be the first derivative of 10*n**3 + t - 5 - 1 + 4*n + 11*n**2. Suppose w(k) = 0. What is k?
-2/5, -1/3
Let i(v) be the first derivative of -1/4*v**2 - 3 - 1/18*v**3 - 1/3*v. Determine f so that i(f) = 0.
-2, -1
Let 0*t**3 + 3*t**3 - t - 4*t**3 + 6*t**2 - 24*t**4 - 16*t**5 = 0. Calculate t.
-1, 0, 1/4
Let u = 772/19 - 5/38. Let j = u + -40. Factor j*n**4 - n**3 + 0*n + 1/2*n**2 + 0.
n**2*(n - 1)**2/2
Let i(s) = -16*s**2 + 7*s - 13. Let o(c) = 3*c**2 - 11*c**2 - 6 + 3*c - 2*c + 3*c. Let a(j) = -4*i(j) + 9*o(j). Factor a(r).
-2*(2*r - 1)**2
Let d(b) be the third derivative of -1/16*b**4 + 1/30*b**5 + 0*b + 7*b**2 + 0 - 1/12*b**3. Factor d(h).
(h - 1)*(4*h + 1)/2
Let n(v) be the second derivative of -v**5/40 + 5*v**4/12 - v**3 - 18*v**2 - 21*v. Find t such that n(t) = 0.
-2, 6
Factor -2/9 - 8*p**2 + 8/3*p.
-2*(6*p - 1)**2/9
Suppose 0 = -4*s - 2*z - 6, 3*s + 3*z = -13 + 4. Determine j so that 3/2*j**3 + 0*j**2 - 2*j + s - 1/2*j**4 = 0.
-1, 0, 2
Let r(b) be the third derivative of 1/10*b**5 - 1/105*b**7 + 0*b**3 + 0*b + 0*b**6 - 3*b**2 + 1/6*b**4 + 0. Factor r(g).
-2*g*(g - 2)*(g + 1)**2
Let q(n) = 30*n**4 + 150*n**3 + 120*n**2 + 25*n. Let w(h) = -5*h**4 - 25*h**3 - 20*h**2 - 4*h. Let o(c) = 4*q(c) + 25*w(c). Factor o(b).
-5*b**2*(b + 1)*(b + 4)
Suppose -v - 79 = -3*r + 7*r, 0 = r - v + 21. Let d be (r/8)/((-2)/4). Find q such that -q**2 + q**4 + 0 + 0*q**3 + 1/2*q**d - 1/2*q = 0.
-1, 0, 1
Let z = -2857/5 - -572. Factor 6/5 + z*v**2 - 9/5*v.
3*(v - 2)*(v - 1)/5
Let g(y) be the second derivative of -11*y**4/24 - 7*y**3/9 - y**2/3 - 5*y. Let g(o) = 0. Calculate o.
-2/3, -2/11
Let c = -3 + 3. Let j(s) be the third derivative of 0 + 1/300*s**5 + 2*s**2 + 1/120*s**4 + c*s**3 + 0*s. Factor j(u).
u*(u + 1)/5
Let h(t) be the second derivative of t**7/105 + t**6/20 + t**5/15 - t**2/2 + 5*t. Let g(p) be the first derivative of h(p). Solve g(n) = 0.
-2, -1, 0
Let r = 203/176 - 12/11. Let m(q) be the first derivative of -1/8*q**2 - 2 + 1/6*q**3 - r*q**4 + 0*q. Factor m(y).
-y*(y - 1)**2/4
Let b = 8 + -9. Let q be b + (0 - 4/(-4)). Find n such that 1/3*n**2 + q + 0*n = 0.
0
Suppose 0*h = -5*p - 4*h + 2, 20 = 5*p - 5*h. Factor 3*o**3 + 0*o**3 + 0*o**3 + 0*o**2 + 6*o**p.
3*o**2*(o + 2)
Let z(v) be the second derivative of v**6/6 + 7*v**5/20 + v**4/6 + 3*v. Factor z(g).
g**2*(g + 1)*(5*g + 2)
Let h be 8 + -7 + (-9)/(-6) + -1. Determine p, given that -3/2*p**2 - h*p + 0 = 0.
-1, 0
Suppose 45 = v + 2*v. Determine y so that -y**2 + v*y**3 - 2*y**4 - 5*y**3 - 8*y + 0*y**2 + 16 - 11*y**2 = 0.
-1, 2
Let f = 217/330 - -1/110. Determine s, given that 2/3*s + 2/3*s**2 - f*s**3 - 2/3 = 0.
-1, 1
Let d(t) be the third derivative of t**8/560 + 4*t**7/525 - t**5/30 - t**4/40 + t**3/15 - 2*t**2. Determine z so that d(z) = 0.
-2, -1, 1/3, 1
Let a(c) be the third derivative of -c**5/90 - c**4/12 + 4*c**3/9 - 8*c**2. Factor a(q).
-2*(q - 1)*(q + 4)/3
Let r be (-26)/(1560/18)*70/(-4). Suppose 27/2*f**2 - 15*f + 6 - r*f**3 + 3/4*f**4 = 0. Calculate f.
1, 2
Let r = 7 - -6. Suppose -92*f**3 - 4 + 120*f**2 + 7*f**4 - 12 - 16 - 16*f + r*f**4 = 0. What is f?
-2/5, 1, 2
Let r(n) = n**2 - 8*n - 18. Let g be r(10). Let i = -1 - -1. Factor -2/5*h**g + 2/5 + i*h.
-2*(h - 1)*(h + 1)/5
Let z(a) = -2*a**3 - a**2 - a + 1. Let l be z(1). Let v = 0 - l. Let 0*h - h**2 + h + 3*h**2 - v*h**2 = 0. What is h?
0, 1
Let i(g) be the second derivative of -g**5/80 - g**4/48 + g**3/24 + g**2/8 - 8*g. Factor i(u).
-(u - 1)*(u + 1)**2/4
Let b(j) be the first derivative of -1/27*j**6 + 0*j**2 + 0*j + 4 + 2/45*j**5 - 2/27*j**3 + 1/18*j**4. What is h in b(h) = 0?
-1, 0, 1
Let q be 1 + 7/((-28)/(-8)). Determine i, given that -4*i**2 - 1 + 3*i - 1 + 0*i**2 + q*i = 0.
1/2, 1
Let d(f) = f - 4. Let t be d(9). Let b = -20 - -24. Let g**b - 4/3*g**t + 0*g + 1/3*g**3 + 0*g**2 + 0 = 0. What is g?
-1/4, 0, 1
Let v = 0 + 0. Suppose v = -5*a + 5 + 10. Factor -4*l**2 + 2 + a*l**4 + 2*l**4 - 3*l**4.
2*(l - 1)**2*(l + 1)**2
Find f, given that -f + 5/8*f**3 - 1/8*f**5 - 1/8*f**4 + 1/8*f**2 + 1/2 = 0.
-2, 1
Let f = 11 + -9. Factor 0*b**2 + 7*b**4 - 5*b**4 - b**5 + b - 2*b**f.
-b*(b - 1)**3*(b + 1)
Let m be 0*(4 + -5 + (-9)/(-6)). Factor m*k + 0 - 3/2*k**2.
-3*k**2/2
Suppose 5*r + 4*y = 12, 0*r = 3*r + 4*y - 12. Suppose -x = -r*x. Factor 0*f**2 + 1/2*f - 1/2*f**3 + x.
-f*(f - 1)*(f + 1)/2
Let o = 240 + -238. Let p = 475 + -3317/7. Factor 2*q**o + 24/7*q - p.
2*(q + 2)*(7*q - 2)/7
Let d(w) = -w + 7. Let h be d(-5). Factor c**4 - 3*c**4 - h*c**2 + 4 - 8*c**3 + 0 - 8*c - 6.
-2*(c + 1)**4
Let y(f) be the third derivative of 0 + 0*f**3 - 1/210*f**5 - 1/84*f**4 + 0*f - 3*f**2. Find u such that y(u) = 0.
-1, 0
Let d(l) be the third derivative of -127/180*l**6 - 8/9*l**4 + 31/30*l**5 - 1/24*l**8 + 4/9*l**3 + 0 + 7*l**2 + 0*l + 83/315*l**7. What is g in d(g) = 0?
2/7, 2/3, 1
Suppose -2*m - 20 = -4*i, m + 14 = 4*i - i. Let o be 3 - (-2)/(-6 + i). Factor 0*w + 0 + 1/2*w**o.
w**2/2
Let m(i) be the second derivative of 0 - 1/3*i**2 - 1/6*i**4 - 4/9*i**3 + 4*i. Factor m(l).
-2*(l + 1)*(3*l + 1)/3
Let s be (-39)/(-6) - 15/(-10). Let -48 - s*g + 48 - 2*g**4 + 6*g**3 = 0. What is g?
-1, 0, 2
Let t be ((-9)/(27/(-2)))/2. Let i(m) be the third derivative of 1/120*m**6 + t*m**3 + m**2 + 0*m - 1/8*m**4 + 0 + 0*m**5. What is h in i(h) = 0?
-2, 1
Let w(g) be the first derivative of -2*g**3/9 + 2*g**2/3 + 2*g + 6. Determine u so that w(u) = 0.
-1, 3
Let o(r) = -26*r + 29. Let w be o(1). Factor 16/3*u + 2/3*u**4 - 2*u**2 - 8/3 - 4/3*u**w.
2*(u - 2)*(u - 1)**2*(u + 2)/3
Let z(x) be the second derivative of -x**6/40 + 3*x**5/20 - 2*x**3 + 2*x**2 - 2*x. Let v(b) be the first derivative of z(b). Factor v(a).
-3*(a - 2)**2*(a + 1)
Solve 11*i - 33 + 13*i - 3 - 4*i**2 = 0 for i.
3
Let m(d) be the first derivative of -d**5/25 + 2*d**3/5 - 4*d**2/5 + 3*d/5 - 34. Factor m(t).
-(t - 1)**3*(t + 3)/5
Let f(j) = -2*j - 3. Let d be f(-5). Factor -2*a + a**5 + 5*a**2 + a**5 + 9*a**3 + d*a**4 + 3*a.
a*(a + 1)**3*(2*a + 1)
Suppose -2*s - s - 9 = 0. Let f be s*(20/36)/(-5). Factor 2/3*q + 1/3 + f*q**2.
(q + 1)**2/3
Let q be ((-14)/(-3))/((-4)/(-6)). Suppose q*x = 2*x. Factor x + 1/2*j**2 - 1/2*j.
j*(j - 1)/2
Let z(j) = j**2 + 8*j + 9. Suppose 44 = -4*i + 16. Let o be z(i). Factor t**2 - 1 + 0*t - 2*t**o - 2*t.
-(t + 1)**2
Factor 2*l**5 + 10*l**4 + 3*l**3 + 6*l**3 + 2 + 7*l**3 + 4*l**3 + 20*l**2 + 10*l.
2*(l + 1)**5
Let o = 3 - 3. Let u(s) be the first derivative of 0*s**2 - 2 - 1/2*s**4 + o*s + 2/3*s**3. Solve u(r) = 0 for r.
0, 1
Let b be (-1)/(12/(-8))*-9. Let g = b + 8. Factor -1/3*m**g + 5/3*m + m**4 - 2/3 - 5/3*m**3.
(m - 1)**2*(m + 1)*(3*m - 2)/3
Let w(b) = -b**2 + b + 1. Let q(c) = 8*c**2 - 2*c - 4. Let o = 1 - 0. Let s be (-6)/(1 - (-2 - -4)). Let g(v) = o*q(v) + s*w(v). Solve g(d) = 0 for d.
-1
Let f(r) be the first derivative of -8/21*r**3 - 8 + 5/7*r**2 - 4/7*r + 1/14*r**4. Let f(h) = 0. What is h?
1, 2
Let w(f) = -f**2 + 2*f - 2. Let l(u) = 6*u**2 - 11*u + 11. Let m(s) = 4*l(s) + 22*w(s). Factor m(z).
2*z**2
Factor 5*u**2 + 2*u**3 - 7*u**2 + 32*u - 4*u**2 - 8*u**2 - 24.
2*(u - 3)*(u - 2)**2
Let m = 11 - 5. Let k(p) = 0 - 2 - 85*p + 89*p + 11*p**2. Let h(a) = 5*a**2 + 2*a - 1. Let f(g) = m*k(g) - 13*h(g). Determine j, given that f(j) = 0.
1
Let u = 467/319 - 24/29. Let y = u - 13/55. Suppose -y*a + 2/5*a**2 - 4/5 = 0. Calculate a.
-1, 2
Let q(v) be the third derivative of -v**7/105 - v**6/12 + 27*v**2. Determine n so that q(n) = 0.
-5, 0
Factor 2/13*n**3 + 0 - 8/13*n**2 + 6/13*n.
2*n*(n - 3)*(n - 1)/13
Let c(v) be the first derivative of v**7/210 - v**6/120 - v**5/30 + v**2 - 1. Let t(b) be the second derivative of c(b). Determine f so that t(f) = 0.
-1, 0, 2
Let u = -123 - -123. What is z in u + 0*z + 1/3*z**2 + 1/3*z**3 = 0?
-1, 0
Suppose 14*l = 9*l. Let q(o) be the third derivative of 0*o + 0 - 2/105*o**7 + l*o**3 + 1/12*o**4 - o**2 + 1/15*o**5 + 0*o**6 - 1/168*o**8. Factor q(u).
-2*u*(u - 1)*(u + 1)**3
Let r(p) = 4*p**3 - 2*p**2 - p + 2. Let o be r(2). Let b be 1/3 + o/9. Factor 2*t**3 + 3 + 10*t + t**3 - b*t**2 - 13*t.
3*(t - 1)**2*(t + 1)
Let o be (-14)/84 - (-17)/30. Suppose o*u**2 + 4/5 - 6/5*u = 0. What is u?
1, 2
Let o(b) be the second derivative of 0 + 1/210*b**7 - 3/100*b**5 + 1/60*b**4 + 1/15*b**3 + 0*b**2 - 7*b - 1/150*b**6. Let o(h) = 0. Calcul