 9*g**2 + n*g**3.
-3*g**2*(g - 3)
Let i = 2805/14 + -1999993/9982. Let z = 1412/4991 - i. Factor 0 + 0*h + z*h**2.
2*h**2/7
Let w(u) be the first derivative of -u**3/3 + u**2 + 11. Factor w(q).
-q*(q - 2)
Let t = -4 - -1. Let s be (-2 - t) + -1 + 2. Determine n, given that 0 - n - 1/2*n**s = 0.
-2, 0
Let h = -38 + 54. Suppose 5*u = 2*j - h, -7 = 3*j - 6*j - u. Factor -10*n + 2*n**2 + 2 + 13*n**2 - 6*n**j - n**2.
-2*(n - 1)**2*(3*n - 1)
Suppose 2*y - 8 = -4*t + 2, -4*t + 3*y + 5 = 0. Factor n**4 - n**t - 1/2*n + 1/2*n**3 + 0.
n*(n - 1)*(n + 1)*(2*n + 1)/2
Let u(o) be the first derivative of 2*o**3/3 + o**2 - 4*o - 6. Find c such that u(c) = 0.
-2, 1
Let j = -516973/7 - -73684. Let z = -169 - j. Factor 6/7*y**4 + 2/7*y**5 + 0*y + z*y**2 + 6/7*y**3 + 0.
2*y**2*(y + 1)**3/7
Suppose -3*n = 2*x - x - 82, 92 = 3*n - 4*x. Let v = 85/3 - n. Factor 0 + v*g + 1/3*g**2.
g*(g + 1)/3
Let w(u) be the third derivative of u**7/70 - u**6/20 + u**5/20 - 6*u**2. Factor w(m).
3*m**2*(m - 1)**2
Let x(a) be the second derivative of -a**5/90 + 2*a**4/27 - 4*a**3/27 - 6*a. What is n in x(n) = 0?
0, 2
Let q be 1/2 - 8/16. Let n(a) be the second derivative of -a**2 + 3*a - 1/15*a**6 + 1/3*a**4 + 0*a**5 + q*a**3 + 0. What is h in n(h) = 0?
-1, 1
Let v(j) = 4*j + 2. Let o(b) be the second derivative of -b + 1/6*b**3 + 1/2*b**2 + 1/12*b**4 + 0. Let p(y) = 2*o(y) - v(y). Factor p(m).
2*m*(m - 1)
Let s(z) be the second derivative of -z**4/66 - 2*z**3/33 + 6*z. Factor s(i).
-2*i*(i + 2)/11
Let v = 84 - 52. Factor -1 + v*a + 48*a**3 + 5 + 77*a**2 + 18*a**3 - 17*a**3.
(a + 1)*(7*a + 2)**2
Suppose 0 = -i - i. Let c(k) be the first derivative of 0*k + i*k**3 + 3 + 0*k**2 + 2/5*k**5 + 1/2*k**4. Solve c(a) = 0 for a.
-1, 0
Factor 0 - 3/7*g - 3/7*g**2.
-3*g*(g + 1)/7
Suppose 6 = 7*m - 4*m. Factor -6/7*p - 2/7 - 6/7*p**m - 2/7*p**3.
-2*(p + 1)**3/7
Let s be ((-5)/(-2))/(25/50). Let k(d) be the third derivative of 1/300*d**s + 0 + 0*d + 1/30*d**4 + 4*d**2 + 2/15*d**3. Let k(v) = 0. What is v?
-2
Let a be (-4)/(-26) + 72/39. Let x(o) = -o**3 + 3*o**2 + 4*o + 2. Let y be x(4). Suppose 0 - h**y - a*h + 0 = 0. What is h?
-2, 0
Factor -5/4*n - 1 - 1/4*n**2.
-(n + 1)*(n + 4)/4
Factor -5*v**3 + 39*v**4 + 8*v - v**2 - 3 - 1 + v**5 - 38*v**4.
(v - 1)**3*(v + 2)**2
Let o(f) be the first derivative of -f**7/4620 + f**6/990 - f**5/660 + 5*f**3/3 - 4. Let u(r) be the third derivative of o(r). Find q such that u(q) = 0.
0, 1
Let g(b) = 2*b**3 - b**2 + b - 4. Let n(y) = y**3 + 1. Let f(q) = g(q) - 3*n(q). Let u(m) be the first derivative of f(m). Factor u(d).
-(d + 1)*(3*d - 1)
Let l = 37/50 - -1/100. Let y = 0 - 0. Factor -1/4*u**5 + 0*u - 3/4*u**4 - 1/4*u**2 - l*u**3 + y.
-u**2*(u + 1)**3/4
Let s(z) be the first derivative of 2*z**6/9 + 4*z**5/5 + 2*z**4/3 - 8*z**3/9 - 2*z**2 - 4*z/3 - 8. Factor s(u).
4*(u - 1)*(u + 1)**4/3
Suppose 0 = j + h - 7, -h + 0*h - 41 = -5*j. Let d = -2 - -4. Solve j*n**2 + 0 + 16*n**d + 16*n + 2 + 8*n**2 = 0.
-1/4
Let n(c) be the second derivative of -7*c**6/36 - 31*c**5/60 - c**4/2 - 7*c**3/6 - 8*c. Let q(p) be the second derivative of n(p). Let q(b) = 0. What is b?
-3/5, -2/7
Let s(f) = 3*f**2 - 3*f. Let j(c) be the second derivative of c**4/4 - c**3/2 - 4*c. Let d(i) = -3*j(i) + 4*s(i). Factor d(k).
3*k*(k - 1)
Let p(s) be the first derivative of 3/2*s**4 + 3/5*s**5 + 0*s + 0*s**2 - 1 + s**3. Factor p(t).
3*t**2*(t + 1)**2
Let y(n) = 7*n**2 + 23 - 21*n - 5*n**2 + 4 + 5*n**2. Let j(w) = 4*w**2 - 11*w + 13. Let d(r) = 10*j(r) - 6*y(r). Determine i so that d(i) = 0.
4
Let z = 94/3 + -458/15. Let c(p) = p**3 - 6*p**2 - p + 6. Let j be c(6). Determine v, given that -2/5*v - 2/5*v**3 - z*v**2 + j = 0.
-1, 0
Let t(s) = -s**2 - 3*s + 1. Let h(d) = 1. Let l = -9 - -12. Let c(y) = l*h(y) - t(y). Factor c(n).
(n + 1)*(n + 2)
Factor -102*u**3 - 2*u**5 + 102*u**3 - 8*u**4.
-2*u**4*(u + 4)
Suppose 0*y = 5*y - 5, 0 = -3*m - 2*y - 4. Let k = 0 - m. Solve -5*r - k + r**3 + 0 + 2*r**2 + 4*r**3 = 0.
-1, -2/5, 1
Let v(i) be the first derivative of 1 + 0*i**3 - 1/12*i**4 + 1/6*i**2 + 0*i. Factor v(o).
-o*(o - 1)*(o + 1)/3
Suppose 35 + 1 = 12*b. Let k(d) be the third derivative of 1/360*d**5 + 0*d + 0 - 1/144*d**4 - 3*d**2 + 0*d**b. Factor k(g).
g*(g - 1)/6
Let v(u) = -u**2 - 5*u + 2. Let s be v(-5). What is x in x**3 - 2*x**2 - s*x**5 + 21*x**4 + x**3 - 19*x**4 = 0?
-1, 0, 1
Let o be (-12)/12*(-1 + 1). Let b(v) be the third derivative of 0*v**3 + 0*v**5 + 1/105*v**7 - 2*v**2 - 1/60*v**6 + 0*v + o + 0*v**4. Let b(g) = 0. Calculate g.
0, 1
Let n(q) be the third derivative of -q**6/60 - 7*q**5/90 + q**4/6 + 6*q**2. Find w, given that n(w) = 0.
-3, 0, 2/3
Let c(w) = 2*w**3 + 32*w**2 - 16*w. Let d(z) = -z**3 - 11*z**2 + 5*z. Let a(o) = 3*c(o) + 8*d(o). Solve a(x) = 0 for x.
0, 2
Let o(i) be the third derivative of 0 + 2/21*i**3 + 3*i**2 + 1/28*i**4 + 0*i + 1/210*i**5. Let o(m) = 0. What is m?
-2, -1
Let c(u) be the third derivative of -u**2 + 0 + 0*u**4 + 1/27*u**3 - 1/270*u**5 + 0*u. Solve c(f) = 0.
-1, 1
Factor -3*y**3 + y - 2*y + 0*y - 1 + 5*y**2.
-(y - 1)**2*(3*y + 1)
Let i(o) be the first derivative of -o**5/40 - o**4/8 + o**2 + 6*o - 1. Let v(q) be the first derivative of i(q). What is d in v(d) = 0?
-2, 1
Let p(k) = k**4 + k + 1. Let j(v) = -8*v**4 + 3*v**3 + 3*v**2 - 8*v - 5. Let o(t) = j(t) + 5*p(t). Let o(l) = 0. What is l?
-1, 0, 1
Let o be (2 - (-1 + 4))*-5. Solve o*u**2 + u - 3*u**2 - u**2 = 0 for u.
-1, 0
Let p(n) = -2*n**5 - 2*n**3 + 3*n**2 - 5*n - 3. Let q(w) = w**5 + w**4 + w**3 - 3*w**2 + 4*w + 2. Let g(l) = 4*p(l) + 6*q(l). Determine v, given that g(v) = 0.
-1, 0, 1, 2
Let m(v) be the third derivative of v**7/70 + 7*v**6/120 + v**5/12 + v**4/24 + 4*v**2. Factor m(c).
c*(c + 1)**2*(3*c + 1)
Suppose -3*f + 3*l = 0, 4*f + 2*l = 3*l + 9. Let r(v) be the first derivative of 31/6*v**f + v + 15/4*v**2 + 3 + 3/2*v**4. Let r(i) = 0. Calculate i.
-2, -1/3, -1/4
Let z = 150 - 102. Let i be 4 + (-6)/(z/20). Factor 3/4*y**2 + 3/4 + i*y.
3*(y + 1)**2/4
Let n(d) be the first derivative of -49*d**6/10 + 21*d**5/2 + 3*d**4/4 - 10*d**3 - 6*d**2 - 4*d - 1. Let r(m) be the first derivative of n(m). Factor r(b).
-3*(b - 1)**2*(7*b + 2)**2
Let h(v) be the third derivative of 0 + 1/60*v**5 + 1/2*v**3 + 0*v - 1/6*v**4 - 6*v**2. Factor h(r).
(r - 3)*(r - 1)
Let u = 89 + -1067/12. Let m(t) be the first derivative of t - 1 + u*t**3 - 1/2*t**2. Suppose m(k) = 0. What is k?
2
Let d = 10 + -7. Let q(w) be the third derivative of 0 - w**2 - 1/672*w**8 + 0*w + 1/120*w**5 + 1/240*w**6 - 1/420*w**7 + 0*w**4 + 0*w**d. Factor q(v).
-v**2*(v - 1)*(v + 1)**2/2
Suppose 5*i = -0*i. Suppose i = 2*t - 7*t - k + 11, 5*t - 5*k = 5. Factor 1 - d**t - d - 3 - 2*d.
-(d + 1)*(d + 2)
Let a = -11 + 22. Let m = -9 + a. Factor 0 - 5/3*n**m - 2/3*n.
-n*(5*n + 2)/3
Suppose 5*m - 24 = m. Let c(g) be the first derivative of 0*g - 2 + 1/9*g**m + 0*g**3 + 0*g**4 + 0*g**2 + 2/15*g**5. Determine q, given that c(q) = 0.
-1, 0
Solve 16*n**2 - 2 + 4*n**3 - 8*n**3 + 2 = 0.
0, 4
Let m(t) = -3*t - 36. Let h be m(-13). Factor 2/7*r**h + 2/7*r**4 - 4/7*r**2 + 0 + 0*r.
2*r**2*(r - 1)*(r + 2)/7
Let s(j) = 5*j**2 - 1. Let x be s(-1). Suppose x*q - 15 - 1 = 0. Suppose 0 + u**5 + 6*u**3 - q*u**4 - 4*u**2 + u + 0 = 0. What is u?
0, 1
Let r(g) be the first derivative of -g**5/25 + 11*g**4/60 - g**3/6 - g**2/5 + 2*g - 4. Let l(t) be the first derivative of r(t). Factor l(w).
-(w - 2)*(w - 1)*(4*w + 1)/5
Let y(g) be the second derivative of g**4/6 + g**3 + 2*g**2 - 27*g. Factor y(n).
2*(n + 1)*(n + 2)
Let c = -3 - -6. Suppose w = -c*p + 17 - 0, 26 = 5*p + 4*w. Let 2*d**3 + 0 + 6*d + p*d**2 + 1 + 1 = 0. What is d?
-1
Let z(y) = -5*y - 1. Let h be z(-1). Solve 3*v - 2*v**2 - h + 2 - 3*v**3 + 8*v**2 - 4 = 0.
-1, 1, 2
Factor 0 + 9/5*s**3 - 3/5*s + 6/5*s**2.
3*s*(s + 1)*(3*s - 1)/5
Let w(x) be the first derivative of x**4/14 + 2*x**3/7 - 8*x/7 - 15. Factor w(v).
2*(v - 1)*(v + 2)**2/7
Let n(t) be the first derivative of 0*t**3 + 1/6*t**2 + 1 - t - 1/36*t**4. Let d(c) be the first derivative of n(c). Let d(x) = 0. What is x?
-1, 1
Suppose 6 = -0*t + 2*t. Find l such that -t*l**3 + 2*l**3 + 5*l**2 + 32*l**5 + 16*l**4 - 13*l**3 - 3*l**2 = 0.
-1, 0, 1/4
Let r(k) = -k**3 - 6*k**2 - k - 4. Let b be r(-6). Suppose b - 4 = -q. Let 4*o**4 - o**2 + o + 9*o**3 