 o(j) be the second derivative of j**5/60 - j**3/18 + 7*j. Factor o(w).
w*(w - 1)*(w + 1)/3
Let r(v) be the first derivative of 7*v**6/27 + 2*v**5/9 - v**4/2 - 10*v**3/27 + 2*v**2/9 + 2. Determine a so that r(a) = 0.
-1, 0, 2/7, 1
Let n = 22 + -12. Factor -n*a + 7 + 4*a**2 - 4 + 1.
2*(a - 2)*(2*a - 1)
Let r(d) be the first derivative of d**6/10 - 3*d**5/10 + d**4/4 - 4*d - 2. Let g(p) be the first derivative of r(p). Find o such that g(o) = 0.
0, 1
Let h(n) be the second derivative of -n**7/12600 + n**6/1800 - n**5/600 + n**4/4 - 5*n. Let u(j) be the third derivative of h(j). Factor u(i).
-(i - 1)**2/5
Let q(w) be the second derivative of w**7/84 - w**6/20 + w**5/40 + w**4/8 - w**3/6 + 9*w. Determine u so that q(u) = 0.
-1, 0, 1, 2
Solve 2/3*d**3 + 10/3*d + 8/3*d**2 + 4/3 = 0.
-2, -1
Suppose 3*x + 57 = -4*w, w - 5*x = 3*w + 25. Let p be w/(-6) - (-2)/12. Factor 0 - n**3 - p*n**2 + 4/3*n + 3*n**4.
n*(n + 1)*(3*n - 2)**2/3
Let g(j) be the first derivative of -j**4/2 - 10*j**3/3 + j**2 + 10*j + 42. Factor g(s).
-2*(s - 1)*(s + 1)*(s + 5)
Let r be 9 + 4/(-2) - 2. Let g(h) be the second derivative of 1/21*h**7 - 2*h + 0 + 1/10*h**r + 0*h**3 + 0*h**4 - 2/15*h**6 + 0*h**2. Factor g(d).
2*d**3*(d - 1)**2
Find v, given that -2/3*v + v**2 - 1/3*v**4 + 0*v**3 + 0 = 0.
-2, 0, 1
Suppose 4*g - 4 = 0, -3*g + 101 + 77 = 5*x. Let k = x - 33. Factor -1/2*z**k + 0 + z - 1/2*z**3.
-z*(z - 1)*(z + 2)/2
Let z(n) be the third derivative of -n**5/60 - n**4/8 - n**3/3 + 12*n**2. Factor z(y).
-(y + 1)*(y + 2)
Let z(f) be the third derivative of 0*f**3 + 0*f + 7*f**2 + 0 + 7/20*f**5 + 1/4*f**4. Find i such that z(i) = 0.
-2/7, 0
Let j be -4*2/(-8)*-3. Let z = j + 5. Solve 4*a + 4*a**z - 1 - 8*a**3 - 6*a**3 - a**2 + 8*a**4 = 0.
-1/2, 1/4, 1
Let w(n) = -n**3 + 4*n**2 + 2*n - 5. Let z be w(4). Let l be 3*78/54 - (2 - 1). Factor 0 - l*k**4 - 8/3*k**5 + 0*k + 0*k**2 - 2/3*k**z.
-2*k**3*(k + 1)*(4*k + 1)/3
Let k(h) be the first derivative of -h**3/12 + h**2/4 + 7. Solve k(w) = 0.
0, 2
Let x be 10 - (1 + 1) - 3. Let h(i) = -i**2. Let q(r) = r**2. Let m be 1/3 - 34/(-6). Let c(l) = m*h(l) + x*q(l). Determine b so that c(b) = 0.
0
Let l(j) be the third derivative of j**5/80 + j**4/16 + j**3/8 + 6*j**2. What is p in l(p) = 0?
-1
Let u = 0 + 2. Suppose m = -4*v + 15, -2*v + 3*v + 4*m - 15 = 0. Factor -j - j**v - j**3 + j**3 + 2*j**u.
-j*(j - 1)**2
Let b be 10/3 + (-2)/6. Suppose -2*m - 15 = -5*m. Factor m*w**3 + 2*w**2 + 14*w**4 + w**3 + 4*w**b + 6*w**5.
2*w**2*(w + 1)**2*(3*w + 1)
Let x(w) be the first derivative of -1/7*w**3 + 3/7*w**2 - 3/7*w + 9. Find f such that x(f) = 0.
1
Let l(r) = 11*r**2 - 6*r - 1. Let v(u) = -6*u**2 + 3*u + 1. Let s(w) = 3*l(w) + 5*v(w). Let y be s(1). Factor 1/4*g**3 + 1/2*g + 0 + 3/4*g**y.
g*(g + 1)*(g + 2)/4
Let a be 3 - (-2 - -6) - -4. Factor 2*l - 2*l**4 - 5 + 0 - 2*l**5 - 4*l**3 + a + 4*l**5 + 4*l**2.
2*(l - 1)**3*(l + 1)**2
Let i(b) = 51*b**4 - 219*b**3 + 741*b**2 - 939*b + 480. Let j(s) = -5*s**4 + 22*s**3 - 74*s**2 + 94*s - 48. Let r(v) = 2*i(v) + 21*j(v). Solve r(h) = 0.
2
Let -283*g + 283*g - 4*g**2 + 4*g**4 = 0. What is g?
-1, 0, 1
Suppose 0*k - 108 = -4*k. Suppose -3*z + 23 = v, 7*v - 3*v - z - k = 0. Find g such that -g**2 - 8*g**4 + 6 + 10*g - v*g**3 + 5*g**2 - 2 - 2*g**5 = 0.
-2, -1, 1
Let y be 2/(-18) + 28/63. Determine x, given that 0 + 1/6*x**5 + 0*x**4 + 0*x**2 - y*x**3 + 1/6*x = 0.
-1, 0, 1
Let z(o) be the first derivative of o**3/9 - o**2/2 + 2*o/3 - 11. Factor z(w).
(w - 2)*(w - 1)/3
Let j(p) be the second derivative of 3*p**5/20 + p**4/2 - 44*p. Factor j(g).
3*g**2*(g + 2)
Let g(a) be the first derivative of a**7/420 - a**6/40 + a**5/10 - a**4/6 + 3*a**2/2 + 1. Let b(n) be the second derivative of g(n). Solve b(q) = 0 for q.
0, 2
Let f(p) be the second derivative of p**6/30 + 3*p**5/10 + p**4 + 4*p**3/3 - 24*p. Let f(d) = 0. What is d?
-2, 0
Let m be ((-15)/(-10))/(5/10). Let n(d) be the third derivative of -2/21*d**m + 1/210*d**5 + 0*d + 4*d**2 - 1/84*d**4 + 0. Factor n(a).
2*(a - 2)*(a + 1)/7
Factor -b**3 + 5 + 5*b - 4*b**3 + b - b - 5*b**2.
-5*(b - 1)*(b + 1)**2
Let k(y) be the third derivative of -y**7/630 - y**6/360 + 15*y**2. Suppose k(r) = 0. Calculate r.
-1, 0
Let o(v) be the first derivative of 4*v**3/5 - 14*v**2/5 + 8*v/5 - 7. Factor o(y).
4*(y - 2)*(3*y - 1)/5
Let a(w) = w**2 + 7*w + 9. Let i be a(-6). Suppose 8*r - 6 = 6*r. Factor -105/2*g**i + 131/4*g**2 - 1225/4*g**4 + r*g - 1.
-(5*g - 1)**2*(7*g + 2)**2/4
Factor 4*w**3 + 6 - 4*w + 5*w**3 - 5*w + 4*w**4 - 3*w**2 - 7*w**4.
-3*(w - 2)*(w - 1)**2*(w + 1)
Let n(d) be the second derivative of d**4/54 - 2*d**3/27 + d**2/9 + 5*d. Factor n(g).
2*(g - 1)**2/9
Let f(o) = 3*o**2 + 16*o + 13. Let w(g) = 16*g**2 + 88*g + 72. Let a(d) = -28*f(d) + 5*w(d). Factor a(k).
-4*(k + 1)**2
Let v(j) = j**2 - j. Let q(z) = 9*z - 12. Let g(w) = -q(w) + 3*v(w). Factor g(b).
3*(b - 2)**2
Let s(x) = 5*x**2 - 8*x. Let m(f) be the second derivative of 7*f**4/4 - 11*f**3/2 - 3*f. Let q(y) = -2*m(y) + 9*s(y). Suppose q(j) = 0. Calculate j.
0, 2
Let g(v) = 7*v**3 + 9*v**2 - 37*v + 9. Let p(j) = 3*j**3 + 5*j**2 - 18*j + 4. Let m(z) = -4*g(z) + 9*p(z). Factor m(t).
-t*(t - 7)*(t - 2)
What is b in -1/2*b**2 + 0 + 0*b = 0?
0
Let t(h) be the first derivative of -2*h**3/21 - 4*h**2/7 - 6*h/7 - 29. Let t(d) = 0. What is d?
-3, -1
Let l(k) be the first derivative of 0*k**2 + 1/20*k**5 - 1/4*k**4 + 1/3*k**3 - 2 - 2*k. Let o(a) be the first derivative of l(a). Factor o(w).
w*(w - 2)*(w - 1)
Factor -3*m**2 + 0 + 12/7*m**3 - 6/7*m.
3*m*(m - 2)*(4*m + 1)/7
Let p = -230 + 4141/18. Let c(h) be the second derivative of 2/27*h**3 + 2*h + 0*h**2 - p*h**5 + 0 - 1/18*h**4. Find n, given that c(n) = 0.
-1, 0, 2/5
Let z be 285/105 + 2/7. Solve -3*r**z + 0 + 3/5*r**2 + 0*r - 9/5*r**5 + 21/5*r**4 = 0.
0, 1/3, 1
What is t in 1/2*t**4 - 1/4*t**5 + 0 + 0*t - 1/4*t**3 + 0*t**2 = 0?
0, 1
Let z(o) be the third derivative of 25*o**8/336 + 4*o**7/21 - o**6/6 - 5*o**5/6 - 5*o**4/24 + 5*o**3/3 + 16*o**2. Suppose z(u) = 0. What is u?
-1, 2/5, 1
Let x be -1 + (1 - 1) - -4. Let r(h) be the second derivative of 0 - 3/4*h**4 - 2*h**2 + h - 2*h**x. Factor r(p).
-(3*p + 2)**2
Let z(d) = -2*d**2 + 16*d + 18. Let t be z(9). Factor 14/3*o**4 - 4/3*o**3 + t + 0*o - 8/3*o**5 - 2/3*o**2.
-2*o**2*(o - 1)**2*(4*o + 1)/3
Let t(o) be the second derivative of 0*o**2 + 2/15*o**3 + 1/30*o**4 + 0 + 2*o. Solve t(l) = 0.
-2, 0
Let 0 + 2/3*q + 13/3*q**2 = 0. What is q?
-2/13, 0
Determine k so that -1/2*k**4 + 1/2*k**2 + 0 + 1/4*k**5 - 1/4*k + 0*k**3 = 0.
-1, 0, 1
Let p(s) = -6*s**3 - 2*s**2 - 4*s - 8. Let b(m) = m**3 + m**2 + m + 1. Let d(v) = 20*b(v) + 4*p(v). Factor d(c).
-4*(c - 3)*(c - 1)*(c + 1)
Let q(n) = -2*n. Let h be q(-1). Let d(p) be the third derivative of 0 + 0*p**3 + 0*p - 1/12*p**4 + 1/30*p**5 + p**h. Factor d(s).
2*s*(s - 1)
Let k = 52102/57 - 914. Let i = 62/19 + k. Find r, given that 4/3*r**3 + 0 - i*r**4 - 4/3*r + 10/3*r**2 = 0.
-1, 0, 2/5, 1
Solve 265*p**2 + 140*p**5 + 5*p**4 + 5514*p**3 - 18 + 40*p - 2 - 5944*p**3 = 0.
-2, -2/7, 1/4, 1
Let l(x) be the first derivative of -x**5/5 - x**4/2 + 9. Factor l(s).
-s**3*(s + 2)
Suppose 4*c = 3*q - 69, 3*q - 36 = -4*c + 57. Let f be -4 - ((-213)/q - -3). Factor -f*d**3 - 4/3*d**2 - 8/9*d - 2/9 - 2/9*d**4.
-2*(d + 1)**4/9
Let m = 186 - 186. Factor -1/2*n - 5/4*n**4 + 1/2*n**3 + m + 5/4*n**2.
-n*(n - 1)*(n + 1)*(5*n - 2)/4
Let l = 177 - 297. Let v = 602/5 + l. Suppose -2/5*h**2 + 4/5*h - v = 0. Calculate h.
1
What is n in 4/5*n**2 - 6/5*n**5 - 6/5*n + 12/5*n**3 - 2/5 - 2/5*n**4 = 0?
-1, -1/3, 1
Let j(q) be the first derivative of -3*q**4 + 6*q + 2/5*q**5 - 1 + 8*q**3 - 10*q**2. Determine p, given that j(p) = 0.
1, 3
Let r(b) be the second derivative of b**4/2 + 4*b**3/3 + b**2 + 11*b. Determine a so that r(a) = 0.
-1, -1/3
Suppose 6*m - 51 = -15. What is s in m*s**2 - 3/2 - 9/2*s = 0?
-1/4, 1
Let n(u) be the second derivative of u**7/2520 - u**6/360 + u**5/120 - u**4/72 - u**3/2 + 2*u. Let p(c) be the second derivative of n(c). Factor p(b).
(b - 1)**3/3
Let o = 4 - 6. Let v(k) = 4*k**3 - 9*k**2 - 9*k + 4. Let t(z) = -2*z**3 + 4*z**2 + 4*z - 2. Let r(w) = o*v(w) - 5*t(w). Determine c so that r(c) = 0.
-1, 1
Let p(y) be the first derivative of y**6/240 + y**5/40 - 3*y**4/16 + y**3/3 + 4. Let v