 1
Let v(y) = -y**3 - 2*y**2 - 7*y - 6. Let s = -1 - -10. Let o be -1 + s + 1*-2. Let d(p) = p**3 + 2*p**2 + 8*p + 7. Let j(c) = o*d(c) + 7*v(c). Factor j(t).
-t*(t + 1)**2
Let o(p) be the second derivative of -p**7/14 + p**6/25 + 3*p**5/10 - p**4/5 - p**3/2 + 3*p**2/5 - 5*p. Suppose o(u) = 0. What is u?
-1, 2/5, 1
Suppose w - 4 = -5*p, -3*p - 5*w = -2*p - 20. Factor -8*j**3 + 8*j**2 + 4*j + p*j**4 + j**4 - 5 + 1 - 5*j**4 + 4*j**5.
4*(j - 1)**3*(j + 1)**2
Let v be ((-14)/(-6) + -3)*-3. Let s be 3/18 - v/(-6). Solve -u**3 + s*u**4 + 0*u + 1/2*u**2 + 0 = 0 for u.
0, 1
Let y(u) be the third derivative of 0 - 7/3*u**4 - 5/12*u**6 - 1/168*u**8 + 8/105*u**7 + 8/3*u**3 + 19/15*u**5 - 3*u**2 + 0*u. Factor y(s).
-2*(s - 2)**3*(s - 1)**2
Let b(l) = -2*l + 6. Let i(t) = 2*t - 5. Let w(p) = 3*b(p) + 4*i(p). Let a be w(3). Let -x**a + 2*x**3 + 0*x**3 + 2*x - 7*x**2 + 4*x**4 = 0. What is x?
-2, 0, 1/3, 1
Find b such that -3/5*b**2 + 3/5 + 0*b = 0.
-1, 1
Let 4*q**2 + 1/2*q + 5/2*q**3 - 1 = 0. Calculate q.
-1, 2/5
Let m be (3*1/(-30))/(-4). Let x(p) be the second derivative of -1/20*p**6 + 0 + 1/12*p**3 + 1/8*p**4 - m*p**5 + 0*p**2 + 2*p. Solve x(f) = 0 for f.
-1, -1/3, 0, 1
Let s be (-2)/4 + 2/4. Let c be 25/10 + (-2 - s). Factor 1/4 - 1/4*z**5 + 1/4*z**4 - 1/4*z + 1/2*z**3 - c*z**2.
-(z - 1)**3*(z + 1)**2/4
Let f = -1/49315 - -29096297/22043805. Let w = f + 2/149. Factor w*m**2 + 0*m + 0*m**3 - 2/3 - 2/3*m**4.
-2*(m - 1)**2*(m + 1)**2/3
Let n be 1/2 + (-1)/(-2). Let k be 4/((-12)/(-15)) - n. Factor -2*v**2 - 2*v**4 - k*v**5 + 5*v**4 + 3*v**4.
-2*v**2*(v - 1)**2*(2*v + 1)
Let o(l) be the first derivative of 0*l + 0*l**2 - 1/6*l**6 + 1/4*l**4 - 1/3*l**3 - 4 + 1/5*l**5. Factor o(p).
-p**2*(p - 1)**2*(p + 1)
Let x be 12/14*(-1 + -20). Let h = 30 + x. Suppose 5*i**5 - i**3 + 3*i**2 + 10*i**3 - i**2 + h*i**4 = 0. What is i?
-1, -2/5, 0
Let v be -2 + 165/72 - 11/44. Let n(q) be the third derivative of q**2 + 0*q + v*q**4 - 1/90*q**5 + 0 - 1/18*q**3. Solve n(f) = 0 for f.
1/2, 1
Suppose -2*g - 3*r = -9, 0 = 5*g + 4*r - 8 - 11. Factor 4/7*j**2 + 0 + 6/7*j**g - 2/7*j**5 + 0*j**4 + 0*j.
-2*j**2*(j - 2)*(j + 1)**2/7
Suppose -14 = -4*c - 14. Let b(g) be the second derivative of 1/48*g**4 - 2*g + 0 + c*g**3 + 0*g**2. Let b(k) = 0. What is k?
0
Let a(w) be the first derivative of 0*w - 1/5*w**3 + 2 - 3/10*w**2. Factor a(t).
-3*t*(t + 1)/5
Suppose -6*v + 0*v + 24 = 0. Find n, given that 0 - 3/5*n**5 + 0*n + 0*n**3 + 3/5*n**v + 0*n**2 = 0.
0, 1
Let u = -10 - -13. Suppose 6*k**2 + 0*k**3 + 6*k + 2 + k**3 + 4*k**3 - u*k**3 = 0. What is k?
-1
Let f(a) = -46*a**2 - 3 + 19*a + 0 + 15*a - 17. Let b(l) = 9*l**2 - 7*l + 4. Let p(u) = 16*b(u) + 3*f(u). Solve p(o) = 0.
2/3, 1
Let j(w) be the first derivative of 3/10*w**4 + 2/25*w**5 - 2 + 1/5*w**2 + 0*w + 2/5*w**3. Solve j(i) = 0 for i.
-1, 0
Let m be 2 - (-2)/4*-2. Let w be 3*m - 25/10. Solve 1/2 + w*f**5 + 5*f**3 + 5/2*f**4 + 5/2*f + 5*f**2 = 0 for f.
-1
Let z(b) be the second derivative of -b**7/6300 - b**6/1800 + b**5/150 - b**4/2 - 2*b. Let l(f) be the third derivative of z(f). Factor l(n).
-2*(n - 1)*(n + 2)/5
Let g = 16 - 9. Let l = -5 + g. Determine v, given that v + v**3 - v + l*v**2 + v = 0.
-1, 0
Let h(o) be the second derivative of -o**7/189 + 2*o**5/45 + 2*o - 6. Solve h(q) = 0 for q.
-2, 0, 2
Let x(k) be the second derivative of k**3/6 + k**2/2 - 2*k. Let m be x(4). Factor -5*t + t**3 + t**2 + m*t.
t**2*(t + 1)
Let a = 6 - 4. Factor a*b**4 - 5*b**4 - 91*b**2 - 3*b**3 + 97*b**2.
-3*b**2*(b - 1)*(b + 2)
Let a(k) be the third derivative of 0*k**3 + 1/90*k**5 + 2*k**2 - 1/120*k**6 + 0 + 1/72*k**4 + 0*k. Solve a(v) = 0.
-1/3, 0, 1
Solve 72/7 - 2/7*g**3 - 22/7*g**2 - 48/7*g = 0 for g.
-6, 1
Suppose 2*j + j = 5*m - 28, -4*m = 5*j + 96. Let w be j/72 + (-37)/(-45). Factor 6/5*u**3 + w*u**5 + 3/5 - 9/5*u**4 - 9/5*u + 6/5*u**2.
3*(u - 1)**4*(u + 1)/5
Suppose -2*v - x = 2*x - 3, 3*x = -v. Factor -3/2*d**5 + 0*d - 3/2*d**2 + 0 + 3/2*d**4 + 3/2*d**v.
-3*d**2*(d - 1)**2*(d + 1)/2
Let w(p) be the first derivative of -3*p**8/2240 - p**7/1120 - 2*p**3 + 5. Let n(t) be the third derivative of w(t). Suppose n(u) = 0. Calculate u.
-1/3, 0
Let t be 14/(-35) + 12/5. Let 0*j + 7*j - 3*j + 3*j**2 - j**t = 0. What is j?
-2, 0
Determine b so that 2/7*b + 0 + 2/7*b**2 = 0.
-1, 0
Suppose -2*k - 20 = -7*k. Suppose 5*s - 6 = k. Let -5*b**3 + 0*b**5 + 3*b**3 + s*b**5 = 0. What is b?
-1, 0, 1
Suppose 5*f = 3*c + 45, 4*c + 10 = 2*c. Let g(h) be the second derivative of 1/20*h**5 + 0*h**2 - 1/6*h**3 - h + 0 + 1/12*h**4 - 1/30*h**f. Factor g(y).
-y*(y - 1)**2*(y + 1)
Let h(z) = z**3. Let r(v) = -5*v**3 - 3*v**2. Let y(b) = -2*h(b) - r(b). Suppose y(n) = 0. Calculate n.
-1, 0
Let w(r) be the third derivative of -r**8/84 + r**6/30 - 3*r**2. Factor w(h).
-4*h**3*(h - 1)*(h + 1)
Let i(o) be the third derivative of -o**7/14 + o**6/60 + 6*o**2. Factor i(a).
-a**3*(15*a - 2)
Let q(y) be the first derivative of y**4/36 - y**3/18 + y + 3. Let d(z) be the first derivative of q(z). Find l such that d(l) = 0.
0, 1
Let f = 12 - 9. Let c(k) be the third derivative of 0*k**5 + 0 - 1/600*k**6 + 0*k + 1/120*k**4 + k**2 + 0*k**f. Suppose c(q) = 0. Calculate q.
-1, 0, 1
Let f(p) be the first derivative of -p**6/15 + p**4/2 + 2*p**3/3 - p - 2. Let m(a) be the first derivative of f(a). Factor m(o).
-2*o*(o - 2)*(o + 1)**2
Let a(c) be the second derivative of -c**6/1440 + c**3/3 + 2*c. Let o(h) be the second derivative of a(h). Determine b, given that o(b) = 0.
0
Let b(n) = -n**2 - 31*n + 95. Let j(t) = -4*t**2 - 154*t + 476. Let g(s) = -14*b(s) + 3*j(s). Let g(u) = 0. Calculate u.
7
Let g(j) = -61*j**4 + 45*j**3 - 12*j**2 + j + 3. Let k(d) = -d**4 + d**3 - 1. Let u(a) = -4*g(a) - 12*k(a). Let u(m) = 0. Calculate m.
0, 1/4
Let k = -19/155 + -9689/620. Let t = k + 16. Find i such that 3/4*i + 1/4 + t*i**3 + 3/4*i**2 = 0.
-1
Let s(c) be the second derivative of c**6/30 + c**5/20 - c**4/12 - c**3/6 + 5*c. Determine r, given that s(r) = 0.
-1, 0, 1
Let k(c) = -c**4 - 11*c**3 - 39*c**2 - 19*c + 67. Let q(f) = -f**4 - 11*f**3 - 38*f**2 - 18*f + 66. Let y(p) = -2*k(p) + 3*q(p). Let y(o) = 0. What is o?
-4, 1
Factor -210*j + 2205/2*j**2 + 10.
5*(21*j - 2)**2/2
Let y(v) be the second derivative of v**6/40 - v**5/20 - v**4/4 - 3*v**2/2 - 3*v. Let h(r) be the first derivative of y(r). Solve h(q) = 0 for q.
-1, 0, 2
Let f(c) = c + 7. Let a be f(-7). Let h = a + 2. Factor -2*g - 2*g**h - 17*g**4 + g**2 + 7*g**5 - 2*g**4 + 15*g**3.
g*(g - 1)**3*(7*g + 2)
Let t(j) be the first derivative of j**4/8 + j**3/2 - 2*j + 4. Determine q so that t(q) = 0.
-2, 1
Let w(d) be the first derivative of -3 + d + 0*d**2 + 1/48*d**4 - 1/24*d**3. Let u(p) be the first derivative of w(p). Factor u(m).
m*(m - 1)/4
Let j be -8*(-5)/(-5) + -4. Let i be j/(-90)*(-6)/(-4). Factor 0*k + 0 + 1/5*k**3 - i*k**2.
k**2*(k - 1)/5
Let n = 1757/9 + -195. Let j(h) be the first derivative of -4/3*h**2 - n*h - 6*h**4 - 4*h**3 - 18/5*h**5 - 2. Factor j(o).
-2*(3*o + 1)**4/9
Suppose -t = 2*m - 0*m - 17, -3*m + 43 = 5*t. Let k = -6 + m. Factor -1/2*o + 0 + o**2 + k*o**3 - o**4 + 1/2*o**5.
o*(o - 1)**3*(o + 1)/2
Let d = -13 + 16. Suppose 4*i - 13 - d = 0. Suppose -2/3*t**2 - 4/3*t**3 + 0 + 2/3*t**i + 4/3*t = 0. What is t?
-1, 0, 1, 2
Let u(w) be the first derivative of -4*w**5/5 - 16*w**4 - 104*w**3 - 224*w**2 - 196*w + 36. Factor u(m).
-4*(m + 1)**2*(m + 7)**2
Let n(d) = -7*d**5 + 33*d**4 - 21*d**3 - 5*d**2 + 8*d - 8. Let x(h) = 2*h**5 - 11*h**4 + 7*h**3 + 2*h**2 - 3*h + 3. Let g(p) = -3*n(p) - 8*x(p). Factor g(c).
c**2*(c - 1)**2*(5*c - 1)
Let z(k) be the third derivative of 0 - 1/75*k**5 + 1/175*k**7 - 1/150*k**6 + 3*k**2 + 1/20*k**4 - 1/840*k**8 + 0*k - 1/15*k**3. Find q, given that z(q) = 0.
-1, 1
Let t = -33721/15 + 2249. Let a(p) be the first derivative of -1/2*p**4 + 8/5*p**2 - 8/5*p + 2 + t*p**3. Let a(g) = 0. What is g?
-1, 2/5, 2
Let s(u) be the first derivative of -u**3/18 + u**2/6 + u/2 + 6. Factor s(p).
-(p - 3)*(p + 1)/6
Let q(l) be the first derivative of l**4/6 + 7*l**3/18 + l**2/6 - l/6 - 20. Determine g, given that q(g) = 0.
-1, 1/4
Let z(x) be the second derivative of -10*x**7/21 + x**6/6 + x**5 - 5*x**4/12 + 25*x. Determine p so that z(p) = 0.
-1, 0, 1/4, 1
Let r = -3/11 + 114/55. Factor r*b + 9/5*b**2 + 