actor h(a).
3*(a - 1)**2*(4*a - 1)
Suppose 3/7*p - 6/7*p**3 + 3/7*p**5 + 0*p**2 + 0 + 0*p**4 = 0. Calculate p.
-1, 0, 1
Let w(t) = -t**3 + 5*t**2 + 7*t - 7. Let b be w(6). Let k be (7/(-21))/(b/9). Factor 4*z**k + z**2 - 5*z**2 - 2*z**3.
2*z**2*(z - 2)
Let u(l) = -l**4 + l**3 - 3*l**2 - l. Suppose -6 = 5*d - 41. Let x(r) = r**4 - r**3 + 6*r**2 + r. Let p(t) = d*u(t) + 4*x(t). Factor p(i).
-3*i*(i - 1)**2*(i + 1)
Solve -4*f**5 + 12*f**2 - 12*f**4 + 3*f**5 - 11*f**3 + 8*f + 7*f**3 - 3*f**5 = 0 for f.
-2, -1, 0, 1
Suppose 0*u + 7*u + 9*u = 0. Factor u*d + 0 + 6/7*d**3 - 27/7*d**4 + 0*d**2.
-3*d**3*(9*d - 2)/7
Factor 4/3*u**2 - 4/3*u + u**3 + 0.
u*(u + 2)*(3*u - 2)/3
Suppose 2*g - 4*l - 12 = 0, -18 = -3*g - 2*l - 0*l. Find v such that 3*v - 9*v**3 + g - 6 - 6*v**4 = 0.
-1, 0, 1/2
Solve 0 + 1/2*u**2 + 3*u = 0.
-6, 0
Let i(v) be the second derivative of v**7/168 + v**6/30 + 3*v**5/40 + v**4/12 + v**3/24 + 8*v. Factor i(j).
j*(j + 1)**4/4
Let g(s) = -10*s**3 + 5*s**2 + 15*s + 15. Let f(o) = -o**3 + o + 1. Let d(c) = -15*f(c) + g(c). Factor d(r).
5*r**2*(r + 1)
Let m(q) be the first derivative of q**4/4 + 2*q**3/3 - q**2/2 - 2*q - 4. Factor m(o).
(o - 1)*(o + 1)*(o + 2)
Let r be 8/(-3)*6/(-4). Suppose -4*k = -2*k - r. Find x, given that x - k*x**2 + x + 2*x - 2 + 0*x = 0.
1
Let u = -36 + 34. Let x(g) = -2 + 4*g + 2 + 23*g**2 + 15*g**3. Let h(w) = 105*w**3 + 162*w**2 + 27*w. Let p(q) = u*h(q) + 15*x(q). Factor p(y).
3*y*(y + 1)*(5*y + 2)
Determine o so that -3*o**4 + 50*o - 180*o**2 - 61*o**3 - 21*o**3 + 4*o**3 - 5*o**4 = 0.
-5, 0, 1/4
Let a(q) = 33*q**3 - 33*q**2 - 3*q - 21. Let p(v) = -2*v - 8*v**3 + 2*v**2 + 8*v**2 + 3*v + 5 - 2*v**2. Let k(o) = 5*a(o) + 21*p(o). Factor k(u).
-3*u*(u - 2)*(u + 1)
Let m = 6 - 1. Suppose -4*f - 3 = -m*f. Determine z so that -1 - f + z**2 + z + 2 = 0.
-2, 1
Let s = 14 - 11. Let d(a) be the first derivative of -1/3*a**s + 1/2*a**2 - 3 + 0*a. Factor d(p).
-p*(p - 1)
Let r(k) be the first derivative of -70*k**5 - 45*k**4 + 8*k**3 + 8*k**2 - 2. Factor r(g).
-2*g*(5*g + 2)**2*(7*g - 2)
Suppose -6 + 10 = 2*z. Factor -2*w**4 + 2*w**3 + w - w**2 + w**z - 5*w**3.
-w*(w + 1)**2*(2*w - 1)
Let y(i) = -i**2 - 11*i - 6. Let u be y(-10). Suppose 3*l + 17 = -0*c + 2*c, u*c - 4 = -4*l. Factor 2*m + 5*m**2 + 4*m**2 - c*m - 3*m**2.
2*m*(3*m - 1)
Suppose 4*t = -5*q + 53, 3*q = -2*t + 7*q - 6. Let o(f) = -f**3 - f**2. Let k(v) = -v**3 - v**2. Let r(n) = t*k(n) - 6*o(n). Factor r(s).
-s**2*(s + 1)
Let o be ((-3)/((-315)/(-10)))/(2/(-6)). Factor -8/7*u + 0 - 8/7*u**2 - o*u**3.
-2*u*(u + 2)**2/7
Factor -4*b + 11*b**2 - 5 - b**2 - 8*b**3 + 5 + 2*b**4.
2*b*(b - 2)*(b - 1)**2
Factor -7/2*b + 0 - 1/2*b**2.
-b*(b + 7)/2
Let u = -5 - -10. Let y(m) be the first derivative of 0*m + 0*m**2 - 2/3*m**3 + 1/2*m**4 + 2/5*m**u - 1 - 1/3*m**6. Factor y(k).
-2*k**2*(k - 1)**2*(k + 1)
Let f(l) = -l - 2. Let y be f(-6). Suppose 9 + 11 = 5*k. Find g, given that 40*g**y - 6*g**3 - k*g**2 + g - g = 0.
-1/4, 0, 2/5
Factor 0 - k**4 + 1/2*k + k**2 + 0*k**3 - 1/2*k**5.
-k*(k - 1)*(k + 1)**3/2
Factor -5*a - 3/2*a**2 + 0 + 1/2*a**3.
a*(a - 5)*(a + 2)/2
Let b(r) be the first derivative of -r**5/300 + r**3/30 + 3*r**2/2 + 1. Let l(u) be the second derivative of b(u). Factor l(v).
-(v - 1)*(v + 1)/5
Factor -30*j**2 + 20*j + 10*j**2 + j**3 + 20*j - 11*j**3 + 5*j**4.
5*j*(j - 2)**2*(j + 2)
Let f(j) be the first derivative of -2*j**5/55 + 7*j**4/11 - 98*j**3/33 - 33. Factor f(k).
-2*k**2*(k - 7)**2/11
Let u(r) = -r**2 + 6*r + 7. Let f be u(7). Factor -l + f*l + 2*l**3 - 2*l**5 + l.
-2*l**3*(l - 1)*(l + 1)
Suppose 0*r = -3*r. Suppose -4*x = -x + 5*y - 12, r = -4*x - 4*y + 16. Solve 15/2*l**x - 1/2*l**3 + 0 + 0*l - l**2 = 0.
-1/3, 0, 2/5
Suppose 3*p = -5*s + 3, -5*s = -4*p + 1 + 3. Suppose -g + s*g = 0. Factor 3*z + 4*z**2 + g*z**2 - 2*z**3 - 5*z.
-2*z*(z - 1)**2
Suppose -g = -2*c + 2, 3*c - 3*g = 2*g - 4. Let k(y) be the third derivative of 4/3*y**3 + 0*y + 49/120*y**6 + 21/10*y**5 + 0 + 5/2*y**4 + y**c. Factor k(d).
(d + 2)*(7*d + 2)**2
Let g = 215/4 + -1497/28. Determine w, given that 2/7*w - g*w**3 + 2/7 - 2/7*w**2 = 0.
-1, 1
Let x be 21/5 - 2/10. Let f be x/(-6)*12/(-16). Determine y, given that 0*y + 1/2*y**2 - y**3 + 0 + f*y**4 = 0.
0, 1
Let f(d) be the second derivative of -d**4/24 - d. Factor f(h).
-h**2/2
Suppose 0 = 3*j - 4 - 11. Suppose -3*i + 5*g = 35 - 10, i - 25 = -j*g. Factor i + 2/5*c**2 + 2/5*c.
2*c*(c + 1)/5
Let k(l) be the first derivative of -2*l**3/15 + 20. Factor k(p).
-2*p**2/5
Determine k, given that -k**2 - 1/5*k**4 + 0 - 2/5*k - 4/5*k**3 = 0.
-2, -1, 0
Let u be 112/24 + 1*-4. Let 0 + u*h**2 + 2/3*h = 0. What is h?
-1, 0
Suppose -2 + 17 = 5*n. Factor -n - l + 1 + 2 - l**2.
-l*(l + 1)
Suppose -7*u = 4*u. Let b(x) be the third derivative of -1/36*x**4 - 1/180*x**5 + u*x + 0 - x**2 + 0*x**3. Suppose b(y) = 0. Calculate y.
-2, 0
Let a(l) be the second derivative of l**6/80 - l**5/20 + 2*l**2 + l. Let j(i) be the first derivative of a(i). Solve j(o) = 0.
0, 2
Factor -7/2*a**2 + 0 + a.
-a*(7*a - 2)/2
Determine f so that 25*f**2 + 5*f**3 - 40*f - 10*f**2 - 5*f + 25 = 0.
-5, 1
Let o(j) be the first derivative of -j**4/14 - 8*j**3/21 - 3*j**2/7 - 9. Factor o(i).
-2*i*(i + 1)*(i + 3)/7
Let d(u) be the first derivative of -49/5*u**3 + 7 - 48/5*u - 84/5*u**2. Suppose d(i) = 0. What is i?
-4/7
Factor 2*h + 13/2*h**3 - 6*h**2 + 0 + 1/2*h**5 - 3*h**4.
h*(h - 2)**2*(h - 1)**2/2
Let k = 691/10 + -69. Let s(j) be the second derivative of -3/2*j**4 - 2*j + 0 - 27*j**2 - 9*j**3 - k*j**5. Factor s(u).
-2*(u + 3)**3
Let i(d) be the third derivative of d**7/1470 - d**6/420 + d**4/84 - d**3/42 + 16*d**2. Determine w, given that i(w) = 0.
-1, 1
Let y(w) = w**4 - w**2 - 1. Let s(l) = 2*l**4 + 40*l**3 - 106*l**2 - 6. Let v(h) = -s(h) + 6*y(h). Determine k so that v(k) = 0.
0, 5
Solve 3/5*o**4 + 12/5*o - 6/5*o**3 - 9/5*o**2 + 12/5 = 0 for o.
-1, 2
Suppose 5*h = o + 23, -4*h - 5*o + 9 = 8. Factor -6/17*r - 6/17*r**h + 4/17*r**2 + 2/17*r**5 + 4/17*r**3 + 2/17.
2*(r - 1)**4*(r + 1)/17
Let m(v) = -2*v**2 + 7*v + 1. Let a(t) = -3*t**2 + 7*t. Let c(i) = 3*a(i) - 2*m(i). Find n, given that c(n) = 0.
2/5, 1
Suppose s**3 + 0 + 5/4*s**2 + 1/2*s + 1/4*s**4 = 0. Calculate s.
-2, -1, 0
Suppose 2*d - 3*z - 12 = -d, -20 = -2*d - 4*z. Find s such that s**2 + 0*s**2 + s**2 + d*s**3 + 2*s**4 + 2*s**2 = 0.
-2, -1, 0
Let g be -1 + 0 - (-5 - 1). Suppose -5*n - 85 = -g*x, -2*x - 4*n = 8 - 36. Factor -q**5 - 3 + 1 + 0 - 9*q - 6*q**4 - 14*q**3 - x*q**2.
-(q + 1)**4*(q + 2)
Let w(b) be the second derivative of b**4/60 - 2*b**2/5 + 7*b. Solve w(m) = 0.
-2, 2
Let l(m) be the first derivative of 4*m**5/5 - 4*m**3/3 + 7. Factor l(s).
4*s**2*(s - 1)*(s + 1)
Let g(j) = j**3 - 10*j**2 + j - 7. Let c be g(10). Suppose 10*s**5 - 8*s**4 - 64*s**2 - 4 - 36*s**4 - 5*s + 31*s + 76*s**c = 0. Calculate s.
2/5, 1
Let q(p) be the first derivative of -p**6/30 + p**4/10 - p**2/10 - 7. Find t, given that q(t) = 0.
-1, 0, 1
Let m(u) be the second derivative of 49*u**5/10 + 77*u**4/6 + 32*u**3/3 + 4*u**2 - 4*u. Factor m(r).
2*(r + 1)*(7*r + 2)**2
Let k(p) = p**2 + 3*p - 13. Let r be k(-6). Let u(b) = 3*b**4 + 3*b**3 + 2*b**2. Let x(c) = 4*c**4 + 3*c**3 + 3*c**2. Let a(v) = r*u(v) - 4*x(v). Factor a(s).
-s**2*(s - 2)*(s - 1)
Factor -17/8*o - 2*o**3 - 1/4 - 5*o**2.
-(o + 2)*(4*o + 1)**2/8
Find m such that -14/9*m + 2/9*m**2 + 4/3 = 0.
1, 6
Let b(f) = -4*f**3 + 5*f**2 + f - 5. Let z(v) = -12*v**3 + 14*v**2 + 2*v - 14. Let u(x) = 10*b(x) - 3*z(x). Factor u(o).
-4*(o - 2)*(o - 1)*(o + 1)
Suppose 8*h - 3*h - 15 = 0. Factor -2*j**2 - 2*j**h - 2*j + 4*j + 0*j + 2.
-2*(j - 1)*(j + 1)**2
Let c(g) be the first derivative of 2*g**3/21 - g**2/7 - 4*g/7 + 28. Factor c(z).
2*(z - 2)*(z + 1)/7
Let o(g) be the first derivative of 0*g + g**2 + 3 + 1/3*g**3. Factor o(v).
v*(v + 2)
Let b(c) be the second derivative of 0 + 1/6*c**3 - 1/24*c**4 + 0*c**5 - 2*c + 0*c**2 + 1/360*c**6. Let l(y) be the second derivative of b(y). Factor l(h).
(h - 1)*(h + 1)
Suppose -3*h + 4 = q, -5*h + 4*h = -2*q - 13. Determine o, given that -o + h + o**2 - o**3 - 4 + 2*o**3 = 0.
-1, 1
Let x be 14/8 + (-3)/(-12). Suppose -3*c = x*c - 25. Factor 5*v**c + 3*v**5 + 8*v**4 + v**3 - 2*v**2 - 3*v**5.
v**2*(v + 1)**2*(5*v - 2)
Let c(w) be the third derivative of -1/525