)*(v + 1)/6
Let g(y) be the first derivative of -y**6/900 - y**5/300 + y**4/30 + 4*y**3/3 + 1. Let z(s) be the third derivative of g(s). Find v, given that z(v) = 0.
-2, 1
Let h be -1 + (-2 - (-3)/1). Let o(y) be the second derivative of 4/5*y**4 + 0*y**2 - 49/75*y**6 + h + 21/50*y**5 + 4/15*y**3 - 2*y. Solve o(g) = 0 for g.
-2/7, 0, 1
Let p(r) be the second derivative of 1/30*r**4 - 1/100*r**5 + 0 - r + 0*r**2 - 1/30*r**3. Factor p(n).
-n*(n - 1)**2/5
Let j(z) be the first derivative of z**3/3 - 41*z**2/8 + 5*z/2 + 14. Solve j(c) = 0.
1/4, 10
Let u(c) be the first derivative of 686*c**6/15 - 1568*c**5/25 - 504*c**4/5 - 128*c**3/3 - 32*c**2/5 - 14. Factor u(g).
4*g*(g - 2)*(7*g + 2)**3/5
Let m be 4/(-10) + 49/(-15) + 5. Determine n, given that 5*n**2 - 25/6*n**3 + m + 6*n = 0.
-2/5, 2
Factor 18 - 6*g + 1/2*g**2.
(g - 6)**2/2
Let g = 48/7 + -46/7. Let l be 2/9 + 59/(-63) + 1. Factor 0 - l*c**3 + g*c**2 + 0*c.
-2*c**2*(c - 1)/7
Let d(m) be the second derivative of m - 1/3*m**3 - 1/20*m**5 - 1/4*m**4 + 0 + 0*m**2. Factor d(z).
-z*(z + 1)*(z + 2)
Let f(b) be the second derivative of b**4/18 - b**3/9 - 2*b**2/3 + 6*b. Factor f(k).
2*(k - 2)*(k + 1)/3
Let f(q) be the third derivative of q**7/1155 + q**6/330 - q**5/330 - q**4/66 - 4*q**2. Find d such that f(d) = 0.
-2, -1, 0, 1
Let d be (-4)/22 - 31497/9900. Let y = -3/100 - d. Factor -y*z**3 + 2*z**4 + 2/3*z**2 + 6*z**5 + 0 + 0*z.
2*z**2*(z + 1)*(3*z - 1)**2/3
Let s(i) be the second derivative of i**4/8 + i**3 + 9*i**2/4 - 5*i. Suppose s(y) = 0. What is y?
-3, -1
Let y be (2 - 1) + 3 + -2. Let 2 + 0 + c - 1 + c + c**y = 0. Calculate c.
-1
Let n(y) = -y**3 + 5*y**2 - 12*y + 35. Let q be n(4). Factor -2*t + q + 1/3*t**2.
(t - 3)**2/3
Suppose 11*d - 3*d - 24 = 0. Factor -9/2*g - d - 3/2*g**2.
-3*(g + 1)*(g + 2)/2
Let q be ((-2)/(-5))/(1/40). Suppose 2*f + 5*a = -q, f - 2*a = -5*a - 10. Factor 4*n**2 + 0*n**f + n**3 + n + n + n**3.
2*n*(n + 1)**2
Suppose 7*z = -11 + 32. Suppose -3*f + 4 = -f. Factor -29*b**2 + b**3 + 2*b**z - 24 + 11*b**f + 36*b.
3*(b - 2)**3
Let 1/2*n**4 + 1/2 + 0*n**3 + 0*n - n**2 = 0. Calculate n.
-1, 1
Let a = 23 + 8. Let x = 31 - a. Factor 4/3*m - 2/3*m**2 + x.
-2*m*(m - 2)/3
Let -12*j + 15 + 3 - 2 - 4*j**2 = 0. Calculate j.
-4, 1
Suppose 2*w - 4*i = -4, 4*w - 4*i = -0*i. Let 13*j**4 - 8 - 63*j**3 + 62*j**w - 2*j**5 + 53*j**4 - 43*j**3 - 12*j**5 = 0. Calculate j.
-2/7, 1, 2
Determine q so that -6 + 659*q**2 + 11*q - 2*q**3 - 663*q**2 + q**3 = 0.
-6, 1
Suppose 0 = -5*w - t + 29, -2 = -2*w - 4*t + 6. Let 4*b**3 - w*b**3 - 1 + 1 = 0. What is b?
0
Let o(l) be the first derivative of 2*l**2 + 4 + 2*l + 2/3*l**3. Find d such that o(d) = 0.
-1
Let f(n) = -n**3 - 7*n**2 - 7*n - 1. Let b be f(-6). Let i(j) be the third derivative of 0*j - 1/90*j**b + 0 - 1/9*j**3 - 1/18*j**4 - 2*j**2. Factor i(z).
-2*(z + 1)**2/3
Let i be (5/10)/((-2)/4) - -4. Let j(k) be the first derivative of -1/3*k**6 + 1/2*k**4 + 4 + 2/5*k**5 - 2/3*k**i + 0*k**2 + 0*k. Factor j(g).
-2*g**2*(g - 1)**2*(g + 1)
Suppose 2*w**2 + 0 + 0*w**3 - 2/3*w**4 + 4/3*w = 0. What is w?
-1, 0, 2
Let 0 + 1/2*v**3 + 0*v - 1/2*v**2 = 0. What is v?
0, 1
Let g(n) be the second derivative of 7*n + 0*n**3 + 0 + 4*n**2 - 1/6*n**4. Factor g(x).
-2*(x - 2)*(x + 2)
Suppose 0*u + 4*u = 12. Suppose 0 = -5*t, y - u*t + t = 2. Factor z**2 + 2*z**2 + 2*z + z**2 + y*z**3.
2*z*(z + 1)**2
Let p(t) be the second derivative of 2*t**7/105 + 7*t**6/50 + 41*t**5/100 + 37*t**4/60 + t**3/2 + t**2/5 - 9*t. Factor p(a).
(a + 1)**3*(a + 2)*(4*a + 1)/5
Let m(l) = -4*l**4 + 4*l**3 + 4*l**2 + 2*l. Let q(f) = -3*f**4 + 3*f**3 + 3*f**2 + 2*f. Let n(h) = -5*m(h) + 6*q(h). Factor n(d).
2*d*(d - 1)**2*(d + 1)
Let y be (-72)/(-8)*(-1 + 0). Let f = y + 12. Factor 0 - 3/2*u**2 - 5/2*u**f + u.
-u*(u + 1)*(5*u - 2)/2
Suppose 0 = -4*n + 3 + 1. Let l be n - (-6)/4 - 2. Let 0*q + 1/2 + 0*q**3 + l*q**4 - q**2 = 0. Calculate q.
-1, 1
Suppose 5*i - 8 = i. Factor 4*j**4 - 3*j**4 - j**i + 0*j**4.
j**2*(j - 1)*(j + 1)
Let x(s) be the first derivative of -s**7/1050 - s**6/200 - s**5/100 - s**4/120 - s**2/2 - 1. Let f(c) be the second derivative of x(c). Factor f(m).
-m*(m + 1)**3/5
Suppose -8 = -5*o + 7. Let j(n) = -3*n**4 + 2*n**3 + n**2 + 2*n - 2. Let h(m) = 4*m**4 - 2*m**3 - 2*m**2 - 3*m + 3. Let v(w) = o*j(w) + 2*h(w). Factor v(u).
-u**2*(u - 1)**2
Suppose s - 5 + 0 = 0. Let f(a) be the third derivative of 2*a**2 + 0 + 0*a**4 + 1/480*a**6 + 0*a + 0*a**3 - 1/240*a**s. Factor f(i).
i**2*(i - 1)/4
Let q(t) be the first derivative of t**3 + 6*t**2 - 3. Determine p, given that q(p) = 0.
-4, 0
Let n be (-2 - 18/(-8)) + 43/20. What is f in -13/5*f**2 - 1/5*f**4 - 4/5 + 6/5*f**3 + n*f = 0?
1, 2
Factor -96 + 6*b**3 + 2*b**2 + 96.
2*b**2*(3*b + 1)
Let a(p) be the third derivative of p**8/504 - 2*p**7/315 - p**6/90 + 2*p**5/45 + p**4/36 - 2*p**3/9 - 4*p**2. Solve a(t) = 0.
-1, 1, 2
Let z be 10/(-35) + 3 + (-6)/(-21). Suppose 1/4*q**2 - 1/4 - 1/4*q**z + 1/4*q = 0. What is q?
-1, 1
What is r in -35*r**4 - 20 + 15*r**5 - 7*r**3 + 1245*r**2 - 1190*r**2 - 8*r**3 = 0?
-1, -2/3, 1, 2
Factor 6/13*k**2 + 8/13*k + 0 - 2/13*k**3.
-2*k*(k - 4)*(k + 1)/13
Let g(t) = -66*t**4 - 222*t**3 - 90*t**2 + 324*t - 27. Let l(a) = 5*a**4 + 17*a**3 + 7*a**2 - 25*a + 2. Let p(u) = -2*g(u) - 27*l(u). Factor p(v).
-3*v*(v - 1)*(v + 3)**2
Factor -2/3*h + h**2 - h**4 + 2/3*h**3 + 0.
-h*(h - 1)*(h + 1)*(3*h - 2)/3
Suppose 4/5 - 12/5*m**2 + 4/5*m - 4/5*m**3 + 8/5*m**4 = 0. Calculate m.
-1, -1/2, 1
Let u(i) be the first derivative of i**4/2 + 11*i**3/6 + 5*i**2/4 - i - 11. Determine v so that u(v) = 0.
-2, -1, 1/4
Let n(x) = -7*x**4 - 4*x**3 - x**2 + 15*x - 3. Let v(d) = 1 - 3*d**3 + 4*d**3 - 7*d + 2*d**4 + d + 2*d. Let k(i) = 6*n(i) + 22*v(i). Factor k(p).
2*(p - 2)*(p - 1)*(p + 1)**2
Let w = -3470/9 - -386. Factor -w*s + 2/9*s**2 + 0.
2*s*(s - 2)/9
Let u(y) be the third derivative of -4/105*y**7 - 1/45*y**5 - 5/504*y**8 - 1/20*y**6 + 0*y**3 + 0 + 0*y**4 + 0*y - y**2. Factor u(q).
-2*q**2*(q + 1)**2*(5*q + 2)/3
Let g(p) = -4*p**4 + 14*p**3 - 8*p**2 - 16*p + 14. Let l(v) = 12*v**4 - 41*v**3 + 24*v**2 + 48*v - 43. Let u(h) = 7*g(h) + 2*l(h). Factor u(r).
-4*(r - 3)*(r - 1)**2*(r + 1)
Suppose -15/2*a**4 + 0 - 3/2*a**5 - 27/2*a**3 - 21/2*a**2 - 3*a = 0. What is a?
-2, -1, 0
Let m be ((-48)/(-28))/((-2)/(-7)). Suppose -5*n = 3*k - 19, -k - 3*n + m + 3 = 0. Factor 0*s**2 + 2/9*s - 2/9*s**k + 0.
-2*s*(s - 1)*(s + 1)/9
Let -45*d**3 - 6*d**2 - 73*d**5 - 30*d**5 + 22*d**5 - 108*d**4 = 0. What is d?
-2/3, -1/3, 0
Let t(m) be the third derivative of 2*m**2 + 1/105*m**7 + 0*m**6 + 0*m**4 + 0*m + 0 + 1/3*m**3 - 1/15*m**5. Let t(o) = 0. Calculate o.
-1, 1
Suppose 12 = -2*v + 16. Let o(w) be the third derivative of 1/120*w**5 + 1/24*w**4 + 0 + 1/12*w**3 + 0*w - v*w**2. Determine a so that o(a) = 0.
-1
Let t(o) = -15*o**3 - 645*o**2 - 1190*o - 615. Let w(f) = -f**3 - 46*f**2 - 85*f - 44. Let d(l) = 4*t(l) - 55*w(l). Determine x, given that d(x) = 0.
-8, -1
Let v = -9 - -13. Let s be 3/(-6) + 2/v. Factor 0 - 2/3*p**3 + 0*p**2 + s*p - 2/3*p**4.
-2*p**3*(p + 1)/3
Let -n**5 - 2*n**5 + 5*n**5 - n**4 - n**3 = 0. What is n?
-1/2, 0, 1
Suppose 4*d - 12 = -4*p, 6*p - 9 = -3*d + 4*p. Suppose d*k = -0*k + 6. Factor -k*a**2 + 4*a + 7*a**2 + a**2.
2*a*(3*a + 2)
Factor -n - 2 + 0*n**2 - 2*n**2 + 3*n**2.
(n - 2)*(n + 1)
Let t = 9 - 6. Factor -2*o**2 + o**t + 4 - 8 + 4.
o**2*(o - 2)
Let s(n) = -n**2 + 9*n - 2. Let c be s(8). Factor 5*j**2 - 2 - 3*j**2 - c*j + 6.
2*(j - 2)*(j - 1)
Suppose 1/2*u + 1/2*u**2 - 1 = 0. What is u?
-2, 1
Let d(s) = -s**2 - 1. Let w(k) = k**2 + 8*k + 1. Let l(z) = -5*d(z) - w(z). Determine m, given that l(m) = 0.
1
Suppose -5*h + 2 + 18 = 0. Let i(k) be the second derivative of 0 - 2/5*k**2 + k + 11/15*k**3 + 7/50*k**5 - 8/15*k**h. What is t in i(t) = 0?
2/7, 1
Suppose 14 = 8*q - 10. Factor -1/2*h**2 + 0 - 1/2*h**4 + 0*h - h**q.
-h**2*(h + 1)**2/2
Suppose -2*u = -4*q + 24, -u + 2*u + 4 = 0. Let s(m) be the first derivative of 7/6*m**3 - 1/2*m**2 - 7/10*m**5 - 2 + 0*m + 1/4*m**q. Let s(i) = 0. Calculate i.
-1, 0, 2/7, 1
Let c(z) be the third derivative of -11*z**7/210 - 13*z**6/120 - 19*z**5/240 - z**4/48 + 10*z**2. Let c(h) = 0. What is h?
-1/2, -2/11, 0
Factor 8/5 - 2/5*t**2 + 6/5*t.
-2*(t - 4)*(t + 1)/5
Let u be (-3)/(-6) + (