e the first derivative of -2/9*v**3 - 1/6*v**4 + 1/2*v**2 + 1/5*v**5 + 5 - 1/3*v - 1/18*v**6. Find c, given that q(c) = 0.
-1, 1
Let k(j) = 40*j**2 + 8*j - 3. Let g(d) be the second derivative of -13*d**4/4 - 3*d**3/2 + d**2 + 4*d. Let p(h) = -4*g(h) - 3*k(h). Factor p(x).
(6*x + 1)**2
Suppose -h = -5*h + 44. Suppose -4*j = -3*r - 2*r - 10, -3*j = -2*r - h. Factor -2/11*n**j + 0*n - 2/11*n**3 + 0*n**2 + 0 + 4/11*n**4.
-2*n**3*(n - 1)**2/11
Let x(p) be the first derivative of 1/10*p**2 + 1/30*p**6 - 1/10*p**4 - 2/15*p**3 + 3 + 1/25*p**5 + 1/5*p. Factor x(m).
(m - 1)**2*(m + 1)**3/5
Let c = -281/18 + 145/9. Factor 7/4*w**2 + 0 + c*w.
w*(7*w + 2)/4
Let n(x) be the second derivative of -2/9*x**3 + 0 + 0*x**2 + 2*x + 1/6*x**4 + 1/6*x**5. Factor n(p).
2*p*(p + 1)*(5*p - 2)/3
Suppose 3*x - 41 + 35 = 0. Factor -5/2*f**x + 3/2*f + 1.
-(f - 1)*(5*f + 2)/2
Let y(n) = -n**3 - 6*n**2 + 6*n - 5. Let c be y(-7). Suppose 0 = 5*g - 30 + 10. Factor -4/7*d**c - 2/7*d**3 + 6/7*d**g + 0 + 0*d.
2*d**2*(d - 1)*(3*d + 2)/7
Let d(m) be the first derivative of m**6/8 - m**5/4 - 19*m**4/8 - 9*m**3/2 - 29*m**2/8 - 5*m/4 + 24. Let d(u) = 0. Calculate u.
-1, -1/3, 5
Let w(m) be the third derivative of -m**8/20160 + m**7/1680 - m**6/360 + m**5/30 + 6*m**2. Let h(u) be the third derivative of w(u). Factor h(v).
-(v - 2)*(v - 1)
Let w(o) be the first derivative of -o**2 + 2/3*o**3 + 0*o + 2. Factor w(x).
2*x*(x - 1)
Let n(c) be the first derivative of 9*c**4/4 + 2*c**3 - 9*c**2/2 - 6*c - 4. Solve n(s) = 0.
-1, -2/3, 1
Let v(t) = 2*t + 19. Let z be v(-8). Let j(a) = a**3 + 1. Let y(m) = 4*m**3 + 2*m**2 - 4*m - 5. Let o(q) = z*j(q) - y(q). Factor o(g).
-(g - 2)*(g + 2)**2
Let n be (-1)/(-1) + 21/(-28). Let i(p) be the first derivative of 1/4*p - 1 + 1/12*p**3 - n*p**2. Factor i(q).
(q - 1)**2/4
Determine d so that 13*d**2 + 3*d**3 - 3*d**5 + 13*d**2 - 26*d**2 = 0.
-1, 0, 1
Let o(h) be the first derivative of h**5/50 - h**4/10 + h**3/5 - h**2/5 + h + 2. Let i(p) be the first derivative of o(p). Factor i(l).
2*(l - 1)**3/5
Find f, given that -20*f**5 + 4 - 68/3*f**4 - 44/3*f - 136/3*f**2 + 296/3*f**3 = 0.
-3, -1/3, 1/5, 1
Let c(a) be the first derivative of -3*a + 2*a**3 + 0*a**2 - 2 - 3/5*a**5 + 0*a**4. Factor c(h).
-3*(h - 1)**2*(h + 1)**2
Let r be -21*4/(-48) + (-24)/16. Let -1/4*s**3 + 0 - 1/4*s**2 + r*s + 1/4*s**4 = 0. What is s?
-1, 0, 1
Let m(r) be the first derivative of -r**3/6 - 3*r**2/4 + 4. Determine j, given that m(j) = 0.
-3, 0
Let l(a) = -a**3 - 5*a**2 + 3. Let x be l(-5). Determine q so that 54/5 - 54/5*q + 18/5*q**2 - 2/5*q**x = 0.
3
Let z(u) be the second derivative of u**4/66 - 2*u**3/3 + 11*u**2 - 29*u. Let z(a) = 0. Calculate a.
11
Let x = 14/5 + -32/15. Factor s**4 - 1/3*s**2 - x*s + 0 + 4/3*s**3.
s*(s + 1)**2*(3*s - 2)/3
Suppose -43 + 23 = -10*x. Suppose 4/13*w + 0 - x*w**4 + 2/13*w**2 - 10/13*w**5 - 18/13*w**3 = 0. What is w?
-1, 0, 2/5
Let t be (965/(-30))/((-1)/(-2)). Let b = t - -65. Determine h, given that 2/3*h**2 - b*h**3 + 2/3*h - 2/3 = 0.
-1, 1
Let m(b) be the first derivative of -b**7/420 + b**5/20 + b**4/6 + b**3 + 4. Let t(a) be the third derivative of m(a). Factor t(h).
-2*(h - 2)*(h + 1)**2
Let z(n) be the second derivative of 7*n**7/15 - 14*n**6/15 - 3*n**5/50 + 2*n**4/3 + 4*n**3/15 + n. Determine x, given that z(x) = 0.
-2/7, 0, 1
Suppose 3 = w - 0*w. Suppose 4 = 4*r - 2*r - 4*d, 0 = w*r + d - 6. Factor -6 + 6 - r*i**2 + i.
-i*(2*i - 1)
Let g(w) be the second derivative of w**7/21 + 2*w**6/15 - 3*w**5/10 - 4*w**4/3 - 4*w**3/3 - 32*w. Determine j, given that g(j) = 0.
-2, -1, 0, 2
Let n(f) = 2*f**2 - 6*f - 12. Let p(s) = s + 1. Suppose -i - 2 = 6. Let l(j) = i*p(j) - n(j). Suppose l(q) = 0. What is q?
-2, 1
Suppose 0 = 5*o - 19 - 1, 3*o - 24 = -4*s. Suppose i - 5*r = -23, i = 2*i + 2*r - 12. Find n, given that -1/4*n + 1/4*n**s + 1/4 - 1/4*n**i = 0.
-1, 1
Let i(l) be the first derivative of -4*l**5/5 + 4*l**4 - 8*l**3 + 8*l**2 - 4*l - 1. Suppose i(k) = 0. Calculate k.
1
Find c, given that -3/2*c**3 - 1/2*c**4 - 1/2*c**2 + 3/2*c + 1 = 0.
-2, -1, 1
Solve -3 - 39*p**3 - 14*p - 17*p - 45*p**2 - 12*p**4 + 10*p = 0 for p.
-1, -1/4
Let u(b) = 5*b**4 - 25*b**3 - 50*b**2 + 25*b + 35. Let p(y) = -8*y**4 + 38*y**3 + 75*y**2 - 38*y - 53. Let c(i) = 5*p(i) + 7*u(i). Factor c(t).
-5*(t - 4)*(t - 1)*(t + 1)**2
Let p = 83 - 81. Suppose 2/9*f**p + 0 - 4/9*f = 0. Calculate f.
0, 2
Suppose 0 = 4*u - 5*u + 2*u. Find c such that u - 2/3*c**3 + 4/3*c**2 - 2/3*c = 0.
0, 1
Let c(o) be the first derivative of -3 - 1/6*o**3 + 1/4*o**2 + 1/2*o - 1/8*o**4. Factor c(f).
-(f - 1)*(f + 1)**2/2
Let i(z) be the second derivative of -z**4/3 + 8*z**3/3 - 8*z**2 + 16*z. Solve i(k) = 0.
2
Let p be 296/(-72) + (-2 - -7). Factor 8/9*b + p + 2/9*b**2.
2*(b + 2)**2/9
Let s be (-3*1/(-6))/(14/8). Factor -s*t**3 + 2/7 - 2/7*t**2 + 2/7*t.
-2*(t - 1)*(t + 1)**2/7
Suppose 0 = -h + 4*p - 16, 2*p + 10 = -h - 3*h. Let a(w) = w**3 + 3*w**2 - 4*w + 4. Let q be a(h). Find x such that 2 + 5 - 2 - q - x**2 = 0.
-1, 1
Let f(d) be the first derivative of -d**3/3 - d**2/2 + 4. Factor f(m).
-m*(m + 1)
Suppose 0 = p + 2*p - 12. Suppose -h + p*h - 9 = 0. Let -4*g + 6*g**2 + 2*g**4 + 0*g**4 + 2*g - 6*g**h = 0. Calculate g.
0, 1
Let d(t) = -t**5 - t**4 + t + 1. Let v(m) = -38*m**4 + 122*m**3 + 360*m**2 + 202*m + 2. Let i(a) = 2*d(a) - v(a). What is l in i(l) = 0?
-1, 0, 10
Let g(w) be the first derivative of -3*w**4/20 - 4*w**3/5 - 6*w**2/5 + 6. Find r, given that g(r) = 0.
-2, 0
Let r(z) be the third derivative of z**8/112 - z**7/35 - z**6/20 + 2*z**5/5 - 7*z**4/8 + z**3 - 13*z**2. Factor r(y).
3*(y - 1)**4*(y + 2)
Let m(w) = -5*w**4 - 31*w**3 - 34*w**2 - 14*w - 6. Let r(z) = -15*z**4 - 92*z**3 - 103*z**2 - 43*z - 17. Let k(g) = -17*m(g) + 6*r(g). Let k(x) = 0. What is x?
-2, -1, 0
Let k(s) = 3*s**3 - s + 1. Let g be k(1). Let t(o) be the first derivative of 1 + 0*o - 1/4*o**4 - 2/3*o**g - 1/2*o**2. Let t(h) = 0. What is h?
-1, 0
Let n(a) be the third derivative of 0*a**5 + 3*a**2 + 0*a**3 + 0 + 0*a - 1/200*a**6 + 0*a**4. Find z, given that n(z) = 0.
0
Suppose -8*m = -u - 13*m + 18, -9 = u - 4*m. Find w, given that -2/5*w**2 - 2/5*w + 2/5*w**u + 2/5 = 0.
-1, 1
Suppose 0 = -6*s + 3*s. Let m be s/(2 + -1 - 3). Factor m*j**2 - 4 + 2*j**2 - 3*j + 3*j**3 + 2.
(j - 1)*(j + 1)*(3*j + 2)
Let u be ((-8)/(-14))/((-8)/(-28)). Let n(m) be the second derivative of 0*m**2 + 1/30*m**5 + 0 + 0*m**4 - 1/27*m**3 + u*m + 2/135*m**6. Factor n(k).
2*k*(k + 1)**2*(2*k - 1)/9
Let r be (-21)/(-231) + 105/297. Factor -2/9 + 8/9*z**4 + 1/3*z**5 - 7/9*z + r*z**3 - 2/3*z**2.
(z - 1)*(z + 1)**3*(3*z + 2)/9
Let p(k) be the third derivative of 0*k - 1/72*k**4 - 1/180*k**5 + 3*k**2 + 0 + 1/9*k**3. Factor p(c).
-(c - 1)*(c + 2)/3
Let m(d) = -d**2 - d. Let h(o) = 4*o**2 + 2*o. Let b(n) = -h(n) - 6*m(n). Suppose b(r) = 0. What is r?
-2, 0
Suppose 2*g + 8 = l, -l - 4*l - 16 = 4*g. Factor -3/5*q**3 - 6/5*q**2 + l + 0*q.
-3*q**2*(q + 2)/5
Let t = 19 + 3. Let h be (-34)/187 - (-15)/t. Determine x, given that -1/4*x**2 + 0 + 0*x - h*x**3 = 0.
-1/2, 0
Let m(k) = -25*k + 27*k**2 - 56*k + k**3 + 21 + 56. Let a(x) = -3*x**3 - 108*x**2 + 324*x - 309. Let i(n) = -4*a(n) - 15*m(n). Factor i(w).
-3*(w - 3)**3
Let j(m) be the second derivative of 1/189*m**7 + 4*m + 0 + 1/9*m**2 - 1/27*m**4 + 1/27*m**3 + 1/135*m**6 - 1/45*m**5. Factor j(i).
2*(i - 1)**2*(i + 1)**3/9
Suppose -4*b**3 + 7*b**3 - 26*b**2 + 17*b**2 - 12*b = 0. What is b?
-1, 0, 4
Let d(m) be the first derivative of -m**3 + 3 + 0*m - 1/36*m**4 + 0*m**2 + 1/1080*m**6 + 1/360*m**5. Let p(x) be the third derivative of d(x). Factor p(y).
(y - 1)*(y + 2)/3
Suppose -3*l = -2*v - 12, 5*l + 0*v = 5*v + 25. Factor 3 - 3*s + 4*s - 3*s**l - s.
-3*(s - 1)*(s + 1)
Let j(u) be the third derivative of -u**8/504 + 2*u**7/315 + u**6/60 - 11*u**2. Factor j(l).
-2*l**3*(l - 3)*(l + 1)/3
Suppose -15 = -5*h - 0*h - 5*m, -3 = -h + 3*m. Let y be 1/(-3)*(-2 - -1). Factor 1/3*d**4 + 2*d**2 + y + 4/3*d + 4/3*d**h.
(d + 1)**4/3
Let u(h) = h**2 - 8*h - 14. Let p(c) = -6*c**2 + 40*c + 69. Let g(k) = -2*p(k) - 11*u(k). Solve g(s) = 0.
-4
Factor -4/3*d**4 - 8/3 - 20/3*d**3 - 28/3*d - 12*d**2.
-4*(d + 1)**3*(d + 2)/3
Let u(d) be the first derivative of d**7/147 + 2*d**6/105 - d**4/21 - d**3/21 - 3*d + 1. Let b(m) be 