 s be 3/(-27) + 2695/(-126). Let u = 22 + s. Factor -11/4*w + u + 7/2*w**2.
(2*w - 1)*(7*w - 2)/4
Let f = 0 + 3. Solve -2*a**4 + a**4 + 0*a**4 - 3*a**2 + 4*a**4 + f*a - 3*a**3 = 0.
-1, 0, 1
Let w(k) be the first derivative of 2/9*k - 2/27*k**3 + 1/18*k**4 + 2 - 1/9*k**2. Let w(y) = 0. Calculate y.
-1, 1
Let k(r) be the first derivative of 0*r**3 - 1/5*r**2 - 1 + 1/30*r**4 - r. Let j(d) be the first derivative of k(d). Factor j(v).
2*(v - 1)*(v + 1)/5
Let d = 119/412 - 4/103. Suppose 0 + 0*p**3 + 0*p - 1/4*p**2 + d*p**4 = 0. What is p?
-1, 0, 1
Let y be (-4 + 205/50)*5/2. Factor -y - 1/4*t**2 - 1/2*t.
-(t + 1)**2/4
Let 6*s**3 - 39*s + 9*s**3 + 12 - 7 + 13 + 6*s**2 = 0. Calculate s.
-2, 3/5, 1
Let g(r) be the second derivative of -r**8/33600 + r**7/6300 - r**6/3600 - r**4/6 + 3*r. Let w(t) be the third derivative of g(t). Factor w(d).
-d*(d - 1)**2/5
Let d(j) be the third derivative of -j**5/30 + j**4/4 + 4*j**3/3 - 5*j**2. Find r such that d(r) = 0.
-1, 4
Let j(h) be the second derivative of h**4/48 + 5*h**3/24 - 3*h**2/4 - 21*h. Determine o, given that j(o) = 0.
-6, 1
Let f(i) = 5*i**2 - 34*i + 25. Let c(k) = -10*k**2 + 69*k - 50. Let a(z) = -4*c(z) - 9*f(z). What is d in a(d) = 0?
1, 5
Suppose -t + 5*t - 8 = 0. Suppose x = -t*x + 12. Factor -2*h**4 - 2*h**3 + 2*h**2 - h**x - h**2.
-h**2*(h + 1)*(3*h - 1)
Suppose -40 = -4*g - g. Suppose -3*s + f = -5, -f = -0*s - 4*s + g. Factor -v**2 + v**s - v**4 + 1 - 1 + v**3.
-v**2*(v - 1)**2
Suppose 12 = -8*q + 11*q. Suppose -1/3 + 1/3*g**5 + 1/3*g + 2/3*g**2 - 2/3*g**3 - 1/3*g**q = 0. What is g?
-1, 1
Let u(y) be the second derivative of -y**5/15 - y**4/9 + 2*y**3/9 + 2*y**2/3 - 9*y. Factor u(r).
-4*(r - 1)*(r + 1)**2/3
Let j be (-12)/(-18)*3/10. Let c(i) be the second derivative of 1/6*i**4 + 0*i**3 + 0*i**2 - j*i**5 + 1/15*i**6 + 4*i + 0. Factor c(q).
2*q**2*(q - 1)**2
Let w(g) be the third derivative of -g**6/480 - g**5/60 - 5*g**4/96 - g**3/12 - g**2. Factor w(x).
-(x + 1)**2*(x + 2)/4
Let d be (-3)/(-4)*(24/(-18) - -2). Factor d*y**4 - 1/2 - y**3 + 0*y**2 + y.
(y - 1)**3*(y + 1)/2
Let y(s) = -3*s**2 + s. Let v be y(-1). Let g(w) = 6*w**3 + 12*w**2 + 2*w. Let r(h) = -12*h**3 - 23*h**2 - 4*h. Let a(n) = v*r(n) - 7*g(n). Factor a(i).
2*i*(i + 1)*(3*i + 1)
Let d = 2 + -6. Let n be 12/(-28)*d/6. Suppose 2/7*z**2 + 0*z + n*z**4 + 4/7*z**3 + 0 = 0. What is z?
-1, 0
Let u be (2 - 6)*(-2)/4. Suppose -u*z - 8 = 0, 4*y - 20 = -0*z - z. Solve 14 - 2*h - 6*h**3 - 14 - 2*h**4 - y*h**2 = 0.
-1, 0
Let a(h) be the third derivative of 0*h**3 + 0 + 0*h - 6*h**2 + 1/144*h**4 - 1/120*h**5. Determine z, given that a(z) = 0.
0, 1/3
Find s, given that -2 + 8*s**3 + 4*s - 1 + 3 + 12*s**2 = 0.
-1, -1/2, 0
Suppose -5*x - 4*c = -0*c - 69, 2 = 2*c. Factor 20*z**2 + 13*z**3 + x*z**3 - z**3 + 4*z.
z*(5*z + 2)**2
Let r(t) = t**3 - 11*t**2 + 5*t + 8. Let c be r(10). Let g be (-28)/c*(-3)/(-4). What is d in -3/4*d**3 + 0 + 1/4*d + g*d**2 = 0?
-1/3, 0, 1
Let i(f) = -3*f**2 - 16*f - 12. Let g(q) = 6*q**2 + 33*q + 24. Let s(t) = -4*g(t) - 9*i(t). Solve s(j) = 0 for j.
-2
Suppose 0 = -5*d + 3*t + 15, d - 4*t - 6 = -d. Let m be (d - 0)*28/21. Let -8/3 - 1/3*j**3 - m*j - 2*j**2 = 0. Calculate j.
-2
Let y = -17 + 11. Let h = 8 + y. Factor -2/3*p**h + 8/3*p - 8/3.
-2*(p - 2)**2/3
What is p in -32/3*p - 10/3*p**3 - 34/3*p**2 - 8/3 = 0?
-2, -1, -2/5
Let p be ((-9)/(-6))/((-3)/(-6)). Factor 5*q**p + 9*q**2 + 27*q + 27 + 3*q**3 - 7*q**3.
(q + 3)**3
Suppose -3 - 7 = -5*z. Find s such that 5*s**2 + 12 + 16 + 12*s - 2*s**z - 16 = 0.
-2
Let v(q) = 3*q**2 - 44*q + 82. Let i(u) = -u**2 + 14*u - 27. Let w(k) = 14*i(k) + 4*v(k). Suppose w(a) = 0. Calculate a.
5
Let l(d) = 6*d**2 - d. Suppose 3*n - 3 = 12. Let j(y) = -2*y**2. Let i(u) = n*j(u) + 2*l(u). Let i(s) = 0. What is s?
0, 1
Let h(b) be the second derivative of -b**5/25 + b**4/60 - b. Suppose h(f) = 0. Calculate f.
0, 1/4
Let f be 438/(-36) - 2/(-12). Let i be (-7)/f - (-4)/(-12). Factor -1/2*x**3 + 3*x**4 + 9/4*x**5 + i*x - x**2 + 0.
x*(x + 1)**2*(3*x - 1)**2/4
Let w(u) be the second derivative of 3*u - 1/21*u**7 - 1/3*u**4 + 1/3*u**3 + 0*u**2 + 0 + 0*u**5 + 2/15*u**6. Factor w(f).
-2*f*(f - 1)**3*(f + 1)
Let h be (3 - 7)*(-3)/6. Let c(w) be the second derivative of 3/10*w**5 - 2*w + 0 + 1/15*w**6 + 0*w**h + 1/2*w**4 + 1/3*w**3. Find n such that c(n) = 0.
-1, 0
Let i be (0 - 6/10)/(3/(-30)). Let -24*m + 69*m**3 + 105/2*m**4 - 27/2*m**2 + i = 0. Calculate m.
-1, 2/7, 2/5
Suppose 9*z = 6*z + 12. Determine x so that -x**3 + 0 + 0*x + x**2 + 1/4*x**z = 0.
0, 2
Let r(a) be the third derivative of -a**5/30 + a**4/4 + 2*a**2 + 15. What is o in r(o) = 0?
0, 3
Let u = -2/305 + 353/7320. Let j(s) be the third derivative of 0 - 1/336*s**8 + 0*s**3 - u*s**4 + s**2 + 1/15*s**5 - 1/20*s**6 + 2/105*s**7 + 0*s. Factor j(l).
-l*(l - 1)**4
Let c(x) be the second derivative of 1/42*x**4 + 1/105*x**6 - 1/7*x**3 + 3/70*x**5 - 2/7*x**2 + 0 - 2*x. Solve c(w) = 0 for w.
-2, -1, 1
Let t(k) be the second derivative of 1/2*k**2 + 1/42*k**4 + 0*k**3 - k + 1/210*k**5 + 0. Let q(m) be the first derivative of t(m). Let q(p) = 0. Calculate p.
-2, 0
Let d(s) be the third derivative of s**6/320 - s**5/32 + s**4/8 - s**3/4 + 11*s**2. Determine i, given that d(i) = 0.
1, 2
Let y(i) be the second derivative of i**9/3024 - i**8/1680 - i**3/3 + 2*i. Let d(u) be the second derivative of y(u). Let d(m) = 0. What is m?
0, 1
Let l(o) be the first derivative of o**5/15 - o**4/6 - o**3/3 + 4*o**2/3 - 4*o/3 - 13. Factor l(j).
(j - 2)*(j - 1)**2*(j + 2)/3
Let f(s) be the second derivative of -s + 2/15*s**3 - 2/105*s**7 + 0*s**2 - 2/15*s**4 + 0*s**5 + 4/75*s**6 + 0. Factor f(u).
-4*u*(u - 1)**3*(u + 1)/5
Let f(y) = y**3 + y**2 + y + 5. Let a be f(0). Suppose -a*l - 3 + 23 = 0. Factor 0*k**2 + 0 + 0*k + 1/4*k**3 + 1/4*k**l.
k**3*(k + 1)/4
Factor -6/5*d**4 - 2/5 - 24/5*d**2 - 4*d**3 - 12/5*d.
-2*(d + 1)**3*(3*d + 1)/5
Let m(j) be the first derivative of -2 + 3/20*j**5 - j**3 + 0*j**2 - 1/4*j**4 - 4*j. Let c(y) be the first derivative of m(y). Let c(a) = 0. What is a?
-1, 0, 2
Suppose 0 = -p - 3*u + 2, -u - 8 = -4*p - 2*u. Suppose -3*q = p*q. Factor -1/2*w**4 + 0*w + 0*w**2 + q + 1/2*w**3.
-w**3*(w - 1)/2
Factor 0*g**4 - 2/9*g**5 - 2/9*g + 0 + 0*g**2 + 4/9*g**3.
-2*g*(g - 1)**2*(g + 1)**2/9
Let p be 4 + 96/(-20) + 1. Determine k so that -1/5*k**2 + 1/5*k - p*k**3 + 1/5 = 0.
-1, 1
Suppose 4*l + 1 = -g + 5, -4*g - 4 = -4*l. Find v such that 6*v**2 + 2 - 4*v + 1 - 4*v**2 - l = 0.
1
Let j(r) be the first derivative of -7*r**4/2 + 10*r**3/3 + 2*r**2 - 7. Factor j(f).
-2*f*(f - 1)*(7*f + 2)
Suppose 2/3*k**4 + 0*k**3 - 4/3*k**2 + 0*k + 2/3 = 0. What is k?
-1, 1
Suppose -b + 12 + 11 = -5*z, 5*z = -25. Let t be (-1)/b*(1 + 3). Factor -2*k**2 + 2*k**t - k**2.
-k**2
Factor 0*m**2 + 0*m + 5/2*m**4 + 0 + 0*m**3 - 5/2*m**5.
-5*m**4*(m - 1)/2
Let l(x) = 8*x**3 - 8*x**2 - 16*x. Let w(b) = -4*b**3 + 4*b**2 + 8*b. Let a(t) = -6*l(t) - 13*w(t). Factor a(r).
4*r*(r - 2)*(r + 1)
Let x(y) be the first derivative of y**4/2 - 8*y**3/3 + 12. Determine z so that x(z) = 0.
0, 4
Let d be -2 - (2 - 1 - -3). Let y be 52/48 + d/8. Find h such that -h**4 - h**3 + 0*h - 1/3*h**5 + 0 - y*h**2 = 0.
-1, 0
Factor 33*b + 6 + 123/8*b**2 + 15/8*b**3.
3*(b + 4)**2*(5*b + 1)/8
Factor 2*m**3 + 21*m + 34*m**2 - 8 - 44*m**2 - 5*m.
2*(m - 2)**2*(m - 1)
Determine g, given that 0*g**2 + 2/23*g**3 - 8/23*g + 0 = 0.
-2, 0, 2
Let i(r) be the first derivative of -5*r**4/2 + 56*r**3/3 - 33*r**2 - 36*r + 11. Determine p so that i(p) = 0.
-2/5, 3
Let q be (3/(-10))/((-27)/18). Let t(g) be the first derivative of -1 + 0*g - 3/5*g**2 - q*g**3. Find i such that t(i) = 0.
-2, 0
Let t = -354 + 2482/7. Suppose -2*o - 25 = -7*o + 3*q, 20 = 5*o - 2*q. Factor t*l**o - 2/7 - 2/7*l**4 + 0*l**3 + 0*l.
-2*(l - 1)**2*(l + 1)**2/7
Suppose 5*z - 3*z = 3*z. Let w(y) be the second derivative of 28/27*y**3 + z + 4/9*y**2 + 2*y + 49/54*y**4. Factor w(q).
2*(7*q + 2)**2/9
Let j(w) be the first derivative of w**4/16 - 3*w**2/8 + w/2 + 11. Factor j(t).
(t - 1)**2*(t + 2)/4
Let w = -1 - 3. Let x(f) = 15*f**2 - 15*f + 21. Let u(v) = 3*v**2 - 3*v + 4. Let t(d) = w*x(d) + 21*u(d). Let t(m) = 0. What is m?
0, 1
Let o be (20/75)/((-6)/176740). Let s = 7866 + o. Find y, given that -68/9*y**2 + s*y**3 + 160/9*y**4 - 40/9*y