j - 2. Let d(m) = 4*l(m) + 5*o(m). Suppose d(v) = 0. Calculate v.
-1/3
Let o(t) be the second derivative of t**6/50 - 9*t**5/100 + t**4/10 + 5*t. Factor o(b).
3*b**2*(b - 2)*(b - 1)/5
Let d be 48/(-84) + (-8)/(-7). Suppose 0*q + d*q**2 - 4/7 = 0. Calculate q.
-1, 1
Let c(h) be the first derivative of -3/10*h**5 - 3/4*h**2 - 3/2*h**3 + 0*h - 9/8*h**4 - 4. Let c(i) = 0. What is i?
-1, 0
Let l(w) be the first derivative of 2/55*w**5 - 4/33*w**3 + 1/22*w**4 - 2 + 0*w**2 + 0*w. Factor l(v).
2*v**2*(v - 1)*(v + 2)/11
Let k(l) be the first derivative of 0*l - 1/5*l**5 + 0*l**2 + 0*l**3 + 2 - 1/6*l**6 + 0*l**4. What is r in k(r) = 0?
-1, 0
Let s(u) be the second derivative of u**6/120 - 3*u**5/80 + u**4/24 - 9*u. Factor s(r).
r**2*(r - 2)*(r - 1)/4
Let u(y) be the second derivative of -y**7/6720 - y**6/1152 - y**5/480 + y**4/12 - 2*y. Let p(l) be the third derivative of u(l). Suppose p(q) = 0. What is q?
-1, -2/3
Let n(u) be the second derivative of 2*u**7/21 - 2*u**5/5 + 2*u**3/3 + 3*u. What is a in n(a) = 0?
-1, 0, 1
Let g(s) = -s**5 - s**4 - 2*s**3 - 6*s**2 - 2*s - 2. Let f(t) = 6*t**5 + 6*t**4 + 9*t**3 + 31*t**2 + 11*t + 11. Let z(q) = -2*f(q) - 11*g(q). Factor z(w).
-w**2*(w - 2)*(w + 1)*(w + 2)
Suppose 82 = 5*u - 4*u + 5*c, -2*c = -2*u + 212. Let z = u - 504/5. Suppose 0 + z*v**3 + 2*v**2 - 8/5*v**5 + 2/5*v - 2*v**4 = 0. Calculate v.
-1, -1/4, 0, 1
Let r(l) be the first derivative of -l**4/12 + 2*l**2/3 + 1. What is z in r(z) = 0?
-2, 0, 2
Suppose 15 = -5*w + 8*w. Let f be (w/(-3))/5 + 1. Let 1/3*n**3 + f*n**2 + 0 + 1/3*n = 0. What is n?
-1, 0
Let x(n) be the second derivative of n**7/21 - 7*n**6/30 + 9*n**5/20 - 5*n**4/12 + n**3/6 - 5*n. Factor x(h).
h*(h - 1)**3*(2*h - 1)
Let m = 97 - 91. Let w(s) be the third derivative of 13/60*s**5 + 3/8*s**4 + 1/20*s**m + 0*s + 0 + 1/3*s**3 - s**2. Factor w(a).
(a + 1)*(2*a + 1)*(3*a + 2)
Suppose -3*c - 20 = -5*j - 4*c, 5*c - 28 = -j. Factor a**3 - a**4 - 2*a + 4*a**3 - j*a**3 + 0 + 1.
-(a - 1)**3*(a + 1)
Let j(s) be the second derivative of -s**5/60 - s**4/36 + s**3/18 + s**2/6 + 2*s. Solve j(u) = 0.
-1, 1
Let c(h) be the first derivative of 5*h**4/16 - h**3 - 11*h**2/8 + 3*h/2 + 11. Find o such that c(o) = 0.
-1, 2/5, 3
Let q(r) be the third derivative of r**5/60 - r**2. Factor q(m).
m**2
Suppose -2*c + 32 = 14*c. Factor 0 - 1/4*w + 1/4*w**c.
w*(w - 1)/4
Let h(a) be the first derivative of a**7/56 + a**6/20 - 3*a**5/80 - a**4/8 - 4*a + 3. Let i(j) be the first derivative of h(j). Find m such that i(m) = 0.
-2, -1, 0, 1
Solve -c**4 - 9*c**2 + 8*c**2 + c**3 - 3*c**3 = 0.
-1, 0
Let c(h) = -h**3 + 46*h**2 - 5*h - 46. Let i(s) = 45*s**2 - 5*s - 45. Let w(o) = 5*c(o) - 6*i(o). Factor w(p).
-5*(p - 1)*(p + 1)*(p + 8)
Let s(v) be the first derivative of 0*v**2 + 5/2*v**6 + 4/3*v**3 - 11/5*v**5 - 2*v**4 + 1 + 0*v. Suppose s(k) = 0. Calculate k.
-2/3, 0, 2/5, 1
Factor 4/11*l - 2/11*l**2 + 6/11.
-2*(l - 3)*(l + 1)/11
Suppose 2/5*p**5 + 0*p**2 + 2/5*p**4 - 4/5*p**3 + 0*p + 0 = 0. Calculate p.
-2, 0, 1
Factor -1/4*q**3 + 1/2*q + 0 + 1/4*q**2.
-q*(q - 2)*(q + 1)/4
Let x(p) be the second derivative of -p**5/10 - 3*p**4/4 - p**3/2 + 2*p**2 - 14*p. Factor x(z).
-(z + 1)*(z + 4)*(2*z - 1)
Let l(y) be the first derivative of 1/120*y**5 + 0*y**3 + 0*y**4 - 3/2*y**2 - 3 + 0*y. Let b(t) be the second derivative of l(t). Factor b(c).
c**2/2
Let 25*x**2 + 40*x + 4*x**3 - 37 + 57 + x**3 = 0. Calculate x.
-2, -1
Let x(a) be the first derivative of a**4/24 - a**3/6 + a**2/4 - a + 1. Let c(g) be the first derivative of x(g). Factor c(m).
(m - 1)**2/2
Let u(d) be the second derivative of -7*d**5/50 - 2*d**4/5 + 5*d**3/3 - 6*d**2/5 - 26*d. Solve u(v) = 0.
-3, 2/7, 1
Let i(g) be the third derivative of g**7/105 - g**6/20 - 2*g**5/15 + g**2. Factor i(h).
2*h**2*(h - 4)*(h + 1)
Let -2/5*s**5 - 1/5*s**2 + 1/5*s**4 + 0*s + 2/5*s**3 + 0 = 0. What is s?
-1, 0, 1/2, 1
Let z(a) be the first derivative of -a**6/12 + a**5/10 + 3*a**4/8 - 5*a**3/6 + a**2/2 + 7. Factor z(l).
-l*(l - 1)**3*(l + 2)/2
Let d(a) = -a**3 + a**2 + 33*a + 31. Let l(s) = -16*s - 16. Let m(r) = -4*d(r) - 7*l(r). Factor m(v).
4*(v - 3)*(v + 1)**2
Let f(q) be the first derivative of 4 + 4*q**2 - 9*q**2 + 4*q**2 - 2*q**3 + 1. Factor f(d).
-2*d*(3*d + 1)
Let c(n) = 11*n**2 + 6*n + 5. Let v(s) = -16*s**2 - 9*s - 7. Let z(q) = -7*c(q) - 5*v(q). Factor z(k).
3*k*(k + 1)
Let j(k) = k**5 + 4*k**4 + 2*k**3 + 2*k**2. Let z(q) = q**3. Let r(v) = 2*j(v) + 6*z(v). Suppose r(p) = 0. What is p?
-2, -1, 0
Let d(y) be the second derivative of y**7/84 + y**6/15 + y**5/8 + y**4/12 - 2*y. Suppose d(h) = 0. What is h?
-2, -1, 0
Factor -2*j**3 - 16*j**2 + 4*j**4 + 6*j**3 - 4*j**5 + 12*j**2.
-4*j**2*(j - 1)**2*(j + 1)
Let g(j) = -4*j + 99. Let k be g(24). Factor 0 - 4/3*d**k + 2/3*d**2 + 4/3*d - 2/3*d**4.
-2*d*(d - 1)*(d + 1)*(d + 2)/3
Suppose 8 = h + h. Let d(u) = -4*u**3 - 12*u**2 - 24*u - 30. Let x(g) = -5*g**3 - 13*g**2 - 23*g - 31. Let c(w) = h*d(w) - 3*x(w). Factor c(b).
-(b + 3)**3
Factor -1/4*k**3 - 1 + 0*k + 3/4*k**2.
-(k - 2)**2*(k + 1)/4
Let c(v) = -25*v**4 + 60*v**3 - 30*v**2 - 50*v + 55. Let h(m) = -8*m**4 + 20*m**3 - 10*m**2 - 17*m + 18. Le