
2*k**2*(k + 1)**2/7
Let s = -3931/24885 - 7676888/2234673. Let j = 3/449 - s. Solve 8/5 + j*f**2 - 24/5*f = 0 for f.
2/3
Let w(a) be the second derivative of 7*a**6/480 + a**5/10 + a**4/8 - a**3 - 3*a. Let k(x) be the second derivative of w(x). Factor k(i).
3*(i + 2)*(7*i + 2)/4
Let u(b) = b**2 + 8 + 0 - 2*b - 5*b. Let r be u(6). Factor -r + 2 + m**3.
m**3
Let n(a) be the third derivative of 0 - 7/24*a**4 + 0*a - 1/6*a**3 - 2/15*a**5 + 5*a**2 + 2/15*a**6. Factor n(h).
(h - 1)*(4*h + 1)**2
Let j(i) = 10*i**3 - 16*i**2 + 7*i - 2. Let g = -19 + 21. Let y(t) = 2*t**2 - t**2 - t**3 + 0 + 1. Let s(f) = g*y(f) + 2*j(f). Solve s(k) = 0 for k.
1/3, 1
Let i(n) be the third derivative of -11*n**5/150 - 3*n**4/20 + 2*n**3/15 + 3*n**2. Factor i(b).
-2*(b + 1)*(11*b - 2)/5
Let b(h) be the first derivative of 55*h**3/6 + 175*h**2/4 + 15*h - 37. Factor b(l).
5*(l + 3)*(11*l + 2)/2
Let p = 34 + -26. Factor 8/3 - p*y + 2/3*y**4 + 26/3*y**2 - 4*y**3.
2*(y - 2)**2*(y - 1)**2/3
Let h = -2/187 - -199/1122. Let d(b) be the first derivative of 0*b**4 + 0*b + 1/2*b**2 + 2/3*b**3 - 2/5*b**5 - h*b**6 + 2. Determine p, given that d(p) = 0.
-1, 0, 1
Let i(l) = -l - 8. Let z be i(-8). Determine r so that -10/7*r**5 - 4/7*r**4 + 0*r**3 + z*r**2 + 0*r + 0 = 0.
-2/5, 0
Suppose -3*u + u + 232 = 0. Suppose -v = v, -u = -2*y + v. Factor -8/5 - 16*d - 98/5*d**5 - y*d**2 - 94*d**3 - 70*d**4.
-2*(d + 1)**3*(7*d + 2)**2/5
Let j be 112/40 - 4/(-20). Factor -3/2 - 3/2*c**j + 3/2*c + 3/2*c**2.
-3*(c - 1)**2*(c + 1)/2
Let a(v) be the third derivative of v**8/23520 - v**7/4410 - v**4/4 + 4*v**2. Let c(i) be the second derivative of a(i). Let c(g) = 0. What is g?
0, 2
Determine z so that 0*z**2 + 2/5*z - 2/5*z**3 + 1/5 - 1/5*z**4 = 0.
-1, 1
Let r(f) be the first derivative of -f**3 + 3*f**2 - 3*f - 9. Solve r(v) = 0 for v.
1
Let o(s) = s**3 - 7*s**2 + 5. Let u be o(7). Suppose 7 = u*f - 3. Suppose 6 - 4 + 6*x + 2*x**2 + 2*x**f = 0. Calculate x.
-1, -1/2
Let l(k) = -5*k**2 - 5*k + 26. Let m(p) = -1. Let u(r) = -l(r) + 4*m(r). Find v such that u(v) = 0.
-3, 2
Let m(x) be the third derivative of -x**7/350 + 3*x**6/50 - 27*x**5/50 + 27*x**4/10 - 81*x**3/10 + 17*x**2. Factor m(p).
-3*(p - 3)**4/5
Suppose 6*c - 2*c = 4*u, -3*u + 15 = 2*c. Suppose -5*n + u*x + 10 = 0, 3*n = 3*x - x + 6. Solve -g**2 + 4*g - g + g**3 - g**n - 2*g = 0 for g.
0, 1
Let i(l) be the first derivative of -l**3/7 + 3*l**2/14 + 6*l/7 + 13. Factor i(h).
-3*(h - 2)*(h + 1)/7
Determine z, given that -2/9 + 2/3*z**4 - 2/9*z**5 - 4/9*z**3 + 2/3*z - 4/9*z**2 = 0.
-1, 1
Let o(w) be the first derivative of -3/10*w**5 - 3*w**3 - 3/2*w + 5 + 3/2*w**4 + 3*w**2. Factor o(f).
-3*(f - 1)**4/2
Let l(n) = 2*n**2. Let o(v) = 8*v**2 - 24*v + 72. Let x(u) = -6*l(u) + 2*o(u). What is t in x(t) = 0?
6
Let j = -1 + 1. Find u such that 6/7*u**4 + j*u**3 + 0*u - 8/7*u**2 - 2/7*u**5 + 0 = 0.
-1, 0, 2
Suppose -4*f = -39 + 27. What is m in 1 + 2*m + 1/4*m**f + 5/4*m**2 = 0?
-2, -1
Factor 15/2*a + 6*a**2 + 3/2*a**3 + 3.
3*(a + 1)**2*(a + 2)/2
Let x be ((-16)/(-10))/4 - 0. Factor -x*d**2 + 1/5*d + 0 + 1/5*d**3.
d*(d - 1)**2/5
Let v be 9/12 + 45/12. Factor 5/2*t - v*t**2 + 7/2*t**4 - 5/2*t**3 + 1.
(t - 1)**2*(t + 1)*(7*t + 2)/2
Let d = 4745/2031 - 2/677. Suppose -65 = 25*b - 140. Factor 0 + d*k**2 + 2/3*k + 5/3*k**b.
k*(k + 1)*(5*k + 2)/3
Let p(b) be the third derivative of 1/80*b**6 - 1/16*b**4 + 0 + 2*b**2 + 0*b + 1/2*b**3 - 1/20*b**5. Factor p(g).
3*(g - 2)*(g - 1)*(g + 1)/2
Let k(s) be the third derivative of -s**8/196 - 3*s**7/490 + s**6/56 + 3*s**5/140 - s**4/56 + 3*s**2. Determine f, given that k(f) = 0.
-1, 0, 1/4, 1
Let w(q) be the second derivative of 1/42*q**4 + 1/105*q**6 + 2*q - 1/35*q**5 + 0*q**3 + 0*q**2 + 0. Factor w(s).
2*s**2*(s - 1)**2/7
Let h(q) = -q**4 + 12*q**3 - 7*q**2 + 12*q - 10. Let k(b) = -b**3 - b**2 + 1. Let d(z) = h(z) + 6*k(z). Factor d(u).
-(u - 2)**2*(u - 1)**2
Let o = -25099/23 - -1091. Let t = 35/46 + o. What is b in -t*b**3 + 1/2*b + 1/4 + 0*b**2 - 1/4*b**4 = 0?
-1, 1
Suppose 0 = a - 5*a + 8. Let w be a/(-6) - (-51)/99. Suppose -4/11 + 2/11*y + w*y**2 = 0. Calculate y.
-2, 1
Let l(s) be the third derivative of -s**5/45 - s**4/18 + 4*s**3/9 - 5*s**2. Determine x, given that l(x) = 0.
-2, 1
Let u(o) be the third derivative of -9*o**6/40 - 11*o**5/20 + 2*o**4 + 2*o**3 + 26*o**2. Factor u(d).
-3*(d - 1)*(d + 2)*(9*d + 2)
Let p(k) be the third derivative of k**8/756 - 8*k**7/945 + k**6/270 + 2*k**5/45 + 62*k**2. Find c, given that p(c) = 0.
-1, 0, 2, 3
Determine y, given that -y**3 + 93 - 93 + 4*y + 12*y**2 - 6*y**3 = 0.
-2/7, 0, 2
Suppose -3*x - 4*r + 9 = 0, -2*x - r + 1 + 5 = 0. Let d = 5 - 1. What is z in -48/5*z**2 + 42/5*z**5 + 44/5*z**d + 2/5*z + 4/5 - 44/5*z**x = 0?
-1, -1/3, 2/7, 1
Let o = -11 - -13. Factor -2*g**5 - 8 - 8*g**2 + 6*g**3 + 4*g**4 - 8*g + 0*g**o + 8.
-2*g*(g - 2)**2*(g + 1)**2
Determine x, given that 2/7*x**4 - 4/7 + 2/7*x**2 + 6/7*x - 6/7*x**3 = 0.
-1, 1, 2
Let y(l) be the third derivative of -l**7/1260 - l**6/60 - 3*l**5/20 + l**4/24 - 3*l**2. Let a(r) be the second derivative of y(r). Solve a(h) = 0 for h.
-3
Let o(j) = j**3 + 10*j**2 - 2*j - 16. Let a be o(-10). Let n(p) be the first derivative of 2 + 5/6*p**a - 14/9*p**3 + 8/3*p - 8/3*p**2. Factor n(c).
2*(c - 2)*(c + 1)*(5*c - 2)/3
Let l(n) be the first derivative of n**6/50 - 3*n**5/20 + 7*n**4/20 - 3*n**3/10 - 5*n + 2. Let c(k) be the first derivative of l(k). Factor c(u).
3*u*(u - 3)*(u - 1)**2/5
Let u(a) = -a**2 - a. Let g(r) = 8*r**2 + 35*r + 75. Let i(z) = g(z) + 5*u(z). Find k such that i(k) = 0.
-5
Let z(n) be the third derivative of -n**5/20 - n**2. Suppose z(i) = 0. Calculate i.
0
Let n(s) be the third derivative of s**5/30 + 5*s**4/6 + 25*s**3/3 - 9*s**2. Factor n(h).
2*(h + 5)**2
Let b(x) be the third derivative of -x**6/120 - x**5/15 - x**4/6 - 16*x**2. What is z in b(z) = 0?
-2, 0
Let k(h) be the first derivative of h**6/21 - 3*h**4/14 - 4*h**3/21 + 10. Solve k(s) = 0 for s.
-1, 0, 2
Factor -5*s - 19*s + 8*s + 9*s**2 - 4.
(s - 2)*(9*s + 2)
Let f(i) = 1 + 1 - 7*i**2 + 0*i**2. Let h(k) = -6*k**2 + 2. Let n(z) = 4*f(z) - 5*h(z). Solve n(s) = 0.
-1, 1
Suppose 76 = -3*l + 4*l. Factor 64*o + 3 - l*o - 20*o**2 + 5.
-4*(o + 1)*(5*o - 2)
Let t(q) = 11*q**2 - 5*q - 24. Let n(u) = -17*u**2 + 8*u + 36. Let c(s) = -5*n(s) - 8*t(s). Find y such that c(y) = 0.
-2, 2
Let f = 726/905 + -2/905. Determine a, given that -2/5*a**2 + f*a + 6/5 = 0.
-1, 3
Let -35*h - 66*h**3 + 44*h**2 - 15*h**5 + 46*h**2 + 5 - 44*h**3 + 65*h**4 = 0. What is h?
1/3, 1
Suppose 3*o - 10 = m, -m - 16 = 3*m. Find g, given that 3*g**3 - g**o + 0*g**2 + 0*g**3 + 4*g**2 = 0.
-1, 0
Suppose 0 = -0*w - w + 2. Suppose -6*s + 8 = -w*s. Determine l, given that -3 - 2*l + 7 + l**s - 3*l**2 = 0.
-2, 1
Suppose -2*o = 3*o - 5*x - 55, -o - 4*x = 9. Let z = 9 - o. What is m in z*m - 1/2 - 2*m**2 = 0?
1/2
Let r be ((-30)/(-165))/(3/33). Suppose -1/5*l**r + 0 + 2/5*l = 0. Calculate l.
0, 2
Let v(a) = -8*a**4 - a**3 + 4*a**2 - a. Let x(t) = -9*t**4 - t**3 + 4*t**2 - t. Let o(d) = -3*v(d) + 2*x(d). Factor o(s).
s*(s + 1)*(2*s - 1)*(3*s - 1)
Let w be (-12)/4*6/(-9). Factor -2*i + i - 4*i + i**2 - w + 6*i.
(i - 1)*(i + 2)
Let i(b) = 13*b + 13. Let w(l) = -20*l - 20. Let z(x) = -8*i(x) - 5*w(x). Let g(n) = -n**2 + 4*n + 5. Let a(y) = -2*g(y) - 3*z(y). Factor a(r).
2*(r + 1)**2
Let n(g) be the first derivative of -g**6/12 - g**5/2 - 7*g**4/8 + g**3/6 + 2*g**2 + 2*g + 6. Determine u, given that n(u) = 0.
-2, -1, 1
Let y be (-2)/6 + (-168)/(-18). Let -y*g - 3*g**2 + 2*g**2 - 6*g**2 - 6 + 4*g**2 = 0. Calculate g.
-2, -1
Let y(d) be the first derivative of d**7/2100 + d**6/450 + d**5/300 + d**3 + 1. Let w(k) be the third derivative of y(k). Factor w(o).
2*o*(o + 1)**2/5
Let q = -11 + 11. Let f(v) be the first derivative of -2/3*v**3 + 1/3*v**6 + 0*v + 1 - 1/2*v**4 + 2/5*v**5 + q*v**2. Find u such that f(u) = 0.
-1, 0, 1
Find c, given that 1/4*c**4 - 1/4*c**5 + 0 + 3/4*c**3 - 1/4*c**2 - 1/2*c = 0.
-1, 0, 1, 2
Let z = -11 - -15. Let j(l) be the first derivative of 2/7*l**z + 1/7*l**2 - 2 + 0*l + 10/21*l**3. Suppose j(h) = 0. What is h?
-1, -1/4, 0
Let g = 6 - 4. Let m(h) = h**3 - 2*h**2 + 2*h + 1. Let w be m(g). Let k(v) = -v**2. Let d(o) = -2*o**3 - o**2. Let x(y) = w*k(y) - d(y). Factor x(p).
2