or 0*g**2 + 4*g**4 + 2*g**t - 6*g**4.
-2*g**2*(g - 1)*(g + 1)
Let m = 24 - 27. Let x be m + 5 + -2 + 2. Suppose -1/3 - 1/3*w + 1/3*w**3 + 1/3*w**x = 0. What is w?
-1, 1
Let c be (-2)/10 + (-4692)/(-30). Let p = c - 155. Factor -p*h**3 - 6/5*h**2 - 2/5*h**4 + 0 - 2/5*h.
-2*h*(h + 1)**3/5
Let a(s) be the third derivative of -s**5/180 + s**4/72 + s**3/9 + 4*s**2. Factor a(l).
-(l - 2)*(l + 1)/3
Let u(y) be the third derivative of y**6/2160 - 5*y**3/6 - 3*y**2. Let q(a) be the first derivative of u(a). Let q(k) = 0. Calculate k.
0
Let u(v) = v - 11. Let d be u(8). Let n be (14/(-21))/(8/d). Solve 1/4 + n*k**2 - 1/2*k = 0.
1
Let r(b) = -2*b**2 - b + 1. Let t(i) = -i**2 - i. Suppose 5*o + 11 = 1. Let n(d) = o*r(d) + 3*t(d). Factor n(s).
(s - 2)*(s + 1)
Let k(p) be the first derivative of -2/3*p**3 + 0*p - 3 + 1/2*p**4 + 0*p**2. Factor k(m).
2*m**2*(m - 1)
Let q(t) be the second derivative of t**7/210 - 2*t**6/75 + t**5/25 + t**4/30 - t**3/6 + t**2/5 - 20*t. Factor q(z).
(z - 2)*(z - 1)**3*(z + 1)/5
Let u(a) = a**4 + 9*a**3 - 13*a**2 + 3*a. Let w(r) = -r**4 + r**2. Let t(x) = u(x) + 4*w(x). What is h in t(h) = 0?
0, 1
Let s(p) = p**2 + p. Let m(u) = -5*u**2 + 18*u - 121. Let q(k) = -m(k) - 4*s(k). Factor q(o).
(o - 11)**2
Let g = -1167 - -1169. Factor 2*z + 2/3*z**g + 0.
2*z*(z + 3)/3
Let n(f) = 9*f**2 - 8*f. Let s(j) = -4*j**2 + 4*j. Let q = 5 - 15. Let y(g) = q*s(g) - 4*n(g). Determine r, given that y(r) = 0.
0, 2
Let w(l) be the first derivative of 9*l**4/4 - 34*l**3/3 + 19*l**2/2 + 6*l + 43. Suppose w(x) = 0. What is x?
-2/9, 1, 3
Let y(d) be the third derivative of -d**7/630 + 7*d**6/180 - 49*d**5/180 - 29*d**2. Factor y(x).
-x**2*(x - 7)**2/3
Let k = -1/34 - -39/170. Factor 1/5*b - 1/5 + k*b**2 - 1/5*b**3.
-(b - 1)**2*(b + 1)/5
Let w(r) = -7*r**3 + 9*r**2 - 2*r + 9. Let g(m) = 3*m**3 - 4*m**2 + m - 4. Let c(d) = 9*g(d) + 4*w(d). Factor c(k).
-k*(k - 1)*(k + 1)
Let z = -2 - -4. Factor w**2 + 2*w + 7*w**2 - 10*w**z.
-2*w*(w - 1)
Factor 0*a**2 - 2/11*a**3 + 0 + 0*a.
-2*a**3/11
Let o(p) be the third derivative of -p**8/1176 - 4*p**7/735 - p**6/84 - p**5/105 + 8*p**2. Factor o(u).
-2*u**2*(u + 1)**2*(u + 2)/7
Let i be (-3)/(0 - -3)*0. Solve 0*q - 7*q**2 + i*q + 14*q**3 + 8*q**4 + 3*q**2 = 0 for q.
-2, 0, 1/4
Let s = -5 + 11. Let p be 9/7 + (5 - s). Solve 4/7*z - 2/7*z**2 - p = 0 for z.
1
Let x(y) be the first derivative of y**4/2 - 2*y**3 + 8*y - 18. Determine o, given that x(o) = 0.
-1, 2
Let p(m) be the second derivative of 0*m**5 + 3*m + 1/273*m**7 + 0*m**3 + 0 - 1/195*m**6 + 0*m**2 + 0*m**4. Factor p(z).
2*z**4*(z - 1)/13
Let z(j) = -j**3 - 3*j**2 - 5*j. Let l be z(-4). Solve -4*n - l*n**3 + 2*n**4 + 2 + 40*n**3 - 4*n**4 = 0.
-1, 1
Let l(c) = 8*c**3 - 2*c**2 - 6*c. Let q(t) = -7*t**3 + 2*t**2 + 5*t. Suppose 3*a + a + 24 = 0. Let x(n) = a*l(n) - 7*q(n). Factor x(r).
r*(r - 1)**2
Let t(x) be the second derivative of x**7/105 + 4*x**6/75 + 3*x**5/25 + 2*x**4/15 + x**3/15 - 6*x. Factor t(l).
2*l*(l + 1)**4/5
Suppose p + 7 = 23. Let b = p + -5. Factor -4*h**2 - 2*h**4 + h**4 - 6*h**3 + b*h**4.
2*h**2*(h - 1)*(5*h + 2)
Let t(s) be the third derivative of -s**8/560 + s**6/200 - 3*s**2. Find f such that t(f) = 0.
-1, 0, 1
Let v = 64 - 60. Let j = 2 + 1. Determine n so that v*n - n**2 + 4*n + j*n**2 + 8 = 0.
-2
Let l(y) be the second derivative of -4*y**6/15 + y**5/10 + 2*y**4/3 - y**3/3 + 63*y. Factor l(p).
-2*p*(p - 1)*(p + 1)*(4*p - 1)
Find f such that 0 - 1/5*f**4 - 3/5*f**2 - 1/5*f - 3/5*f**3 = 0.
-1, 0
Let w(l) be the first derivative of l**4/2 - 2*l**3/3 - l**2 + 2*l - 9. Factor w(k).
2*(k - 1)**2*(k + 1)
Let b(p) = -2*p**2 - 3*p - 4. Let s be b(4). Let d be (-3)/(-9) + 4/s. Factor -d*v**3 + 1/4*v + 0*v**2 + 0.
-v*(v - 1)*(v + 1)/4
Suppose -3*x - x + 32 = 0. Let r be 2/(-4)*(4 - x). Let -2*v + v + v**r + 0*v = 0. What is v?
0, 1
Let u = -143/1026 - -3/19. Let m(v) be the third derivative of u*v**4 - 2*v**2 - 1/270*v**5 + 0 - 1/27*v**3 + 0*v. Determine w so that m(w) = 0.
1
Let l(q) be the first derivative of -q**8/4200 + q**7/2100 - q**3 + 1. Let j(o) be the third derivative of l(o). Suppose j(c) = 0. Calculate c.
0, 1
Let c(i) be the second derivative of 0*i**2 - 1/3*i**4 + 1/3*i**3 - 5*i + 0 + 2/15*i**6 - 1/21*i**7 + 0*i**5. Factor c(s).
-2*s*(s - 1)**3*(s + 1)
Let g be (-90)/(-42) + 2/(-14). Suppose a - 6 = -g*a. Factor 1/4*y**5 + 3/4*y**4 + 0*y**a + 1/2*y**3 + 0 + 0*y.
y**3*(y + 1)*(y + 2)/4
Let c(a) = 2*a**2 - 11*a - 156. Let p be c(12). Determine t so that 2/7*t**3 + p + 6/7*t - 2/7*t**4 + 10/7*t**2 = 0.
-1, 0, 3
Suppose 5*v - 199 = c, 3*v - 4*c = 2*v + 36. Let l be (-2)/(-5) - v/(-50). Factor 0*i + 0 + l*i**3 + 4/5*i**2 - 2*i**4.
-2*i**2*(i - 1)*(5*i + 2)/5
Factor -18*s**3 + 27*s**5 - 28*s**2 + 15*s**4 - 8*s + 2*s**3 - 2*s**3 + 12*s**4.
s*(s - 1)*(3*s + 2)**3
Let v(c) be the first derivative of -16*c**6/7 - 432*c**5/35 - 339*c**4/14 - 150*c**3/7 - 54*c**2/7 + 1. Suppose v(b) = 0. Calculate b.
-2, -1, -3/4, 0
Let u be (-4)/14 - 30/(-7). Find f such that -2*f**4 + 2*f**4 + 0*f**3 + 14*f**3 - 6*f**5 - 4*f**u - 4*f**2 = 0.
-2, 0, 1/3, 1
Let i(m) = -m**3 + 7*m**2 + 1. Let s be i(7). Suppose 6*y**3 - 1 - 5*y**3 + y + s + 2*y**2 = 0. Calculate y.
-1, 0
Let f(q) = -89*q**3 + 55*q**2 + 49*q + 6. Let k(s) = -30*s**3 + 18*s**2 + 16*s + 2. Let d(u) = 2*f(u) - 7*k(u). Let d(z) = 0. What is z?
-1/4, 1
Let v(u) = -u. Let b(x) be the second derivative of x**4/6 + 5*x**3/3 + 6*x. Let c be (0 + -1)*(-2)/2. Let i(q) = c*b(q) + 12*v(q). Factor i(m).
2*m*(m - 1)
Factor 0 - 4/3*c**3 + 2/3*c**4 + 2/3*c**2 + 0*c.
2*c**2*(c - 1)**2/3
Let b(r) = 9*r**4 - 27*r**3 + 13*r**2 - 5*r + 3. Let c(h) = -9*h**4 + 28*h**3 - 13*h**2 + 6*h - 4. Let n(m) = -4*b(m) - 3*c(m). Factor n(p).
-p*(p - 2)*(3*p - 1)**2
Let s be ((-22)/(-33) - (-1)/(-1))*0. Factor -2/7*u**2 - 2/7*u**3 + s*u + 0.
-2*u**2*(u + 1)/7
Let d(b) be the first derivative of -b**4/10 - 2*b**3/15 + b**2 - 6*b/5 - 14. Factor d(u).
-2*(u - 1)**2*(u + 3)/5
Let b(c) be the third derivative of 0*c**4 + 0*c**3 + 0 + 0*c + 3*c**2 + 1/150*c**7 - 1/300*c**6 + 0*c**5. Suppose b(h) = 0. Calculate h.
0, 2/7
Let o be -2 - (-28)/(1 + 1). Let v(r) = -r**3 + 12*r**2 + 3. Let t be v(o). Let m**3 - 9*m**t + 2*m + 6*m**3 = 0. Calculate m.
-1, 0, 1
Let u(x) = 5*x. Let n be u(2). Let y(t) = t**3 - t**2 + t - 1. Let j(a) = 6*a**3 - 4*a**2 + 4*a - 6. Let f(z) = n*y(z) - 2*j(z). Factor f(h).
-2*(h - 1)*(h + 1)**2
Suppose -3*j = -6*j. Suppose j = -3*c - 2*b + 8, 0 = 3*c - 3*b - 0*b - 3. Factor 5/3*l**c + 4/3 - 4*l.
(l - 2)*(5*l - 2)/3
Factor 10*q**3 + 14 + 18*q**4 - 18*q + 6*q**2 - 16*q**4 - 14.
2*q*(q - 1)*(q + 3)**2
Let n(a) = 17*a**4 + a**3 - 18*a**2 - 37*a - 35. Let t(s) = -6*s**4 + 6*s**2 + 12*s + 12. Let u(c) = -4*n(c) - 11*t(c). Factor u(q).
-2*(q - 2)*(q + 1)**2*(q + 2)
Suppose 0 = -0*d - 4*d - 16. Let r = d + 6. Let b(x) = 2*x**3 + 9*x**2 - 3*x - 5. Let t(n) = -n**3 - 4*n**2 + n + 2. Let p(l) = r*b(l) + 5*t(l). Factor p(g).
-g*(g + 1)**2
Determine i so that -3/2*i**2 - 6 - 6*i = 0.
-2
Let i = 10 - 0. Let j be 4/i - 4/10. Factor 2*g**5 + 0*g**4 + 2*g**3 + j*g**3 - 4*g**4.
2*g**3*(g - 1)**2
Let h(i) = -i**3 + 4*i**2 + 5*i + 2. Let m be h(5). Let o be m/(-3) - (-11)/3. Factor 0*p**4 + 10*p**2 + 2*p**4 + 6*p**o - 4*p**2 + 2*p.
2*p*(p + 1)**3
Let h = 37 - 221/6. Let t(s) be the first derivative of -1 + 1/2*s + 1/2*s**2 + h*s**3. Suppose t(v) = 0. What is v?
-1
Let g = 7 + -5. Suppose 12 = -3*m - m, g*m = 5*z - 6. Find s such that 0*s + 1/2*s**3 + z*s**2 + 0 = 0.
0
Let k(t) be the second derivative of -4*t**7/21 - 8*t**6/15 - t**5/10 + 5*t**4/6 + t**3/3 - t**2 - 7*t. What is v in k(v) = 0?
-1, 1/2
Let f(x) be the first derivative of -2*x**3/3 + 8*x**2 - 30*x - 18. Let f(b) = 0. Calculate b.
3, 5
Factor 0 + 1/4*y**3 - 1/2*y**2 + 1/4*y.
y*(y - 1)**2/4
Factor 30*r**3 + 33*r + 251*r**4 - 242*r**4 + r**5 + 16 - 7 + 46*r**2.
(r + 1)**3*(r + 3)**2
Let t(w) be the third derivative of w**6/240 - w**5/120 - w**4/24 - 8*w**2. Determine d so that t(d) = 0.
-1, 0, 2
Let q be (-6)/54*3*-12. Let m(d) be the third derivative of -2*d**2 + 1/48*d**q + 0*d**3 + 0 - 7/240*d**5 - 3/160*d**6 + 0*d. Factor m(f).
-f*(f + 1)*(9*f - 2)/4
Let z(x) be the third derivative of 1/96*x**4 - 1/480*x**6 + 0 - 1/24*x**3 + 0*x + 2*x**2 + 1/240*x**5. Factor z(u).
-(u - 